Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze68.0ms (0.5%)

Memory

-1.8MiB live, 79.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.0s (46.7%)

Memory

-107.5MiB live, 7 307.3MiB allocated

Samples

4.0s	26 264×	0	invalid
997.0ms	5 431×	0	valid
501.0ms	2 825×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 4.2s

ival-tan: 915.0ms (21.7% of total)

const: 890.0ms (21.1% of total)

ival-<=: 563.0ms (13.4% of total)

ival-sub: 404.0ms (9.6% of total)

ival-mult: 360.0ms (8.5% of total)

ival-fabs: 348.0ms (8.3% of total)

ival-add: 259.0ms (6.1% of total)

ival-<: 202.0ms (4.8% of total)

ival-and: 113.0ms (2.7% of total)

adjust: 104.0ms (2.5% of total)

exact: 46.0ms (1.1% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

explain91.0ms (0.6%)

Memory

1.4MiB live, 123.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
222	6	(1.8108691400316763e-249 9.814208414101727e-252)	2	(2.683220340783668e-194 3.703869171771409e-196)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
1	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	226	9
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	221	2
-	5	28

Precision

0.9778761061946902

Recall

0.9910313901345291

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	221	2	0
-	5	7	21

Precision?

0.948936170212766

Recall?

1.0

Freqs

test

number	freq
0	30
1	225
2	1

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

18.0ms	344×	0	valid
18.0ms	168×	1	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-tan: 9.0ms (45.3% of total)

adjust: 4.0ms (20.1% of total)

ival-sub: 3.0ms (15.1% of total)

ival-add: 3.0ms (15.1% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess39.0ms (0.3%)

Memory

-20.6MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Outputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)

Outputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(tan.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(tan.f64 x)

localize23.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.0623522384027723	(tan.f64 (+.f64 x eps))
accuracy	23.502327495863817	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

9.0ms	84×	1	valid
8.0ms	172×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-tan: 4.0ms (42.3% of total)

adjust: 2.0ms (21.2% of total)

ival-sub: 2.0ms (21.2% of total)

ival-add: 2.0ms (21.2% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (taylor 0 eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) (taylor -inf eps) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (taylor -inf eps) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (cos eps)) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (taylor 0 x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) (taylor inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (+ eps x)) (cos (+ eps x))) (taylor inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (taylor -inf x) (#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
1.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify173.0ms (1.2%)

Memory

1.3MiB live, 147.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))) eps (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x)))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/6 binary64)))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 x x) #s(literal 2/15 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

rewrite167.0ms (1.1%)

Memory

-5.7MiB live, 188.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 259

Calls

Call 1

Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(tan.f64 x)

Outputs
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eval75.0ms (0.5%)

Memory: -10.0MiB live, 65.7MiB allocated
Compiler: Compiled 8 346 to 1 016 computations (87.8% saved)

prune44.0ms (0.3%)

Memory

-13.7MiB live, 61.6MiB allocated

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	313	23	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	313	24	337

Accuracy

100.0%

Counts

337 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.5%	(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
▶	63.2%	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	63.3%	(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.3%	(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	33.4%	(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
	63.2%	(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
	63.2%	(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	62.1%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
	63.2%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
	63.2%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	63.2%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	63.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
	63.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	63.2%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	28.9%	(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
	19.4%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
	33.4%	(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.4%	(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
▶	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 1 023 to 566 computations (44.7% saved)

simplify146.0ms (1%)

Memory

9.7MiB live, 156.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	320	(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
cost-diff	6080	(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))
cost-diff	6080	(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
cost-diff	14400	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(cos.f64 (+.f64 eps x))
cost-diff	0	(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
cost-diff	6080	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
cost-diff	0	(tan.f64 (+.f64 eps x))
cost-diff	0	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
cost-diff	0	(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(sin.f64 eps)
cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
cost-diff	26816	(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	716
0	104	710
1	163	634
2	337	616
3	1038	615
4	3670	608
5	7267	608
0	8204	601

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(literal -1/6 binary64)
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/6 binary64)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
eps
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal -1 binary64)
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal -1 binary64)
(sin.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
#s(literal 1 binary64)
(cos.f64 x)
x
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
#s(literal -1 binary64)
(neg.f64 (sin.f64 x))
(sin.f64 x)
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (fma.f64 eps (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 eps (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(fma.f64 eps (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
#s(literal -1/6 binary64)
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(fma.f64 (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin.f64 x)
x
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 1/6 binary64)
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
eps
(/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
#s(literal 1 binary64)
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal -1 binary64)
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal -1 binary64)
(sin.f64 (+.f64 eps x))
(neg.f64 (tan.f64 x))
(tan.f64 x)
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
(-.f64 (cos.f64 x) (/.f64 (sin.f64 x) (tan.f64 (+.f64 eps x))))
#s(literal 1 binary64)
(cos.f64 x)
x
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) (tan.f64 (+.f64 eps x)))
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
#s(literal -1 binary64)
(neg.f64 (sin.f64 x))
(sin.f64 x)
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))
(/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x)))

localize252.0ms (1.7%)

Memory

25.1MiB live, 380.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.240566259768442	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
accuracy	0.2578125	(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))
accuracy	0.3203125	(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
accuracy	23.549975681263938	(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
accuracy	0.01953125	(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
accuracy	0.0338211386044992	(cos.f64 (+.f64 eps x))
accuracy	0.04363251953688403	(sin.f64 (+.f64 eps x))
accuracy	23.475310581477732	(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
accuracy	0.01171875	(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
accuracy	0.0623522384027723	(tan.f64 (+.f64 eps x))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
accuracy	23.502327495863817	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	0.0078125	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	1.9535189558284942	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.04753876953688403	(pow.f64 (sin.f64 x) #s(literal 4 binary64))
accuracy	0.12037867884061519	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
accuracy	0.125	(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.9772262695368841	(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))

Samples

89.0ms	166×	0	valid
89.0ms	88×	1	valid
3.0ms	2×	3	valid

Compiler

Compiled 1 366 to 115 computations (91.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-pow: 21.0ms (15.5% of total)

ival-mult: 21.0ms (15.5% of total)

ival-div: 20.0ms (14.8% of total)

ival-add: 16.0ms (11.8% of total)

adjust: 13.0ms (9.6% of total)

ival-tan: 7.0ms (5.2% of total)

const: 7.0ms (5.2% of total)

ival-sin: 7.0ms (5.2% of total)

ival-pow2: 7.0ms (5.2% of total)

ival-sub: 6.0ms (4.4% of total)

ival-cos: 6.0ms (4.4% of total)

ival-neg: 3.0ms (2.2% of total)

exact: 1.0ms (0.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series228.0ms (1.5%)

Memory

4.2MiB live, 119.5MiB allocated

Counts

24 → 504

Calls

Call 1

Inputs
#s(alt (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (patch (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (patch (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 eps) (cos.f64 eps)) (patch (/.f64 (sin.f64 eps) (cos.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (cos.f64 eps) (patch (cos.f64 eps) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)) (patch (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (patch (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 (+.f64 eps x)) (patch (tan.f64 (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) (patch (fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))) #<representation binary64>) () ())
#s(alt (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))) (patch (/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) (patch (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)) (patch (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (patch (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) #<representation binary64>) () ())) ())
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#s(alt (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (patch (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 4) (taylor -inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 4) (taylor -inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 4) (taylor -inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin x) 4) (taylor -inf x) (#s(alt (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sin.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 eps x)) (patch (sin.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (patch (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
64.0ms	eps	@	0	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (/ (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (* (pow (tan (+ eps x)) -1) (cos x))) (* (pow (tan (+ eps x)) -1) (neg (sin x))) (* (pow (tan (+ eps x)) -1) (cos x)) (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (sin (+ eps x)) (pow (tan (+ eps x)) -1))
61.0ms	x	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (/ (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (* (pow (tan (+ eps x)) -1) (cos x))) (* (pow (tan (+ eps x)) -1) (neg (sin x))) (* (pow (tan (+ eps x)) -1) (cos x)) (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (sin (+ eps x)) (pow (tan (+ eps x)) -1))
48.0ms	x	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (/ (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (* (pow (tan (+ eps x)) -1) (cos x))) (* (pow (tan (+ eps x)) -1) (neg (sin x))) (* (pow (tan (+ eps x)) -1) (cos x)) (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (sin (+ eps x)) (pow (tan (+ eps x)) -1))
11.0ms	eps	@	inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (/ (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (* (pow (tan (+ eps x)) -1) (cos x))) (* (pow (tan (+ eps x)) -1) (neg (sin x))) (* (pow (tan (+ eps x)) -1) (cos x)) (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (sin (+ eps x)) (pow (tan (+ eps x)) -1))
9.0ms	eps	@	-inf	((+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (pow (- (tan (+ eps x)) (tan x)) -1) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (+ (* (pow (cos (+ eps x)) -1) (sin (+ eps x))) (neg (tan x))) (pow (cos (+ eps x)) -1) (cos (+ eps x)) (+ eps x) (/ (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (* (pow (tan (+ eps x)) -1) (cos x))) (* (pow (tan (+ eps x)) -1) (neg (sin x))) (* (pow (tan (+ eps x)) -1) (cos x)) (+ (* 1 (cos x)) (* (pow (tan (+ eps x)) -1) (neg (sin x)))) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sin x) 4) (sin (+ eps x)) (pow (tan (+ eps x)) -1))

simplify425.0ms (2.8%)

Memory

-7.5MiB live, 185.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	821	14107
1	2660	13394
0	8623	13045

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 496

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
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eps
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1
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(cos x)
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x
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(/ (* (sin x) (+ (cos x) (* -1 (cos x)))) (pow (cos x) 2))
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(sin x)
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(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
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(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
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eps
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(sin (- x (* -1 eps)))
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-1/2
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1/3
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(/ (sin eps) (cos eps))
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eps
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1
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(* 1/3 (pow eps 2))
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(pow x 4)
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(sin eps)
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(/ (cos (+ eps x)) (sin (+ eps x)))
(/ (cos (+ eps x)) (sin (+ eps x)))
(/ (cos (+ eps x)) (sin (+ eps x)))
(/ (cos (+ eps x)) (sin (+ eps x)))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/2)
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(/ 1 (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(pow (sin x) 4)
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))

Outputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (+.f64 (/.f64 (.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x)) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64) (.f64 (sin.f64 x) (/.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (cos.f64 x)))) eps (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) eps (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin eps)
(sin.f64 eps)
(sin eps)
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(sin eps)
(sin.f64 eps)
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(cos eps)
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
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(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
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(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
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(/ 1 (cos (+ eps x)))
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(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(/ 1 (cos (+ eps x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (+ eps x)) (+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (+ eps x))) (sin (+ eps x)))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (+ eps x)) (sin x)) (sin (+ eps x)))))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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(/ 1 (cos eps))
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(cos eps)
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eps
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(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
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(* -1 (/ (* x (cos eps)) (sin eps)))
(*.f64 (neg.f64 x) (/.f64 (cos.f64 eps) (sin.f64 eps)))
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1
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(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(/ 1 (cos (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x) x)
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(/ (* (sin (- eps (* -1 x))) (+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x)) (cos.f64 x)) (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin (- eps (* -1 x))))
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 (+.f64 x eps)))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (cos x) (* -1 (/ (* (cos (- eps (* -1 x))) (sin x)) (sin (- eps (* -1 x))))))
(fma.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (cos.f64 x))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (-.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(pow (sin x) 4)
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 x eps))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))

rewrite406.0ms (2.7%)

Memory

22.9MiB live, 181.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	452
0	104	433
1	465	327
2	3937	319
0	8840	307

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

24 → 576

Calls

Call 1

Inputs
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
(cos.f64 eps)
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x))))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow.f64 (sin.f64 x) #s(literal 4 binary64))
(sin.f64 (+.f64 eps x))
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))

Outputs
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eval336.0ms (2.2%)

Memory: -15.6MiB live, 306.5MiB allocated
Compiler: Compiled 50 498 to 3 749 computations (92.6% saved)

prune61.0ms (0.4%)

Memory

-9.5MiB live, 155.3MiB allocated

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	1 367	19	1 386
Fresh	7	11	18
Picked	5	0	5
Done	0	1	1
Total	1 379	31	1 410

Accuracy

100.0%

Counts

1 410 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.5%	(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
	63.3%	(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.3%	(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
	63.2%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	33.4%	(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
	63.2%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
	63.2%	(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	62.1%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))
	29.0%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (cos.f64 x)))
▶	63.2%	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	62.3%	(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
	63.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	99.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (tan (+ eps x)) (tan x)) -1) (/.f64 (fma.f64 (neg.f64 eps) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) eps)))
▶	63.3%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	63.2%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	19.4%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
	33.4%	(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
▶	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.4%	(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	98.5%	#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
▶	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))

Compiler

Compiled 1 451 to 838 computations (42.2% saved)

simplify221.0ms (1.5%)

Memory

-8.4MiB live, 230.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (tan.f64 x) (tan.f64 eps))
cost-diff	0	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
cost-diff	256	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
cost-diff	19712	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
cost-diff	0	(tan.f64 eps)
cost-diff	0	(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff	0	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
cost-diff	0	(/.f64 (sin.f64 x) (cos.f64 x))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
cost-diff	0	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff	192	(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))
cost-diff	6144	(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
cost-diff	6400	(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	760
0	131	757
1	240	715
2	574	694
3	1772	692
4	7178	692
0	8054	675

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))
eps
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))
(pow.f64 (cos.f64 x) #s(literal -2 binary64))
(cos.f64 x)
x
#s(literal -2 binary64)
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
(sin.f64 x)
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (tan.f64 x))
(tan.f64 x)
#s(literal 2 binary64)
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))
#s(literal -1/6 binary64)
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
#s(literal -1/3 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
x
(tan.f64 eps)
eps
(cos.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
#s(literal 1 binary64)
(*.f64 (tan.f64 x) (tan.f64 eps))
(sin.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (fma.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))
eps
(fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))))
(fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (cos.f64 x) #s(literal -2 binary64))
(cos.f64 x)
x
#s(literal -2 binary64)
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(sin.f64 x)
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (tan.f64 x))
(*.f64 (tan.f64 x) (sin.f64 x))
(tan.f64 x)
#s(literal 2 binary64)
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))
#s(literal -1/6 binary64)
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
#s(literal -1/3 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(/.f64 (sin.f64 x) (cos.f64 x))
(sin.f64 x)
(cos.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
eps
(tan.f64 x)
x
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))
(neg.f64 (tan.f64 eps))
#s(literal 1 binary64)
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
(fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 x)
x
(tan.f64 eps)
eps
(cos.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 (tan.f64 eps) (tan.f64 x))
(sin.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (cos.f64 x))

localize495.0ms (3.3%)

Memory

0.0MiB live, 481.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.0234375	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
accuracy	0.02734375	(+.f64 (tan.f64 x) (tan.f64 eps))
accuracy	23.434835427502712	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
accuracy	0	(neg.f64 (tan.f64 eps))
accuracy	0.0078125	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
accuracy	0.02734375	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	23.502327495863817	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0	(cos.f64 x)
accuracy	0.01953125	(/.f64 (sin.f64 x) (cos.f64 x))
accuracy	0.0623522384027723	(tan.f64 (+.f64 x eps))
accuracy	23.502327495863817	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
accuracy	0	(*.f64 eps eps)
accuracy	0.12037867884061519	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
accuracy	0.1796875	(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
accuracy	26.847928541289484	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
accuracy	0.10546875	(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
accuracy	0.12037867884061519	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
accuracy	0.125	(fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
accuracy	0.9912300293053261	(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))

Samples

307.0ms	166×	0	valid
118.0ms	88×	1	valid
6.0ms	2×	3	valid

Compiler

Compiled 1 154 to 131 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-add: 67.0ms (30% of total)

ival-mult: 45.0ms (20.1% of total)

ival-div: 20.0ms (8.9% of total)

adjust: 16.0ms (7.2% of total)

ival-pow2: 16.0ms (7.2% of total)

const: 15.0ms (6.7% of total)

ival-pow: 14.0ms (6.3% of total)

ival-sub: 12.0ms (5.4% of total)

ival-tan: 9.0ms (4% of total)

ival-cos: 3.0ms (1.3% of total)

ival-neg: 3.0ms (1.3% of total)

ival-sin: 2.0ms (0.9% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series111.0ms (0.7%)

Memory

7.1MiB live, 123.4MiB allocated

Counts

26 → 504

Calls

Call 1

Inputs
#s(alt (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (patch (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (patch (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) (patch (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps) (patch (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) (patch #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) (patch (.f64 (.f64 eps eps) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (patch (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (tan.f64 (+.f64 x eps)) (patch (tan.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 x) (cos.f64 x)) (patch (/.f64 (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) (patch (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (patch (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (tan.f64 eps) (tan.f64 x)) (patch (+.f64 (tan.f64 eps) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 eps) (patch (tan.f64 eps) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) (patch (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (patch (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (patch (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (+.f64 (tan.f64 x) (tan.f64 eps)) (patch (+.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())
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#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())

Outputs
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#s(alt (/ (pow (sin x) 4) (pow (cos x) 2)) (taylor -inf x) (#s(alt (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) (taylor -inf x) (#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
33.0ms	x	@	-inf	((+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (+ (tan x) (tan eps)) (cos x)) (+ (tan x) (tan eps)) (+ (* (+ (* eps (+ (* (pow (cos x) -2) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (* (sin x) (tan x)) 2) (* eps eps) (cos x) (neg (tan eps)) (* (tan x) (tan eps)))
12.0ms	x	@	inf	((+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (+ (tan x) (tan eps)) (cos x)) (+ (tan x) (tan eps)) (+ (* (+ (* eps (+ (* (pow (cos x) -2) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (* (sin x) (tan x)) 2) (* eps eps) (cos x) (neg (tan eps)) (* (tan x) (tan eps)))
12.0ms	eps	@	inf	((+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (+ (tan x) (tan eps)) (cos x)) (+ (tan x) (tan eps)) (+ (* (+ (* eps (+ (* (pow (cos x) -2) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (* (sin x) (tan x)) 2) (* eps eps) (cos x) (neg (tan eps)) (* (tan x) (tan eps)))
10.0ms	eps	@	0	((+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (+ (tan x) (tan eps)) (cos x)) (+ (tan x) (tan eps)) (+ (* (+ (* eps (+ (* (pow (cos x) -2) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (* (sin x) (tan x)) 2) (* eps eps) (cos x) (neg (tan eps)) (* (tan x) (tan eps)))
8.0ms	eps	@	-inf	((+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (+ (* (sin x) (pow (tan x) 2)) (sin x)) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (* eps eps) 1/3) (- (tan (+ x eps)) (/ (sin x) (cos x))) (tan (+ x eps)) (+ x eps) (/ (sin x) (cos x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (+ (tan x) (tan eps)) (cos x)) (+ (tan x) (tan eps)) (+ (* (+ (* eps (+ (* (pow (cos x) -2) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (- -1/6 (+ (* (pow (tan x) 2) -1/3) -1/2)))) (/ (+ (* (sin x) (pow (tan x) 2)) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (* (sin x) (tan x)) 2) (* eps eps) (cos x) (neg (tan eps)) (* (tan x) (tan eps)))

simplify228.0ms (1.5%)

Memory

-2.5MiB live, 183.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	690	12510
1	2265	12182
2	7659	12040
0	8054	11649

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 495

Calls

Call 1

Inputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x))))))
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x)))))))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(* -1 (/ (sin eps) (cos eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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(/ (pow (sin x) 4) (pow (cos x) 2))
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(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
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(+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))
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(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
x
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(/ (sin x) (cos x))
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(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
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(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 4) (pow (cos x) 2))
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(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))

Outputs
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (* -1/3 (pow eps 2)) 1))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 eps eps) #s(literal -1 binary64)) eps)
(* eps (- (* (pow eps 2) (- (* -2/15 (pow eps 2)) 1/3)) 1))
(.f64 (fma.f64 (fma.f64 #s(literal -2/15 binary64) (.f64 eps eps) #s(literal -1/3 binary64)) (*.f64 eps eps) #s(literal -1 binary64)) eps)
(* eps (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3)) 1))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -17/315 binary64) (.f64 eps eps) #s(literal -2/15 binary64)) (.f64 eps eps) #s(literal -1/3 binary64)) (.f64 eps eps) #s(literal -1 binary64)) eps)
(/ (* eps (sin x)) (cos x))
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 2/15 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (.f64 (sin.f64 x) (/.f64 eps (cos.f64 x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 17/315 binary64) (.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))) (.f64 eps eps) (/.f64 (.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (.f64 (sin.f64 x) (/.f64 eps (cos.f64 x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 (+.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/3 binary64)) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps eps) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps eps))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (*.f64 eps eps))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(+.f64 (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
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(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
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x
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x
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(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))) (.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (cos.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 eps)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))
(*.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))

rewrite192.0ms (1.3%)

Memory

-3.7MiB live, 152.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	544
0	131	494
1	637	360
2	6419	360
0	8103	360

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

26 → 700

Calls

Call 1

Inputs
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x))
(-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(/.f64 (sin.f64 x) (cos.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))
(*.f64 eps eps)
(cos.f64 x)
(neg.f64 (tan.f64 eps))
(*.f64 (tan.f64 x) (tan.f64 eps))

Outputs
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eval201.0ms (1.3%)

Memory: -10.8MiB live, 295.0MiB allocated
Compiler: Compiled 50 137 to 3 544 computations (92.9% saved)

prune79.0ms (0.5%)

Memory

9.9MiB live, 174.1MiB allocated

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	1 365	8	1 373
Fresh	7	18	25
Picked	3	2	5
Done	0	1	1
Total	1 375	29	1 404

Accuracy

100.0%

Counts

1 404 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	32.5%	(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
	63.2%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
▶	63.2%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
	63.2%	(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	62.1%	(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))
▶	98.0%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	99.8%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	99.4%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
▶	62.3%	(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
	63.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	63.1%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	63.2%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	62.9%	(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	19.4%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
	33.4%	(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.4%	(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	98.5%	#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (/ (sin x) (cos x))) (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
▶	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
▶	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))

Compiler

Compiled 1 301 to 780 computations (40% saved)

simplify193.0ms (1.3%)

Memory

-4.8MiB live, 154.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))))
cost-diff	0	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
cost-diff	7360	(fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))
cost-diff	13824	(fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)))
cost-diff	0	(log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
cost-diff	0	(exp.f64 #s(literal -1 binary64))
cost-diff	0	(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
cost-diff	0	(tan.f64 (+.f64 eps x))
cost-diff	0	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
cost-diff	0	(sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
cost-diff	7104	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
cost-diff	320	(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff	128	(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
cost-diff	6720	(fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
cost-diff	13312	(fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	849
0	149	843
1	253	803
2	533	772
3	1606	752
4	5610	743
0	8294	706

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(tan.f64 x)
x
(+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1/3 binary64)
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
#s(literal -1/3 binary64)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
eps
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
(*.f64 x eps)
x
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
#s(literal 1 binary64)
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
#s(literal 5/24 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))
(*.f64 #s(literal 1/2 binary64) (sin.f64 eps))
#s(literal 1/2 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
#s(literal 1 binary64)
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 x)
(tan.f64 eps)
(cos.f64 x)

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) (fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))
(fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 eps (fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x)))
(fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(fma.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(tan.f64 x)
x
(+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
eps
(/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))
(*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps)) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps)) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
(*.f64 (fma.f64 eps #s(literal 1/3 binary64) x) eps)
(*.f64 eps eps)
eps
#s(literal 1/3 binary64)
(*.f64 x eps)
(*.f64 eps x)
x
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
#s(literal 1 binary64)
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
(tan.f64 x)
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 5/24 binary64) #s(literal 1 binary64))))) (*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (cos.f64 x)))
#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))))
#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 5/24 binary64) #s(literal 1 binary64)))))
(fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 5/24 binary64) #s(literal 1 binary64))))
(fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)))
(.f64 (fma.f64 (.f64 #s(literal 5/24 binary64) x) x #s(literal 1/2 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64))
(*.f64 (/.f64 #s(literal 5/24 binary64) (cos.f64 eps)) (sin.f64 eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin.f64 eps)
eps
(cos.f64 eps)
#s(literal 5/24 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (sin.f64 eps))
(*.f64 #s(literal 1/2 binary64) (sin.f64 eps))
#s(literal 1/2 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 x)
(tan.f64 eps)
(cos.f64 x)

localize397.0ms (2.7%)

Memory

23.6MiB live, 400.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))
accuracy	0.015625	(*.f64 (tan.f64 x) (tan.f64 eps))
accuracy	0.25390625	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64))
accuracy	1.3099067721484352	#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))))
accuracy	0.0623522384027723	(tan.f64 (+.f64 eps x))
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
accuracy	5.944471622141097	(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
accuracy	23.502327495863817	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	0	(sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
accuracy	0.0623522384027723	(tan.f64 (+.f64 eps x))
accuracy	0.484375	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
accuracy	23.502327495863817	(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
accuracy	0	(*.f64 eps eps)
accuracy	0.12037867884061519	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
accuracy	0.1328125	(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
accuracy	27.610239430568328	#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
accuracy	0.05535126953688403	(pow.f64 (tan.f64 x) #s(literal 4 binary64))
accuracy	0.12037867884061519	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
accuracy	0.125	(fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
accuracy	0.1875	(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))

Samples

129.0ms	80×	1	valid
109.0ms	153×	0	valid
70.0ms	18×	3	valid
10.0ms	5×	2	valid

Compiler

Compiled 1 228 to 151 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 275.0ms

ival-mult: 52.0ms (18.9% of total)

ival-sin: 35.0ms (12.7% of total)

ival-add: 29.0ms (10.5% of total)

adjust: 28.0ms (10.2% of total)

ival-pow: 24.0ms (8.7% of total)

const: 23.0ms (8.4% of total)

ival-div: 22.0ms (8% of total)

ival-pow2: 17.0ms (6.2% of total)

ival-sub: 12.0ms (4.4% of total)

ival-tan: 11.0ms (4% of total)

ival-cos: 10.0ms (3.6% of total)

ival-exp: 5.0ms (1.8% of total)

ival-log: 5.0ms (1.8% of total)

ival-sqrt: 3.0ms (1.1% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series302.0ms (2%)

Memory

-12.3MiB live, 346.3MiB allocated

Counts

27 → 540

Calls

Call 1

Inputs
#s(alt (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (patch (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)) (patch (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps) (patch (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps) #<representation binary64>) () ())
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#s(alt (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) (patch (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) #<representation binary64>) () ())
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#s(alt (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (patch (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (patch (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (patch (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) (patch (/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x))) #<representation binary64>) () ())
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#s(alt (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())
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#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (patch (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (tan.f64 x) (tan.f64 eps)) (patch (.f64 (tan.f64 x) (tan.f64 eps)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)) (patch (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) (patch (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
107.0ms	eps	@	inf	((+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (+ (* (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (- 1/3 (* -1/3 (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (* eps eps) 1/3) (* x eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (sqrt (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (pow (exp -1) (log (- (tan (+ eps x)) (tan x))))) (pow (exp -1) (log (- (tan (+ eps x)) (tan x)))) (exp -1) (log (- (tan (+ eps x)) (tan x))) (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (* (/ (sin eps) (cos eps)) 5/24) (* (tan x) (tan eps)) (/ (* 1/2 (sin eps)) (cos eps)))
50.0ms	x	@	inf	((+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (+ (* (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (- 1/3 (* -1/3 (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (* eps eps) 1/3) (* x eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (sqrt (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (pow (exp -1) (log (- (tan (+ eps x)) (tan x))))) (pow (exp -1) (log (- (tan (+ eps x)) (tan x)))) (exp -1) (log (- (tan (+ eps x)) (tan x))) (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (* (/ (sin eps) (cos eps)) 5/24) (* (tan x) (tan eps)) (/ (* 1/2 (sin eps)) (cos eps)))
43.0ms	x	@	-inf	((+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (+ (* (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (- 1/3 (* -1/3 (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (* eps eps) 1/3) (* x eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (sqrt (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (pow (exp -1) (log (- (tan (+ eps x)) (tan x))))) (pow (exp -1) (log (- (tan (+ eps x)) (tan x)))) (exp -1) (log (- (tan (+ eps x)) (tan x))) (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (* (/ (sin eps) (cos eps)) 5/24) (* (tan x) (tan eps)) (/ (* 1/2 (sin eps)) (cos eps)))
39.0ms	eps	@	-inf	((+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (+ (* (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (- 1/3 (* -1/3 (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (* eps eps) 1/3) (* x eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (sqrt (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (pow (exp -1) (log (- (tan (+ eps x)) (tan x))))) (pow (exp -1) (log (- (tan (+ eps x)) (tan x)))) (exp -1) (log (- (tan (+ eps x)) (tan x))) (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (* (/ (sin eps) (cos eps)) 5/24) (* (tan x) (tan eps)) (/ (* 1/2 (sin eps)) (cos eps)))
13.0ms	eps	@	0	((+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (+ (* (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) eps) eps) (- 1/3 (* -1/3 (pow (tan x) 2))) (- (tan (+ x eps)) (tan x)) (+ (* (* eps eps) 1/3) (* x eps)) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (sqrt (- (tan (+ eps x)) (tan x))) (- (tan (+ eps x)) (tan x)) (tan (+ eps x)) (/ 1 (pow (exp -1) (log (- (tan (+ eps x)) (tan x))))) (pow (exp -1) (log (- (tan (+ eps x)) (tan x)))) (exp -1) (log (- (tan (+ eps x)) (tan x))) (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* -1/3 (pow (tan x) 2)) (+ (* (+ (* (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) eps) (/ (* (+ (* (tan x) (tan x)) 1) (sin x)) (cos x))) eps) (pow (tan x) 2)) (pow (tan x) 4) (* eps eps) (* (/ (sin eps) (cos eps)) 5/24) (* (tan x) (tan eps)) (/ (* 1/2 (sin eps)) (cos eps)))

simplify262.0ms (1.8%)

Memory

29.6MiB live, 300.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	952	18180
1	3320	17561
0	8553	16943

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

Calls

Call 1

Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps x)
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* 1/3 eps)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(sqrt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (sqrt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* 1/2 (* (sqrt (* (pow eps 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (sin x) (cos x)))))
(+ (sqrt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* (pow eps 2) (+ (* -1/2 (* (sqrt (/ eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* 1/2 (* (sqrt (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (/ (sin x) (cos x)))))))
(+ (sqrt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (/ (sin x) (cos x)))) (* eps (+ (* -1/2 (* (sqrt (/ 1 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1/2 (* (sqrt (/ eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/4 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* eps (pow (cos x) 2)))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))))))))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ 1 (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
(+ (/ 1 (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (/ (* eps (sin x)) (* (cos x) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))))
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (+ (* -1/2 (/ (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (* 1/2 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))))))) (* -1 (/ (sin x) (* (cos x) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))))) (/ 1 (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (+ (* -6 (/ (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* 2 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 6 (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (+ (* -1/6 (/ (pow (sin x) 3) (* (pow (cos x) 3) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (+ (* 1/2 (/ (* (sin x) (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (cos x) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (+ (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (+ (* -1/2 (/ (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (* 1/2 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))))))) (cos x)) (/ (* (sin x) (+ (* -1/2 (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* (cos x) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))))))))) (+ (* -1 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (+ (* -1/2 (/ (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (* 1/2 (/ (pow (sin x) 2) (* (pow (cos x) 2) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))))))) (* -1 (/ (sin x) (* (cos x) (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))))) (/ 1 (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))
(exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))
(+ (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* eps (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (sin x))) (cos x))))
(+ (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* eps (+ (* -1 (/ (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (sin x)) (cos x))) (* eps (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (+ (* -1/2 (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))
(+ (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* eps (+ (* -1 (/ (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (sin x)) (cos x))) (* eps (+ (* eps (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (+ (* -1/6 (+ (* -6 (/ (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* 2 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 6 (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))))) (+ (* -1/6 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 1/2 (/ (* (sin x) (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))))) (* (exp (* -1 (+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (+ (* -1/2 (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/2 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))
(+ (log eps) (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (log eps) (+ (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* eps (sin x)) (cos x))))
(+ (log eps) (+ (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* eps (+ (* 1/2 (* eps (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (sin x) (cos x))))))
(+ (log eps) (+ (log (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* eps (+ (* eps (+ (* 1/6 (* eps (+ (* -6 (/ (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* 2 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 6 (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))))))) (* 1/2 (+ (* -2 (/ (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (sin x) (cos x))))))
(* eps (+ 1/2 (* 5/24 (pow x 2))))
(* eps (+ 1/2 (+ (* 5/24 (pow x 2)) (* (pow eps 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))))
(* eps (+ 1/2 (+ (* 5/24 (pow x 2)) (* (pow eps 2) (+ 1/6 (+ (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* (pow eps 2) (+ 1/15 (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2)))))))))))))
(* eps (+ 1/2 (+ (* 5/24 (pow x 2)) (* (pow eps 2) (+ 1/6 (+ (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* (pow eps 2) (+ 1/15 (+ (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (* (pow eps 2) (+ 17/630 (* 5/24 (- (* -1/5040 (pow x 2)) (+ (* -1/2 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (+ (* -1/720 (pow x 2)) (* 1/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))))))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2))))))
(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (+ (* (pow eps 2) (+ 2/15 (* (pow x 2) (+ 1/15 (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))))))) (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2))))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (+ (* (pow eps 2) (+ 2/15 (+ (* (pow eps 2) (+ 17/315 (* (pow x 2) (+ 17/630 (* 5/24 (- (* -1/5040 (pow x 2)) (+ (* -1/2 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (+ (* -1/720 (pow x 2)) (* 1/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))))))) (* (pow x 2) (+ 1/15 (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2)))))))))) (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2))))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 5/24 eps)
(* eps (+ 5/24 (* 5/72 (pow eps 2))))
(* eps (+ 5/24 (* (pow eps 2) (+ 5/72 (* 1/36 (pow eps 2))))))
(* eps (+ 5/24 (* (pow eps 2) (+ 5/72 (* (pow eps 2) (+ 1/36 (* 17/1512 (pow eps 2))))))))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/6 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (+ 1/6 (* 1/15 (pow eps 2))))))
(* eps (+ 1/2 (* (pow eps 2) (+ 1/6 (* (pow eps 2) (+ 1/15 (* 17/630 (pow eps 2))))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(sqrt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(sqrt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(sqrt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(sqrt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
(+ (* (pow x 2) (+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(+ (* (pow x 2) (+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 5/24 (/ (sin eps) (cos eps)))
(* 5/24 (/ (sin eps) (cos eps)))
(* 5/24 (/ (sin eps) (cos eps)))
(* 5/24 (/ (sin eps) (cos eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(* 1/2 (/ (sin eps) (cos eps)))
(* 1/2 (/ (sin eps) (cos eps)))
(* 1/2 (/ (sin eps) (cos eps)))
(* 1/2 (/ (sin eps) (cos eps)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) eps)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps)))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* (pow eps 2) (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(sqrt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(sqrt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
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(/ 1 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
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(log (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
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(+ (* (pow x 2) (+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))
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(* (pow x 4) (+ (* 5/24 (/ (sin eps) (cos eps))) (+ (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps)))) (/ (sin eps) (* (pow x 4) (cos eps))))))
(* (pow x 4) (+ (* 5/24 (/ (sin eps) (cos eps))) (+ (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps)))) (/ (sin eps) (* (pow x 4) (cos eps))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))

Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64) (.f64 (sin.f64 x) (/.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (cos.f64 x)))) eps (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps x)
(*.f64 x eps)
(* eps (+ x (* 1/3 eps)))
(*.f64 (fma.f64 #s(literal 1/3 binary64) eps x) eps)
(* eps (+ x (* 1/3 eps)))
(*.f64 (fma.f64 #s(literal 1/3 binary64) eps x) eps)
(* eps (+ x (* 1/3 eps)))
(*.f64 (fma.f64 #s(literal 1/3 binary64) eps x) eps)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64) (.f64 (sin.f64 x) (/.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (cos.f64 x)))) eps (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)
(/ (pow (sin x) 2) (pow (cos x) 2))
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(* eps (+ 1/2 (+ (* 5/24 (pow x 2)) (* (pow eps 2) (+ 1/6 (+ (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* (pow eps 2) (+ 1/15 (+ (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (* (pow eps 2) (+ 17/630 (* 5/24 (- (* -1/5040 (pow x 2)) (+ (* -1/2 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (+ (* -1/720 (pow x 2)) (* 1/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))))))))))))))
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(* eps (+ 1 (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (+ (* (pow eps 2) (+ 2/15 (* (pow x 2) (+ 1/15 (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))))))) (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2))))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
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(* eps (+ 1 (+ (* (pow eps 2) (+ 1/3 (+ (* (pow eps 2) (+ 2/15 (+ (* (pow eps 2) (+ 17/315 (* (pow x 2) (+ 17/630 (* 5/24 (- (* -1/5040 (pow x 2)) (+ (* -1/2 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2))))) (+ (* -1/720 (pow x 2)) (* 1/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))))))))))) (* (pow x 2) (+ 1/15 (* 5/24 (- (* 1/120 (pow x 2)) (+ (* -1/2 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2)))) (* 1/24 (pow x 2)))))))))) (* (pow x 2) (+ 1/6 (* 5/24 (- (* -1/6 (pow x 2)) (* -1/2 (pow x 2))))))))) (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))))
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(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x))
(*.f64 eps (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (fma.f64 eps (/.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps)
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))
(*.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x)))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* 5/24 eps)
(*.f64 #s(literal 5/24 binary64) eps)
(* eps (+ 5/24 (* 5/72 (pow eps 2))))
(.f64 (fma.f64 #s(literal 5/72 binary64) (.f64 eps eps) #s(literal 5/24 binary64)) eps)
(* eps (+ 5/24 (* (pow eps 2) (+ 5/72 (* 1/36 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 eps eps) #s(literal 5/72 binary64)) (*.f64 eps eps) #s(literal 5/24 binary64)) eps)
(* eps (+ 5/24 (* (pow eps 2) (+ 5/72 (* (pow eps 2) (+ 1/36 (* 17/1512 (pow eps 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/1512 binary64) (.f64 eps eps) #s(literal 1/36 binary64)) (.f64 eps eps) #s(literal 5/72 binary64)) (.f64 eps eps) #s(literal 5/24 binary64)) eps)
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal 1/3 binary64) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal 2/15 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal 17/315 binary64) (/.f64 (.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))) (.f64 eps eps) (/.f64 (.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* 1/6 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (+ 1/6 (* 1/15 (pow eps 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/15 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (+ 1/6 (* (pow eps 2) (+ 1/15 (* 17/630 (pow eps 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/630 binary64) (.f64 eps eps) #s(literal 1/15 binary64)) (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (sin.f64 x) eps) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (-.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (sin.f64 x) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 (-.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (sin.f64 x) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(.f64 (+.f64 (/.f64 x eps) #s(literal 1/3 binary64)) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(.f64 (+.f64 (/.f64 x eps) #s(literal 1/3 binary64)) (.f64 eps eps))
(* (pow eps 2) (+ 1/3 (/ x eps)))
(.f64 (+.f64 (/.f64 x eps) #s(literal 1/3 binary64)) (.f64 eps eps))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* (pow eps 3) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 3) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (-.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/3 (+ (/ 1 (pow eps 2)) (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (-.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (.f64 eps eps) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps eps))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps eps))
(* (pow eps 2) (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (/ (pow (sin x) 3) (* eps (pow (cos x) 3))) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (/.f64 (sin.f64 x) eps) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps eps))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(sqrt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(sqrt.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
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(sqrt.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
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(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ 1 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(+ (* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))
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(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(/ 1 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(log (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))))
(log.f64 (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
(* 5/24 (/ (* (pow x 2) (sin eps)) (cos eps)))
(.f64 (/.f64 (.f64 (sin.f64 eps) (*.f64 x x)) (cos.f64 eps)) #s(literal 5/24 binary64))
(* (pow x 2) (+ (* 5/24 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (.f64 #s(literal 5/24 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x))
(* (pow x 2) (+ (* 5/24 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (.f64 #s(literal 5/24 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x))
(* (pow x 2) (+ (* 5/24 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (.f64 #s(literal 5/24 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x))
(* 5/24 (/ (* (pow x 4) (sin eps)) (cos eps)))
(.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) #s(literal 5/24 binary64))
(* (pow x 4) (+ (* 5/24 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 #s(literal 5/24 binary64) (sin.f64 eps)) (cos.f64 eps))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* 5/24 (/ (sin eps) (cos eps))) (+ (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps)))) (/ (sin eps) (* (pow x 4) (cos eps))))))
(.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 eps) (*.f64 (pow.f64 x #s(literal 4 binary64)) (cos.f64 eps))))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ (* 5/24 (/ (sin eps) (cos eps))) (+ (* 1/2 (/ (sin eps) (* (pow x 2) (cos eps)))) (/ (sin eps) (* (pow x 4) (cos eps))))))
(.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 eps) (*.f64 (pow.f64 x #s(literal 4 binary64)) (cos.f64 eps))))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (cos.f64 x)))
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(/.f64 (-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (cos.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x)))
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(-.f64 (.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))) (sin.f64 x)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (fma.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (pow (sin x) 4) (pow (cos x) 4))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 eps)))

rewrite226.0ms (1.5%)

Memory

-15.8MiB live, 184.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	682
0	149	627
1	688	549
2	5861	549
0	8020	522

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

27 → 507

Calls

Call 1

Inputs
(fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps)
(-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
(fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps)
#s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan.f64 (+.f64 eps x))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(exp.f64 #s(literal -1 binary64))
(log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps)))
(fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))))
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
(*.f64 eps eps)
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64))
(*.f64 (tan.f64 x) (tan.f64 eps))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))

Outputs
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eval216.0ms (1.4%)

Memory: 23.8MiB live, 334.9MiB allocated
Compiler: Compiled 45 346 to 3 733 computations (91.8% saved)

prune96.0ms (0.6%)

Memory

0.7MiB live, 122.6MiB allocated

Pruning

32 alts after pruning (28 fresh and 4 done)

	Pruned	Kept	Total
New	1 126	19	1 145
Fresh	12	9	21
Picked	4	1	5
Done	0	3	3
Total	1 142	32	1 174

Accuracy

100.0%

Counts

1 174 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.2%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
	62.3%	(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	63.3%	(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
✓	63.2%	(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
	62.3%	(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
	99.4%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	97.9%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	97.7%	(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	90.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(approx (log (- (tan (+ eps x)) (tan x))) (+.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) (log.f64 eps))))))
	63.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	63.1%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	63.2%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
	62.9%	(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	19.4%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
	33.4%	(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	63.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	62.4%	(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
	98.5%	#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
✓	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
	96.9%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
	97.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))

Compiler

Compiled 2 342 to 813 computations (65.3% saved)

regimes81.0ms (0.5%)

Memory

-31.9MiB live, 72.6MiB allocated

Counts

70 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
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(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(approx (log (- (tan (+ eps x)) (tan x))) (+.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) (log.f64 eps))))))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (/ (sin x) (cos x))) (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (tan (+ eps x)) (tan x)) -1) (/.f64 (fma.f64 (neg.f64 eps) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) (.f64 eps eps) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal -1/6 binary64) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/6 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

39.0ms	eps
20.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`
99.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes75.0ms (0.5%)

Memory

12.8MiB live, 50.9MiB allocated

Counts

65 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(approx (log (- (tan (+ eps x)) (tan x))) (+.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) (log.f64 eps))))))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) #s(literal 1/3 binary64)) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (/ (sin x) (cos x))) (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (tan (+ eps x)) (tan x)) -1) (/.f64 (fma.f64 (neg.f64 eps) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) eps)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

39.0ms	eps
17.0ms	x
16.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`
99.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes55.0ms (0.4%)

Memory

-13.2MiB live, 61.2MiB allocated

Counts

57 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)) (cos.f64 x)) eps)) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (.f64 (pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (tan.f64 (+.f64 eps x)) (/.f64 (tan.f64 (+.f64 eps x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (fma.f64 (fma.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 5/24 binary64)) (.f64 x x) (/.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(approx (log (- (tan (+ eps x)) (tan x))) (+.f64 (log1p.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) (log.f64 eps))))))
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

19.0ms	x
19.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms	eps

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

18.1MiB live, 59.7MiB allocated

Counts

42 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 eps x))))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

16.0ms	eps
11.0ms	x
11.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.3%)

Memory

-3.6MiB live, 69.2MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (/ 1 (pow (- (tan (+ eps x)) (tan x)) -1)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (pow (sqrt (- (tan (+ eps x)) (tan x))) 2) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 #s(approx (neg (tan eps)) (neg.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan eps) (tan x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(pow.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))

Calls

3 calls:

14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	x
11.0ms	eps

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`eps`
98.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory

7.8MiB live, 45.3MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(exp.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(fma.f64 (sin.f64 x) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))

Outputs

(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 eps eps) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))

Calls

3 calls:

10.0ms	eps
8.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`
97.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.2%)

Memory

-7.0MiB live, 40.1MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))

Outputs

(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))

Calls

3 calls:

10.0ms	eps
7.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`eps`
97.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.2%)

Memory

-7.7MiB live, 30.0MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (tan.f64 (-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))) (tan.f64 x))
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (tan.f64 x))
(-.f64 (tan.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (sin.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps (*.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))

Calls

3 calls:

17.0ms	eps
7.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps (*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))

Calls

3 calls:

3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
97.6%	1	`eps`
97.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
97.6%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))

Calls

3 calls:

3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

-22.6MiB live, 15.6MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 eps (fma.f64 eps #s(literal 1/3 binary64) x))) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 x eps))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps eps))

Calls

3 calls:

2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`eps`
96.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

18.1MiB live, 18.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))

Calls

3 calls:

1.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`eps`
96.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify36.0ms (0.2%)

Memory

7.9MiB live, 86.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	166	921
1	191	921
2	202	921
3	208	921
4	212	921
5	213	921

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64) #s(literal 1/3 binary64)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)))) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (+.f64 #s(approx (- 1/3 (* -1/3 (pow (tan x) 2))) #s(literal 1/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) (fma.f64 #s(literal 4/3 binary64) (.f64 x x) #s(literal 1/3 binary64))) eps (/.f64 (.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (+ (* (tan x) (tan x)) (+ (pow (tan x) 4) (- 1/3 (* -1/3 (pow (tan x) 2))))) #s(literal 1/3 binary64)) eps (/.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x))) eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 5/24 binary64) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (.f64 eps eps) (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 #s(approx (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) #s(approx (+ (* (+ (* (* (/ (sin eps) (cos eps)) 5/24) (* x x)) (/ (* 1/2 (sin eps)) (cos eps))) (* x x)) (/ (sin eps) (cos eps))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 5/24 binary64) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)) eps))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 #s(literal 4/3 binary64) (.f64 eps eps)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps (.f64 (.f64 (.f64 eps eps) #s(literal 4/3 binary64)) x)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 x eps) eps) #s(literal 1 binary64)) x eps) x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (.f64 eps eps) #s(literal 1/3 binary64))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (+ (* (- -1/6 (- (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) 1/6) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) -1/2) -1/2)) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)))) eps) (/ (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x)) (cos x))) eps) (/ (pow (sin x) 2) (pow (cos x) 2))) #s(approx (+ (* (* eps eps) 1/3) (* x eps)) (*.f64 x eps))) eps eps))

soundness1.6s (10.8%)

Memory

-24.6MiB live, 935.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	544
0	131	494
1	637	360
2	6419	360
0	8103	360
0	821	14107
1	2660	13394
0	8623	13045
0	95	682
0	149	627
1	688	549
2	5861	549
0	8020	522
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	690	12510
1	2265	12182
2	7659	12040
0	8054	11649
0	952	18180
1	3320	17561
0	8553	16943
0	56	452
0	104	433
1	465	327
2	3937	319
0	8840	307
0	157	1351
1	464	1285
2	1534	1274
3	5964	1242
0	8538	1195

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 514 to 246 computations (52.1% saved)

preprocess111.0ms (0.7%)

Memory: 27.1MiB live, 103.9MiB allocated
Compiler: Compiled 644 to 232 computations (64% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze68.0ms (0.5%)

sample7.0s (46.7%)

explain91.0ms (0.6%)

preprocess39.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0%)

localize23.0ms (0.2%)

series12.0ms (0.1%)

simplify173.0ms (1.2%)

rewrite167.0ms (1.1%)

eval75.0ms (0.5%)

prune44.0ms (0.3%)

simplify146.0ms (1%)

localize252.0ms (1.7%)

series228.0ms (1.5%)

simplify425.0ms (2.8%)

rewrite406.0ms (2.7%)

eval336.0ms (2.2%)

prune61.0ms (0.4%)

simplify221.0ms (1.5%)

localize495.0ms (3.3%)

series111.0ms (0.7%)

simplify228.0ms (1.5%)

rewrite192.0ms (1.3%)

eval201.0ms (1.3%)

prune79.0ms (0.5%)

simplify193.0ms (1.3%)

localize397.0ms (2.7%)

series302.0ms (2%)

simplify262.0ms (1.8%)

rewrite226.0ms (1.5%)

eval216.0ms (1.4%)

prune96.0ms (0.6%)

regimes81.0ms (0.5%)

regimes75.0ms (0.5%)

regimes55.0ms (0.4%)

regimes41.0ms (0.3%)

regimes40.0ms (0.3%)

regimes28.0ms (0.2%)

regimes26.0ms (0.2%)

regimes32.0ms (0.2%)

regimes11.0ms (0.1%)

regimes8.0ms (0.1%)

regimes34.0ms (0.2%)

regimes4.0ms (0%)

simplify36.0ms (0.2%)

soundness1.6s (10.8%)

preprocess111.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18