Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze63.0ms (0.5%)

Memory

23.8MiB live, 62.9MiB 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)

sample6.7s (51.1%)

Memory

-199.4MiB live, 6 768.5MiB allocated

Samples

3.8s	25 716×	0	invalid
914.0ms	5 544×	0	valid
511.0ms	2 712×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-tan: 1.2s (34.1% of total)

const: 654.0ms (18.9% of total)

ival-mult: 298.0ms (8.6% of total)

ival-<=: 253.0ms (7.3% of total)

ival-add: 242.0ms (7% of total)

ival-sub: 210.0ms (6.1% of total)

ival-fabs: 209.0ms (6% of total)

ival-<: 187.0ms (5.4% of total)

ival-and: 99.0ms (2.9% of total)

adjust: 77.0ms (2.2% of total)

exact: 44.0ms (1.3% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

explain84.0ms (0.6%)

Memory

7.3MiB live, 120.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
221	5	(3.09313807738064e-102 1.3927607681776575e-104)	2	(-1.1389919948520682e-283 1.1397733581164892e-285)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`(tan.f64 (+.f64 x eps))`
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	224	7

Confusion

	Predicted +	Predicted -
+	219	2
-	5	30

Precision

0.9776785714285714

Recall

0.9909502262443439

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	219	2	0
-	5	5	25

Precision?

0.9567099567099567

Recall?

1.0

Freqs

test

number	freq
0	32
1	224

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	170×	1	valid
17.0ms	336×	0	valid
3.0ms	6×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-tan: 11.0ms (52.6% of total)

adjust: 4.0ms (19.1% of total)

ival-add: 3.0ms (14.4% of total)

ival-sub: 3.0ms (14.4% of total)

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

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

preprocess25.0ms (0.2%)

Memory

-23.6MiB live, 22.0MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

5.3MiB live, 5.3MiB 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)

localize22.0ms (0.2%)

Memory

26.2MiB live, 26.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(tan.f64 x)
accuracy	0.0234375	(tan.f64 (+.f64 x eps))
accuracy	23.458017401026968	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

8.0ms	85×	1	valid
8.0ms	168×	0	valid
1.0ms	3×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-tan: 5.0ms (50.3% of total)

adjust: 2.0ms (20.1% of total)

ival-add: 2.0ms (20.1% of total)

ival-sub: 1.0ms (10.1% of total)

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

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

series14.0ms (0.1%)

Memory

-23.0MiB live, 15.1MiB 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
4.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	x	@	0	((- (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))

simplify170.0ms (1.3%)

Memory

17.2MiB live, 140.2MiB 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))

rewrite188.0ms (1.4%)

Memory

-13.3MiB live, 177.6MiB 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
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (neg.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(*.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.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))) (pow.f64 (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (pow.f64 (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
(.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))))
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(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(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)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x))
(*.f64 (neg.f64 (sin.f64 x)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (sin.f64 x) (cos.f64 x))
(neg.f64 (neg.f64 (tan.f64 x)))
(tan.f64 x)
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64)))

eval42.0ms (0.3%)

Memory: 1.7MiB live, 73.5MiB allocated
Compiler: Compiled 8 346 to 1 016 computations (87.8% saved)

prune42.0ms (0.3%)

Memory

-8.8MiB live, 79.0MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	329	7	336
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	329	8	337

Accuracy

100.0%

Counts

337 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.4%	(/.f64 (fma.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)) (neg.f64 (sin.f64 x)))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
	62.3%	(/.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)))
▶	63.4%	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
▶	63.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	100.0%	#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))
▶	99.7%	#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))
▶	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 269 to 164 computations (39% saved)

simplify152.0ms (1.2%)

Memory

36.2MiB live, 183.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.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 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
cost-diff	384	(-.f64 (+.f64 eps x) x)
cost-diff	384	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	384	(-.f64 (+.f64 eps x) x)
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	(/.f64 eps (cos.f64 x))
cost-diff	0	#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))
cost-diff	960	(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)
cost-diff	25344	(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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	315
0	60	299
1	95	293
2	178	287
3	379	287
4	1657	278
5	4940	270
0	8258	266

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

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

localize169.0ms (1.3%)

Memory

-19.2MiB live, 227.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01171875	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.01953125	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.21939761954935152	#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))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x)))
accuracy	0.0078125	(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	23.431069326929936	(-.f64 (+.f64 eps x) x)
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	23.431069326929936	(-.f64 (+.f64 eps x) x)
accuracy	0	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	0	(sin.f64 eps)
accuracy	0	(cos.f64 eps)
accuracy	1.0806264147614564	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.015625	(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01953125	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.0234375	(pow.f64 (sin.f64 x) #s(literal 3 binary64))
accuracy	0.1171875	(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))))

Samples

89.0ms	171×	0	valid
53.0ms	85×	1	valid

Compiler

Compiled 272 to 36 computations (86.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-add: 51.0ms (42.9% of total)

adjust: 16.0ms (13.5% of total)

ival-div: 12.0ms (10.1% of total)

ival-pow2: 9.0ms (7.6% of total)

ival-mult: 7.0ms (5.9% of total)

ival-sin: 6.0ms (5.1% of total)

ival-cos: 5.0ms (4.2% of total)

ival-pow: 5.0ms (4.2% of total)

ival-tan: 4.0ms (3.4% of total)

ival-sub: 2.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series77.0ms (0.6%)

Memory

10.5MiB live, 50.2MiB allocated

Counts

23 → 444

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	x	@	inf	((+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)) (* (cos (+ eps x)) (cos x)) (cos x) (pow (cos x) 2))
9.0ms	eps	@	-inf	((+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)) (* (cos (+ eps x)) (cos x)) (cos x) (pow (cos x) 2))
8.0ms	eps	@	0	((+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)) (* (cos (+ eps x)) (cos x)) (cos x) (pow (cos x) 2))
6.0ms	x	@	-inf	((+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)) (* (cos (+ eps x)) (cos x)) (cos x) (pow (cos x) 2))
6.0ms	eps	@	inf	((+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (- (tan (+ x eps)) (tan x)) (/ eps (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (cos x)) (/ (sin (- (+ eps x) x)) (cos (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (pow (sin x) 3) (/ (pow (sin x) 3) (pow (cos x) 2)) (* (cos (+ eps x)) (cos x)) (cos x) (pow (cos x) 2))

simplify280.0ms (2.1%)

Memory

20.5MiB live, 177.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	543	6452
1	1722	6199
2	5508	6038
0	8727	5800

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 408

Calls

Call 1

Inputs
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (+ 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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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 (* -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 (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (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)))))
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
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
eps
eps
eps
eps
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(- (/ (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)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (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) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
eps
eps
eps
eps
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(- (/ (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)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ 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 eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
eps
eps
eps
eps
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 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 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* (cos x) (cos (- x (* -1 eps))))
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps)))))))
(* x (+ eps (* x (+ 1 (* x (- (+ (* 2/3 x) (* 5/6 eps)) (* -1/2 eps)))))))
eps
(+ eps (* (pow eps 2) x))
(+ eps (* x (+ (* eps x) (pow eps 2))))
(+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))
(/ (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)))
eps
(+ eps (* 1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 eps) (* 1/24 eps)))) (* -1/2 eps))))
(+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 eps) (+ (* 1/48 eps) (* 1/2 (+ (* -1/4 eps) (* 1/24 eps))))))) (+ (* -1/4 eps) (* 1/24 eps)))) (* -1/2 eps))))
(/ (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)))
eps
eps
eps
eps
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(+ eps x)
(+ eps x)
(+ eps x)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(pow x 3)
(* (pow x 3) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* 13/120 (pow x 2)) 1/2))))
(* (pow x 3) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 13/120 (* -41/3024 (pow x 2)))) 1/2))))
(pow x 3)
(* (pow x 3) (+ 1 (* 1/2 (pow x 2))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1/2 (* 11/40 (pow x 2))))))
(* (pow x 3) (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 11/40 (* 421/3024 (pow x 2))))))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (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)))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (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)))
eps
eps
eps
eps
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(cos x)
(cos x)
(cos x)
(cos x)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (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 (cos x))
(/ eps (cos x))
(/ eps (cos x))
(/ eps (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)))
eps
eps
eps
eps
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(pow (sin x) 3)
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/ (pow (sin x) 3) (pow (cos x) 2))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(cos x)
(cos x)
(cos x)
(cos x)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)

Outputs
(/ (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) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (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)
(* 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 (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)
(* 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 (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)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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)
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(/ eps (cos x))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
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eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
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(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
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eps
eps
eps
eps
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(fma.f64 (*.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(fma.f64 (*.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 eps (cos.f64 x)))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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eps
eps
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(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (+ eps x)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (/.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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (/.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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (/.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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (/.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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.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 (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.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 (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.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 (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (fma.f64 (/.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 (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(/ eps (cos x))
(/.f64 eps (cos.f64 x))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
eps
eps
eps
eps
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 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) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps 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 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (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)))
(/ (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)))
(/ (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)))
(/ (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)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(pow (sin x) 3)
(pow.f64 (sin.f64 x) #s(literal 3 binary64))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (pow (sin x) 3) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* (cos x) (cos (- eps (* -1 x))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

rewrite588.0ms (4.5%)

Memory

-91.1MiB live, 198.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	242
0	60	236
1	262	178
2	2237	178
0	8989	175

Stop Event

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

Counts

23 → 731

Calls

Call 1

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

Outputs
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (-.f64 (*.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x)))) (pow.f64 (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 (fma.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 eps (cos.f64 x))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64))
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(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (log.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) (cos.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 x)))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64))) #s(literal -2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
(exp.f64 (+.f64 (log.f64 (cos.f64 x)) (log.f64 (cos.f64 x))))
(exp.f64 (.f64 (.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))

eval386.0ms (2.9%)

Memory: -1.0MiB live, 276.9MiB allocated
Compiler: Compiled 40 587 to 4 084 computations (89.9% saved)

prune235.0ms (1.8%)

Memory

-20.3MiB live, 300.7MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	1 616	10	1 626
Fresh	2	0	2
Picked	5	0	5
Done	0	1	1
Total	1 623	11	1 634

Accuracy

100.0%

Counts

1 634 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
▶	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
▶	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))

Compiler

Compiled 293 to 198 computations (32.4% saved)

simplify141.0ms (1.1%)

Memory

-18.1MiB live, 196.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(tan.f64 x)
cost-diff	0	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
cost-diff	0	(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
cost-diff	320	(fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
cost-diff	384	(fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps))
cost-diff	384	(fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)))
cost-diff	0	(*.f64 #s(literal 2/3 binary64) eps)
cost-diff	0	(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
cost-diff	0	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
cost-diff	0	(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
cost-diff	0	(cos.f64 (+.f64 eps x))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	404
0	75	383
1	135	361
2	256	357
3	606	352
4	2749	352
5	6278	352
0	8288	337

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
eps
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps)
(fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
(fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)))
#s(literal 2/45 binary64)
eps
(fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps))
#s(literal -1/3 binary64)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
eps

Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
eps
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
x
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
x
eps
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (*.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64))))))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (*.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)
(*.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64))))
(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
eps
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 17/45 binary64) eps) (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64)))))))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 17/45 binary64) eps) (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 17/45 binary64) eps) (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps)
(.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/45 binary64) (fma.f64 #s(literal 2/3 binary64) (.f64 x x) #s(literal 1 binary64))))
(fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
(.f64 (fma.f64 (.f64 #s(literal 17/45 binary64) x) x #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)))
(*.f64 #s(literal 17/45 binary64) eps)
#s(literal 2/45 binary64)
eps
(fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps))
(*.f64 #s(literal 1/3 binary64) eps)
#s(literal -1/3 binary64)
(*.f64 #s(literal 2/3 binary64) eps)
#s(literal 2/3 binary64)
(*.f64 x x)
x
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
eps

localize191.0ms (1.5%)

Memory

42.9MiB live, 276.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
accuracy	0	(tan.f64 x)
accuracy	0.01953125	(pow.f64 (tan.f64 x) #s(literal 2 binary64))
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
accuracy	0.2421875	(fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)))
accuracy	0.29296875	(fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps))
accuracy	0.29296875	(*.f64 #s(literal 2/3 binary64) eps)
accuracy	0.5120601575110153	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))
accuracy	0	(*.f64 x x)
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
accuracy	0.29296875	(*.f64 #s(literal 2/3 binary64) eps)
accuracy	0.5946733796192539	#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
accuracy	0	(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
accuracy	0	(*.f64 x x)
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
accuracy	1.0591377673891291	#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
accuracy	0	(cos.f64 x)
accuracy	0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy	0.00390625	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Samples

104.0ms	174×	0	valid
57.0ms	82×	1	valid

Compiler

Compiled 277 to 45 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-mult: 21.0ms (20.7% of total)

ival-sin: 21.0ms (20.7% of total)

ival-add: 15.0ms (14.8% of total)

const: 12.0ms (11.8% of total)

adjust: 9.0ms (8.9% of total)

ival-pow2: 9.0ms (8.9% of total)

ival-div: 4.0ms (3.9% of total)

ival-tan: 4.0ms (3.9% of total)

ival-cos: 4.0ms (3.9% of total)

ival-sub: 2.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series71.0ms (0.5%)

Memory

-36.0MiB live, 85.0MiB allocated

Counts

23 → 444

Calls

Call 1

Inputs
#s(alt #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (patch #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) (patch #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (patch (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2/3 binary64) eps) (patch (.f64 #s(literal 2/3 binary64) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (patch (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps)) (patch (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (patch (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) (patch (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) #<representation binary64>) () ())
#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())

Outputs
#s(alt eps (taylor 0 eps) (#s(alt #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (patch #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (patch #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (patch #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (patch #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/6 (pow eps 2)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) (taylor 0 eps) (#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())) ())
#s(alt (pow (cos x) 2) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (patch (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1 (* eps (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (taylor 0 eps) (#s(alt (cos.f64 (+.f64 eps x)) (patch (cos.f64 (+.f64 eps x)) #<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 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) 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 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps 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))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) #<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 #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps eps) (patch (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) 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)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x 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))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x 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))))) (taylor 0 eps) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<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 #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
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#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) #<representation binary64>) () ())) ())
#s(alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) (taylor -inf x) (#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) (patch (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) (patch (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) (patch (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) (patch (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (patch (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #<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) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (patch (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) (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 (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ ( (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	eps	@	0	((sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* 2/3 eps) (* x x)) eps) (* 2/3 eps) (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (+ (* -1/3 eps) (* 2/3 eps)) (+ (* (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (tan x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (cos x) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps))
5.0ms	eps	@	-inf	((sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* 2/3 eps) (* x x)) eps) (* 2/3 eps) (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (+ (* -1/3 eps) (* 2/3 eps)) (+ (* (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (tan x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (cos x) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps))
5.0ms	eps	@	inf	((sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* 2/3 eps) (* x x)) eps) (* 2/3 eps) (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (+ (* -1/3 eps) (* 2/3 eps)) (+ (* (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (tan x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (cos x) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps))
4.0ms	x	@	0	((sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* 2/3 eps) (* x x)) eps) (* 2/3 eps) (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (+ (* -1/3 eps) (* 2/3 eps)) (+ (* (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (tan x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (cos x) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps))
4.0ms	x	@	inf	((sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (+ (* (* 2/3 eps) (* x x)) eps) (* 2/3 eps) (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (+ (* -1/3 eps) (* 2/3 eps)) (+ (* (+ (* 2/45 eps) (+ (* -1/3 eps) (* 2/3 eps))) (* x x)) (* 2/3 eps)) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (tan x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (cos x) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps))

simplify174.0ms (1.3%)

Memory

49.0MiB live, 197.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	374	6333
1	1167	5988
2	3612	5821
0	8307	5534

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 436

Calls

Call 1

Inputs
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin 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)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* 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))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* 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))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ eps (pow (cos x) 2))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
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(/ (sin eps) (cos eps))
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(+ (* 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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
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(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
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(+ (* 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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
eps
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(+ eps (* 2/3 (* eps (pow x 2))))
(* 2/3 eps)
(+ (* 2/3 eps) (* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 eps)))))
(+ (* 2/3 eps) (* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 eps)))))
(+ (* 2/3 eps) (* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 eps)))))
(/ (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))
(+ (/ (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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
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) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(* (cos x) (cos (+ eps x)))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ 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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(pow x 2)
(pow x 2)
(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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 eps))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (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 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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(cos x)
(cos x)
(cos x)
(cos x)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(* (cos x) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- 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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow 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 (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 2/3 (* eps (pow x 2)))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (* 2/3 eps))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow 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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(cos x)
(cos x)
(cos x)
(cos x)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))

Outputs
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(*.f64 (cos.f64 x) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (.f64 (cos.f64 x) (-.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (sin.f64 x)) (cos.f64 x)) #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 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (sin.f64 x) (.f64 (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)) eps (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 (- (* 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 (fma.f64 (neg.f64 eps) (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.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) #s(literal 1/6 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 (.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1/3 binary64))) (-.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.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 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (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 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* 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)))))
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(* 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 (- (+ 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)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(/ eps (pow (cos x) 2))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
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(cos (+ eps x))
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (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)))
(- (/ (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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (* 2/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* 2/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* 2/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* 2/3 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
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(- (/ (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)))
(- (/ (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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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (sin eps) (* (cos x) (cos (+ eps x))))
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(/ (sin eps) (* (cos x) (cos (+ eps x))))
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(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(sin (neg (* -1 eps)))
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(sin (neg (* -1 eps)))
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(fma.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) (neg.f64 eps) eps)
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(fma.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) (neg.f64 eps) eps)
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(fma.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) (neg.f64 eps) eps)
(* -1 (* eps (- (* -2/3 (pow x 2)) 1)))
(fma.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) (neg.f64 eps) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 2/3 eps)
(*.f64 #s(literal 2/3 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 17/45 eps)
(*.f64 #s(literal 17/45 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (neg.f64 eps))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (neg.f64 eps))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (neg.f64 eps))
(* -1 (* eps (- (* -17/45 (pow x 2)) 2/3)))
(.f64 (fma.f64 #s(literal -17/45 binary64) (.f64 x x) #s(literal -2/3 binary64)) (neg.f64 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)))
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eps
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eps
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x
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(.f64 (.f64 (*.f64 x x) eps) #s(literal 17/45 binary64))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(.f64 (.f64 eps (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (.f64 x x)))) (.f64 x x))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(.f64 (.f64 eps (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (.f64 x x)))) (.f64 x x))
(* (pow x 2) (+ (* -1/3 eps) (+ (* 2/45 eps) (+ (* 2/3 eps) (* 2/3 (/ eps (pow x 2)))))))
(.f64 (.f64 eps (+.f64 #s(literal 17/45 binary64) (/.f64 #s(literal 2/3 binary64) (.f64 x x)))) (.f64 x 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)))) (/ (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (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)))
(/ (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)))
(/ (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)))
(/ (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)))
(/ (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) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)

rewrite295.0ms (2.2%)

Memory

-46.7MiB live, 242.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	317
0	75	302
1	334	247
2	2748	247
0	8176	247

Stop Event

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

Counts

23 → 286

Calls

Call 1

Inputs
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 x x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps))
(fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)
(*.f64 #s(literal 2/3 binary64) eps)
(fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)))
(fma.f64 #s(literal -1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) eps))
(fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (*.f64 #s(literal 2/3 binary64) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(cos.f64 x)
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))

Outputs
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(sin.f64 eps)
(*.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x))) #s(literal 1/2 binary64))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal -1 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal -2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 (-.f64 x (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))))
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))) (.f64 (sin.f64 (/.f64 (.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 eps x)))) (.f64 (sin.f64 (/.f64 (.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 eps x)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
(.f64 (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x))) eps)
(.f64 (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 eps eps)) (pow.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps)) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 eps (+.f64 #s(literal 1 binary64) #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x))))
(pow.f64 (/.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps)) (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps)) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps))) (.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps)) (.f64 eps eps))) (.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps))))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64))) (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps)) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) (*.f64 eps eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps)) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps)) (-.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps)) (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)
(fma.f64 eps #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps)
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) #s(literal 2 binary64)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps (neg.f64 eps))) (/.f64 (.f64 eps eps) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps))))
(+.f64 (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps) eps)
(+.f64 eps (.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (.f64 x x)) eps))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(exp.f64 (.f64 (log.f64 (.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)))
(pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (log.f64 (cos.f64 x)))
#s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps #s(literal 17/45 binary64)) x) x (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))

eval106.0ms (0.8%)

Memory: 19.2MiB live, 136.1MiB allocated
Compiler: Compiled 17 850 to 1 920 computations (89.2% saved)

prune76.0ms (0.6%)

Memory

20.8MiB live, 96.4MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	848	2	850
Fresh	1	4	5
Picked	1	4	5
Done	0	1	1
Total	850	11	861

Accuracy

100.0%

Counts

861 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
▶	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
✓	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
▶	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
▶	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
▶	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
✓	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))

Compiler

Compiled 235 to 161 computations (31.5% saved)

simplify212.0ms (1.6%)

Memory

-13.1MiB live, 140.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 4 binary64))
cost-diff	0	#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
cost-diff	0	(fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
cost-diff	0	(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
cost-diff	0	(fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
cost-diff	0	#s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
cost-diff	0	#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
cost-diff	0	(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
cost-diff	0	(*.f64 (+.f64 eps x) x)
cost-diff	0	#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x))
cost-diff	0	(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
cost-diff	0	(tan.f64 x)
cost-diff	0	(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
cost-diff	256	(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	591
0	95	591
1	174	591
2	337	591
3	758	591
4	2237	567
5	4255	567
6	5552	567
7	5963	567
8	6148	567
9	6181	567
10	6252	567
0	8992	545

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(tan.f64 x)
x
#s(literal 1 binary64)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x))
(*.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps)
(fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64))
(fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
#s(literal 4/3 binary64)
eps
(*.f64 #s(literal 2/3 binary64) x)
#s(literal 2/3 binary64)
x
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)
(fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps)
#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
(fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
#s(literal 62/315 binary64)
(*.f64 x x)
#s(literal 17/45 binary64)
#s(literal 2/3 binary64)
eps

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(tan.f64 x)
x
#s(literal 1 binary64)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x))
(*.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
x
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps)
(fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64))
(fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
#s(literal 4/3 binary64)
eps
(*.f64 #s(literal 2/3 binary64) x)
#s(literal 2/3 binary64)
x
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps)))
#s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))
#s(approx (+ (* (pow (tan x) 2) eps) eps) (.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)
(.f64 (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) #s(literal 1 binary64))) eps)
(fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(.f64 (fma.f64 (.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64)) eps)
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
#s(literal 17/45 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 62/315 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/45 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))))) eps eps))
(fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps)
(fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 62/315 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/45 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))))) eps eps)
#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 62/315 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/45 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 62/315 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/45 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
(fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
#s(literal 62/315 binary64)
(*.f64 x x)
#s(literal 17/45 binary64)
#s(literal 2/3 binary64)
eps

localize214.0ms (1.6%)

Memory

16.2MiB live, 301.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
accuracy	0.01171875	(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
accuracy	0.49666237634177185	#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
accuracy	0.0078125	(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
accuracy	0.30078125	(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
accuracy	0.5120601575110153	#s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))
accuracy	0.11328125	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
accuracy	0.279802174297186	(fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
accuracy	0.421875	(*.f64 #s(literal 2/3 binary64) x)
accuracy	0.7216994515120783	#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
accuracy	0	(+.f64 eps x)
accuracy	0	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
accuracy	0.10546875	(*.f64 (+.f64 eps x) x)
accuracy	1.0591377675369902	#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x))
accuracy	0	(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
accuracy	0	(tan.f64 x)
accuracy	0.015625	(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)
accuracy	0.21939761954935152	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))

Samples

100.0ms	82×	1	valid
71.0ms	170×	0	valid
4.0ms	3×	3	valid
2.0ms	1×	5	exit

Compiler

Compiled 374 to 59 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 145.0ms

ival-add: 42.0ms (29% of total)

ival-mult: 36.0ms (24.9% of total)

const: 14.0ms (9.7% of total)

adjust: 14.0ms (9.7% of total)

ival-pow2: 11.0ms (7.6% of total)

ival-pow: 10.0ms (6.9% of total)

ival-div: 6.0ms (4.1% of total)

ival-tan: 5.0ms (3.5% of total)

ival-sin: 3.0ms (2.1% of total)

ival-cos: 2.0ms (1.4% of total)

ival-sub: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series115.0ms (0.9%)

Memory

-9.9MiB live, 65.1MiB allocated

Counts

26 → 528

Calls

Call 1

Inputs
#s(alt (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (patch (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (+.f64 eps x) x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (+.f64 eps x) x)) eps eps) (patch (fma.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (+.f64 eps x) x)) (patch #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 eps x) x) (patch (.f64 (+.f64 eps x) x) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps) (patch (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) (patch #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))) (patch #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)) (patch #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (patch (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (patch (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) (patch (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) #<representation binary64>) () ())
#s(alt #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) (patch #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2/3 binary64) x) (patch (.f64 #s(literal 2/3 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) (patch (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (patch (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps) (patch (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) 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)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) 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)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)) (patch #s(approx (- (tan (+ x eps)) (tan x)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
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#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) (patch (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) (patch (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) (patch (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) (patch (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) eps eps) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) (patch #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) (patch #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) (patch #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (pow (cos x) 2)) (taylor -inf x) (#s(alt #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) (patch #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2/3 binary64) x) (patch (.f64 #s(literal 2/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2/3 binary64) x) (patch (.f64 #s(literal 2/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2/3 binary64) x) (patch (.f64 #s(literal 2/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2/3 binary64) x) (patch (.f64 #s(literal 2/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) (patch (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -4/3 (/ eps x)) 2/3))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) (patch (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -4/3 (/ eps x)) 2/3))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) (patch (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -4/3 (/ eps x)) 2/3))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) (patch (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 17/45 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 62/315 (pow x 8)) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 62/315 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (patch (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (patch (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (patch (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (patch (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	inf	((* (+ (* (tan x) (tan x)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (tan x) (tan x)) 1) (tan x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ eps x) x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ (* (+ (* (+ (* 4/3 eps) (* 2/3 x)) x) 1) x) eps) x) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* (+ (* 17/45 (* x x)) 2/3) eps) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (pow x 4) (+ eps x) (* 2/3 x) (+ (* 4/3 eps) (* 2/3 x)) (+ (* 17/45 (* x x)) 2/3) (+ (* (pow x 4) (+ (* (+ (* 62/315 (* x x)) 17/45) (* x x)) 2/3)) (* x x)) (+ (* 62/315 (* x x)) 17/45))
5.0ms	eps	@	0	((* (+ (* (tan x) (tan x)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (tan x) (tan x)) 1) (tan x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ eps x) x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ (* (+ (* (+ (* 4/3 eps) (* 2/3 x)) x) 1) x) eps) x) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* (+ (* 17/45 (* x x)) 2/3) eps) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (pow x 4) (+ eps x) (* 2/3 x) (+ (* 4/3 eps) (* 2/3 x)) (+ (* 17/45 (* x x)) 2/3) (+ (* (pow x 4) (+ (* (+ (* 62/315 (* x x)) 17/45) (* x x)) 2/3)) (* x x)) (+ (* 62/315 (* x x)) 17/45))
5.0ms	x	@	inf	((* (+ (* (tan x) (tan x)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (tan x) (tan x)) 1) (tan x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ eps x) x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ (* (+ (* (+ (* 4/3 eps) (* 2/3 x)) x) 1) x) eps) x) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* (+ (* 17/45 (* x x)) 2/3) eps) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (pow x 4) (+ eps x) (* 2/3 x) (+ (* 4/3 eps) (* 2/3 x)) (+ (* 17/45 (* x x)) 2/3) (+ (* (pow x 4) (+ (* (+ (* 62/315 (* x x)) 17/45) (* x x)) 2/3)) (* x x)) (+ (* 62/315 (* x x)) 17/45))
5.0ms	eps	@	-inf	((* (+ (* (tan x) (tan x)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (tan x) (tan x)) 1) (tan x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ eps x) x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ (* (+ (* (+ (* 4/3 eps) (* 2/3 x)) x) 1) x) eps) x) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* (+ (* 17/45 (* x x)) 2/3) eps) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (pow x 4) (+ eps x) (* 2/3 x) (+ (* 4/3 eps) (* 2/3 x)) (+ (* 17/45 (* x x)) 2/3) (+ (* (pow x 4) (+ (* (+ (* 62/315 (* x x)) 17/45) (* x x)) 2/3)) (* x x)) (+ (* 62/315 (* x x)) 17/45))
5.0ms	x	@	-inf	((* (+ (* (tan x) (tan x)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (tan x) (tan x)) 1) (tan x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ eps x) x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) eps) eps) (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (* (+ (* (+ (* (+ (* 4/3 eps) (* 2/3 x)) x) 1) x) eps) x) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (+ (* (* (+ (* 17/45 (* x x)) 2/3) eps) (* x x)) eps) (* (+ (* 17/45 (* x x)) 2/3) eps) (- (tan (+ x eps)) (tan x)) (+ (* (pow (tan x) 2) eps) eps) (pow (tan x) 2) (pow x 4) (+ eps x) (* 2/3 x) (+ (* 4/3 eps) (* 2/3 x)) (+ (* 17/45 (* x x)) 2/3) (+ (* (pow x 4) (+ (* (+ (* 62/315 (* x x)) 17/45) (* x x)) 2/3)) (* x x)) (+ (* 62/315 (* x x)) 17/45))

simplify178.0ms (1.4%)

Memory

28.9MiB live, 179.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	369	9202
1	1205	8869
2	3642	8635
0	8838	8161

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 515

Calls

Call 1

Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 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 (* -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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))))
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow 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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))))
(/ (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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (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)))
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow 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 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow 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 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* 2/3 x)
(+ (* 2/3 x) (* 4/3 eps))
(+ (* 2/3 x) (* 4/3 eps))
(+ (* 2/3 x) (* 4/3 eps))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (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)))
(- (/ (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 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps x)
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) 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 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (* x (+ 1 (* 4/3 (pow x 2)))))
(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)))
(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)))
(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) 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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(* eps (+ 2/3 (* 17/45 (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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* 4/3 eps)
(* eps (+ 4/3 (* 2/3 (/ x eps))))
(* eps (+ 4/3 (* 2/3 (/ x eps))))
(* eps (+ 4/3 (* 2/3 (/ x eps))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (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)))
(- (/ (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 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) 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 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* (pow eps 2) (+ (* -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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* eps (* x (- (* -4/3 (pow x 2)) 1))))
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)) (* x (- (* -4/3 (pow x 2)) 1)))))
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)) (* x (- (* -4/3 (pow x 2)) 1)))))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(* -1 (* eps (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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eps
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eps
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1
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x
(* x (+ 1 (* 1/3 (pow x 2))))
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin eps) (cos eps))
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(+ (* 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)))
eps
(+ eps (* (pow eps 2) x))
(+ eps (* x (+ (* eps x) (pow eps 2))))
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(* eps x)
(* x (+ eps x))
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(* x (+ eps (* x (+ 1 (* x (- (+ (* 2/3 x) (* 5/6 eps)) (* -1/2 eps)))))))
(* eps x)
(* x (+ eps x))
(* x (+ eps x))
(* x (+ eps x))
(/ (sin eps) (cos eps))
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(+ (* 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)))
eps
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(* eps x)
(* x (+ eps x))
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(* x (+ eps (* x (+ 1 (* x (+ (* 2/3 x) (* 4/3 eps)))))))
(/ (sin eps) (cos eps))
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(+ (* 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)))
eps
(+ eps (* eps (pow x 2)))
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eps
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(+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))
(* 2/3 eps)
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(+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))
(+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))
(/ (sin eps) (cos eps))
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(+ (* 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)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
eps
(+ eps x)
(+ eps x)
(+ eps x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 4/3 eps)
(+ (* 2/3 x) (* 4/3 eps))
(+ (* 2/3 x) (* 4/3 eps))
(+ (* 2/3 x) (* 4/3 eps))
2/3
(+ 2/3 (* 17/45 (pow x 2)))
(+ 2/3 (* 17/45 (pow x 2)))
(+ 2/3 (* 17/45 (pow x 2)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
17/45
(+ 17/45 (* 62/315 (pow x 2)))
(+ 17/45 (* 62/315 (pow x 2)))
(+ 17/45 (* 62/315 (pow x 2)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(- (/ (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 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (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)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ 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)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 2/3 (pow x 4))
(* (pow x 4) (+ 2/3 (* 4/3 (/ eps x))))
(* (pow x 4) (+ 2/3 (+ (* 4/3 (/ eps x)) (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/3 (+ (* 4/3 (/ eps x)) (+ (/ 1 (pow x 2)) (/ eps (pow x 3))))))
(- (/ (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 17/45 (* eps (pow x 4)))
(* (pow x 4) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* 17/45 (* eps (pow x 2)))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* x (+ 2/3 (* 4/3 (/ eps x))))
(* x (+ 2/3 (* 4/3 (/ eps x))))
(* x (+ 2/3 (* 4/3 (/ eps x))))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 62/315 (pow x 2))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
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(- (/ (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 (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps 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)))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 2/3 (pow x 4))
(* (pow x 4) (+ 2/3 (* 4/3 (/ eps x))))
(* (pow x 4) (+ 2/3 (* -1 (/ (- (* -4/3 eps) (/ 1 x)) x))))
(* (pow x 4) (+ 2/3 (* -1 (/ (+ (* -4/3 eps) (* -1 (/ (+ 1 (/ eps x)) x))) 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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(* 17/45 (* eps (pow x 4)))
(* (pow x 4) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* 17/45 (* eps (pow x 2)))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 2) (+ (* 17/45 eps) (* 2/3 (/ eps (pow 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 (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 62/315 (pow x 2))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))

Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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 (- (* -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 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.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)) #s(literal -1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 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 (neg.f64 eps) (fma.f64 (+.f64 (fma.f64 (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.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)) #s(literal -1/3 binary64))) (-.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.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)) #s(literal -1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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 (- (* -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 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.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)) #s(literal -1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 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 (neg.f64 eps) (fma.f64 (+.f64 (fma.f64 (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.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 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.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)) #s(literal -1/3 binary64))) (-.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.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)) #s(literal -1/6 binary64)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/2 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 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (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)
(* 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 (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)
(* 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 (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)
(/ (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) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 x 2)
(*.f64 x x)
(+ (* eps x) (pow x 2))
(*.f64 (+.f64 x eps) x)
(+ (* eps x) (pow x 2))
(*.f64 (+.f64 x eps) x)
(+ (* eps x) (pow x 2))
(*.f64 (+.f64 x eps) x)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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 (- (* -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 (- (+ 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)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (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)
(* 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 (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)
(* 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 (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)
(/ (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)))
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(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(fma.f64 (+.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 x 2) (+ 1 (* 2/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)))
(+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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 (- (* -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 (- (+ 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)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (+ 2/3 (* 17/45 (pow x 2))))
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) 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 (+.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 (- (* -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 (- (+ 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)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(+ (* 2/3 x) (* 4/3 eps))
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(+ (* 2/3 x) (* 4/3 eps))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps x)
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(* eps (+ x (/ (pow x 2) eps)))
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(* eps (+ x (/ (pow x 2) eps)))
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(* (pow eps 2) (+ (/ 1 eps) (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3))))))
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(* eps (* x (+ 1 (* 4/3 (pow x 2)))))
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(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)))
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(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)))
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(* eps (+ (* x (+ 1 (* 4/3 (pow x 2)))) (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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(* eps (+ 4/3 (* 2/3 (/ x eps))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
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(- (/ (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)))
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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 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x)))
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(/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
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(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* eps x)
(*.f64 x eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) x) eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) x) eps)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) x) eps)
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(-.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)))
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(- (/ (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)))
(* (pow eps 2) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(.f64 (.f64 eps eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(/ (* eps (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2)))) (cos x))
(*.f64 (/.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)
(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* eps (+ (* -1 (/ (+ (sin x) (/ (pow (sin x) 3) (pow (cos x) 2))) (cos x))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* eps (* x (- (* -4/3 (pow x 2)) 1))))
(.f64 (fma.f64 (.f64 #s(literal -4/3 binary64) (*.f64 x x)) (neg.f64 eps) eps) x)
(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)) (* x (- (* -4/3 (pow x 2)) 1)))))
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(* -1 (* eps (+ (* -1 (/ (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) eps)) (* x (- (* -4/3 (pow x 2)) 1)))))
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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(* -1 (* eps (- (* -1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))) 1)))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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(* eps (+ 2/3 (* 17/45 (pow x 2))))
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eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 x eps) eps eps)
(* 4/3 eps)
(*.f64 #s(literal 4/3 binary64) eps)
(* -1 (* eps (- (* -2/3 (/ x eps)) 4/3)))
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(*.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 x eps) #s(literal -4/3 binary64)) (neg.f64 eps))
eps
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(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
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(/ (sin eps) (cos eps))
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2/3
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(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(/ (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)))
(/ (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)))
(/ (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)))
(/ (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)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 (/.f64 eps x) x x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 x))
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 x))
(* -1 (* x (- (* -4/3 (/ eps x)) 2/3)))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 x))
(* 17/45 (pow x 2))
(.f64 #s(literal 17/45 binary64) (.f64 x x))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* 62/315 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 62/315 binary64))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 17/45 binary64) (.f64 x x)) #s(literal 62/315 binary64)) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 62/315 binary64)) (/.f64 #s(literal 17/45 binary64) (.f64 x x))) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 62/315 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 17/45 binary64) (.f64 x x)))) (pow.f64 x #s(literal 8 binary64)))
(* 62/315 (pow x 2))
(.f64 #s(literal 62/315 binary64) (.f64 x x))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
(* (pow x 2) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))

rewrite241.0ms (1.8%)

Memory

-25.7MiB live, 180.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	515
0	95	515
1	438	473
2	3601	473
0	9035	457

Stop Event

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

Counts

26 → 434

Calls

Call 1

Inputs
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x))
(*.f64 (+.f64 eps x) x)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
(fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps)
#s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps))
(fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps)
(.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps)
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps)
#s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)))
(pow.f64 x #s(literal 4 binary64))
(+.f64 eps x)
(*.f64 #s(literal 2/3 binary64) x)
(fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))

Outputs
(.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (*.f64 (neg.f64 eps) eps)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))) #s(literal -1 binary64)))
(*.f64 eps (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps)
(pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) eps)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) eps)) (neg.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 eps (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) eps) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) eps) (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) #s(literal 2 binary64))) (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps))) (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (tan.f64 x) eps) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)))
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (tan.f64 x) eps) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 (neg.f64 eps) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (.f64 eps eps) (.f64 eps (-.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(fma.f64 (.f64 eps (tan.f64 x)) (tan.f64 x) (.f64 eps #s(literal 1 binary64)))
(fma.f64 (.f64 eps (tan.f64 x)) (tan.f64 x) (.f64 #s(literal 1 binary64) eps))
(fma.f64 (*.f64 eps (tan.f64 x)) (tan.f64 x) eps)
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (*.f64 eps #s(literal 1 binary64)))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (*.f64 #s(literal 1 binary64) eps))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)
(fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps #s(literal 1 binary64)))
(fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) eps))
(fma.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps)
(fma.f64 eps #s(literal 1 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
(fma.f64 #s(literal 1 binary64) eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
(fma.f64 (tan.f64 x) (.f64 (tan.f64 x) eps) (.f64 eps #s(literal 1 binary64)))
(fma.f64 (tan.f64 x) (.f64 (tan.f64 x) eps) (.f64 #s(literal 1 binary64) eps))
(fma.f64 (tan.f64 x) (*.f64 (tan.f64 x) eps) eps)
(-.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps))) (/.f64 (.f64 eps eps) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps (neg.f64 eps))))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (.f64 eps #s(literal 1 binary64)))
(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) (.f64 #s(literal 1 binary64) eps))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(+.f64 eps (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
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(-.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (pow.f64 x #s(literal 4 binary64)) (*.f64 (neg.f64 x) x))))
(+.f64 (fma.f64 x x (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)))
(+.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 x x))
(+.f64 (.f64 x x) (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64)) (pow.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal -17/45 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64)) (pow.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (*.f64 x x) #s(literal 1054/14175 binary64)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64)) (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64)))) (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 289/2025 binary64) (.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 17/45 binary64) (.f64 #s(literal 62/315 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64)))))))
(/.f64 (-.f64 #s(literal 289/2025 binary64) (.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 17/45 binary64) (.f64 #s(literal 62/315 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64))) (neg.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64))) (neg.f64 (+.f64 #s(literal 289/2025 binary64) (-.f64 (.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 1054/14175 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64))) (neg.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64)) (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64)))) (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64)))))
(/.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64)) (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64)))
(/.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64)) (+.f64 #s(literal 289/2025 binary64) (-.f64 (.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 (*.f64 x x) #s(literal 1054/14175 binary64)))))
(/.f64 (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64)) (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64)) (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -289/2025 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 289/2025 binary64) (.f64 (.f64 x x) #s(literal 1054/14175 binary64)))) (fma.f64 #s(literal 238328/31255875 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 4913/91125 binary64))))
(fma.f64 (*.f64 #s(literal 62/315 binary64) x) x #s(literal 17/45 binary64))
(fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64))
(fma.f64 (*.f64 x x) #s(literal 62/315 binary64) #s(literal 17/45 binary64))
(fma.f64 x (*.f64 #s(literal 62/315 binary64) x) #s(literal 17/45 binary64))
(-.f64 (/.f64 (.f64 #s(literal 3844/99225 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal -17/45 binary64))) (/.f64 #s(literal 289/2025 binary64) (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal -17/45 binary64))))
(+.f64 (.f64 #s(literal 62/315 binary64) (.f64 x x)) #s(literal 17/45 binary64))
(+.f64 #s(literal 17/45 binary64) (.f64 #s(literal 62/315 binary64) (.f64 x x)))

eval134.0ms (1%)

Memory: 13.0MiB live, 238.1MiB allocated
Compiler: Compiled 24 339 to 2 742 computations (88.7% saved)

prune87.0ms (0.7%)

Memory

-11.9MiB live, 187.3MiB allocated

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	969	6	975
Fresh	0	1	1
Picked	2	3	5
Done	1	4	5
Total	972	14	986

Accuracy

100.0%

Counts

986 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.4%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	63.4%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
✓	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
✓	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
	99.6%	#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
	98.3%	#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
✓	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
	98.8%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
✓	99.1%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))

Compiler

Compiled 598 to 269 computations (55% saved)

regimes23.0ms (0.2%)

Memory

-2.0MiB live, 42.5MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.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))
(/.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 (fma.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)) (neg.f64 (sin.f64 x)))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))
#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))

Outputs

#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))

Calls

3 calls:

9.0ms	x
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

6.9MiB live, 45.8MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.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))
(/.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 (fma.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)) (neg.f64 (sin.f64 x)))) (.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))

Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory

24.3MiB live, 24.3MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

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

Calls

3 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	eps
5.0ms	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)

regimes56.0ms (0.4%)

Memory

-26.6MiB live, 12.6MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) eps (fma.f64 #s(literal -1/3 binary64) eps (.f64 #s(literal 2/3 binary64) eps))) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x))) eps eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x)) (*.f64 x x) (*.f64 x x))) eps eps))

Calls

3 calls:

47.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	x
4.0ms	eps

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 (+.f64 #s(approx (+ ( (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))

Outputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) eps) (*.f64 x x) eps) (*.f64 x x) eps)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

-22.7MiB live, 15.4MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

4.0ms	eps
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) 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
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) 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
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

-50.3MiB live, 12.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))

Calls

3 calls:

12.0ms	eps
2.0ms	x
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

7.6MiB live, 7.6MiB 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)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) 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
98.3%	1	`x`
98.3%	1	`eps`
98.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify25.0ms (0.2%)

Memory

1.9MiB live, 39.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	374
1	119	374

Stop Event

1×

saturated

Calls

Call 1

Inputs
#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))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))

Outputs
#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))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (pow (tan x) 2) (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (.f64 x x) #s(literal 17/45 binary64)) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) (.f64 x x) (.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) eps) (.f64 x x) eps) (.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 4/3 eps) (* 2/3 x)) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (/ eps (cos x)) (+ (/ (pow (sin x) 3) (pow (cos x) 2)) (sin x))) (/ (pow (sin x) 2) (pow (cos x) 2))) (*.f64 (+.f64 eps x) x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 x eps) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (pow (tan x) 2) eps) eps) (fma.f64 (*.f64 eps x) x eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (.f64 #s(approx (+ ( (tan x) (tan x)) 1) #s(literal 1 binary64)) eps))

soundness1.3s (10%)

Memory

32.5MiB live, 938.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	369	9202
1	1205	8869
2	3642	8635
0	8838	8161
0	6	16
0	10	16
1	50	16
2	402	16
3	6117	16
0	8095	16
0	59	515
0	95	515
1	438	473
2	3601	473
0	9035	457
0	374	6333
1	1167	5988
2	3612	5821
0	8307	5534
0	34	242
0	60	236
1	262	178
2	2237	178
0	8989	175
0	543	6452
1	1722	6199
2	5508	6038
0	8727	5800
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×	node limit
1×	iter 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

Compiler

Compiled 365 to 242 computations (33.7% saved)

preprocess127.0ms (1%)

Memory: 1.8MiB live, 114.7MiB allocated
Compiler: Compiled 372 to 176 computations (52.7% 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%)

analyze63.0ms (0.5%)

sample6.7s (51.1%)

explain84.0ms (0.6%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0%)

localize22.0ms (0.2%)

series14.0ms (0.1%)

simplify170.0ms (1.3%)

rewrite188.0ms (1.4%)

eval42.0ms (0.3%)

prune42.0ms (0.3%)

simplify152.0ms (1.2%)

localize169.0ms (1.3%)

series77.0ms (0.6%)

simplify280.0ms (2.1%)

rewrite588.0ms (4.5%)

eval386.0ms (2.9%)

prune235.0ms (1.8%)

simplify141.0ms (1.1%)

localize191.0ms (1.5%)

series71.0ms (0.5%)

simplify174.0ms (1.3%)

rewrite295.0ms (2.2%)

eval106.0ms (0.8%)

prune76.0ms (0.6%)

simplify212.0ms (1.6%)

localize214.0ms (1.6%)

series115.0ms (0.9%)

simplify178.0ms (1.4%)

rewrite241.0ms (1.8%)

eval134.0ms (1%)

prune87.0ms (0.7%)

regimes23.0ms (0.2%)

regimes25.0ms (0.2%)

regimes17.0ms (0.1%)

regimes56.0ms (0.4%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

regimes16.0ms (0.1%)

regimes4.0ms (0%)

simplify25.0ms (0.2%)

soundness1.3s (10%)

preprocess127.0ms (1%)

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