Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze131.0ms (1.1%)

Memory

-47.2MiB live, 51.3MiB allocated; 165ms collecting garbage

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)

sample6.8s (55.8%)

Memory

-59.6MiB live, 7 240.6MiB allocated; 2.6s collecting garbage

Samples

3.5s	25 651×	0	invalid
1.2s	5 132×	1	valid
536.0ms	3 124×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.9s

ival-tan: 1.1s (28.5% of total)

const: 552.0ms (14% of total)

ival-<: 450.0ms (11.4% of total)

adjust: 315.0ms (8% of total)

ival-<=: 293.0ms (7.4% of total)

ival-fabs: 286.0ms (7.2% of total)

ival-add: 284.0ms (7.2% of total)

ival-mult: 252.0ms (6.4% of total)

ival-sub: 226.0ms (5.7% of total)

ival-and: 103.0ms (2.6% of total)

exact: 46.0ms (1.2% of total)

ival-assert: 14.0ms (0.4% of total)

Bogosity

explain115.0ms (0.9%)

Memory

-33.0MiB live, 158.6MiB allocated; 17ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
238	1	(2.4185364921987094e-228 6.762651286286268e-231)	4	(-7.858801752117988e-290 1.293256148064356e-291)	`(-.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	235	7

Confusion

	Predicted +	Predicted -
+	234	4
-	1	17

Precision

0.9957446808510638

Recall

0.9831932773109243

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	234	4	0
-	1	3	14

Precision?

0.9834710743801653

Recall?

1.0

Freqs

test

number	freq
0	21
1	235

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms	318×	1	valid
10.0ms	192×	0	valid
7.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-tan: 17.0ms (44.1% of total)

adjust: 13.0ms (33.7% of total)

ival-add: 4.0ms (10.4% of total)

ival-sub: 4.0ms (10.4% of total)

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

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

preprocess198.0ms (1.6%)

Memory

21.0MiB live, 250.3MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	35	43
2	62	43
3	109	43
4	184	43
5	328	43
6	664	43
7	1518	43
8	2905	43
9	4357	43
0	6	7
0	10	7
1	16	7
2	25	7
3	41	7
4	66	7
5	117	7
6	221	7
7	472	7
8	1313	7
9	3234	7
10	5204	7
0	8088	7

Stop Event

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

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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify147.0ms (1.2%)

Memory

-3.3MiB live, 187.7MiB allocated; 27ms collecting garbage

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	16	18
2	25	18
3	41	18
4	66	18
5	117	18
6	221	18
7	472	18
8	1313	18
9	3234	18
10	5204	18
0	8088	18

Stop Event

1×	iter limit
1×	node limit
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)

localize52.0ms (0.4%)

Memory

26.3MiB live, 78.3MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(tan.f64 x)
accuracy	0.01171875	(tan.f64 (+.f64 x eps))
accuracy	24.293676406315882	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

38.0ms	159×	1	valid
5.0ms	96×	0	valid
3.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

adjust: 13.0ms (51.1% of total)

ival-tan: 8.0ms (31.5% of total)

ival-add: 2.0ms (7.9% of total)

ival-sub: 2.0ms (7.9% of total)

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

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

series18.0ms (0.1%)

Memory

-26.9MiB live, 18.0MiB allocated; 11ms collecting garbage

Counts

4 → 34

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
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms	eps	@	0	((- (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	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))

simplify160.0ms (1.3%)

Memory

13.2MiB live, 153.6MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	1167
1	534	1107
2	1935	1046
0	8305	994

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 34

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

rewrite720.0ms (5.9%)

Memory

-140.6MiB live, 218.9MiB allocated; 861ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	440	16
3	6630	16
0	8617	16

Stop Event

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

Counts

4 → 158

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

eval35.0ms (0.3%)

Memory: 17.4MiB live, 61.5MiB allocated; 5ms collecting garbage
Compiler: Compiled 5 988 to 854 computations (85.7% saved)

prune10.0ms (0.1%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	178	10	188
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	11	189

Accuracy

100.0%

Counts

189 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	3.5%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) eps) (PI.f64)) (PI.f64))) (tan.f64 x))
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	61.0%	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
▶	61.4%	(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
	61.3%	(-.f64 (tan.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (tan.f64 x))
	7.9%	(-.f64 (tan.f64 #s(approx (+ x eps) eps)) (tan.f64 x))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (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) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
	99.6%	#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))
▶	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 465 to 268 computations (42.4% saved)

simplify236.0ms (1.9%)

Memory

-16.2MiB live, 274.7MiB allocated; 27ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
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	4	(-.f64 (+.f64 eps x) x)
cost-diff	0	#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
cost-diff	0	(tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps)))
cost-diff	0	(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
cost-diff	3	(fma.f64 (/.f64 x eps) eps eps)
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	#s(approx (tan x) x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(tan.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
cost-diff	1	(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
cost-diff	2	(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) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
cost-diff	6	(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
cost-diff	10	(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 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	688
0	103	677
1	183	643
2	456	612
3	2007	538
0	8467	532

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

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

localize315.0ms (2.6%)

Memory

34.5MiB live, 448.6MiB allocated; 57ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	24.28056046509669	(-.f64 (+.f64 eps x) x)
accuracy	0.0	#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
accuracy	0.0078125	(tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps)))
accuracy	0.260761279305326	(fma.f64 (/.f64 x eps) eps eps)
accuracy	24.289770156315882	(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
accuracy	0.0	(sin.f64 eps)
accuracy	0.0	(cos.f64 eps)
accuracy	0.00390625	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	1.0258092658713123	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.0	(+.f64 x eps)
accuracy	0.0078125	(tan.f64 (+.f64 x eps))
accuracy	0.9811300227084828	#s(approx (tan x) x)
accuracy	24.289770156315882	(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
accuracy	0.171875	(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
accuracy	0.2109375	(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
accuracy	0.3359375	(.f64 (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) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
accuracy	0.9889450195368841	(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) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))

Samples

205.0ms	159×	1	valid
59.0ms	96×	0	valid
5.0ms	1×	5	exit

Compiler

Compiled 625 to 56 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-mult: 53.0ms (22.6% of total)

ival-cos: 50.0ms (21.4% of total)

ival-add: 37.0ms (15.8% of total)

adjust: 35.0ms (14.9% of total)

ival-div: 21.0ms (9% of total)

ival-sin: 10.0ms (4.3% of total)

ival-tan: 9.0ms (3.8% of total)

ival-pow2: 8.0ms (3.4% of total)

const: 7.0ms (3% of total)

ival-sub: 4.0ms (1.7% of total)

exact: 1.0ms (0.4% of total)

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

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

series83.0ms (0.7%)

Memory

-27.3MiB live, 129.1MiB allocated; 28ms collecting garbage

Counts

25 → 138

Calls

Call 1

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

Outputs
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 -1/2))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* -5/6 (pow x 2))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 1/3))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 -1))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* -1 (pow x 2)) 1)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (+ eps x)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (* 1/3 eps)))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 x))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow (sin x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	eps	@	-inf	((+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (/ x eps) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (cos x))
12.0ms	x	@	-inf	((+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (/ x eps) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (cos x))
9.0ms	x	@	0	((+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (/ x eps) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (cos x))
7.0ms	eps	@	0	((+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (/ x eps) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (cos x))
7.0ms	x	@	inf	((+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (/ x eps) eps) eps) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (* (pow (sin x) 2) 1/6) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (cos x))

simplify216.0ms (1.8%)

Memory

-2.8MiB live, 181.6MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	628	4009
1	1661	3724
2	5966	3528
0	8204	3378

Stop Event

1×	iter limit
1×	node limit

Counts

138 → 138

Calls

Call 1

Inputs
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 -1/2))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* -5/6 (pow x 2))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 1/3))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 -1))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* -1 (pow x 2)) 1)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (+ eps x)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (* 1/3 eps)))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)))
#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 x))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow (sin x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))

Outputs
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 -1/2))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(literal -1/2 binary64))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (fma.f64 (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (fma.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -248/135 binary64) (.f64 x x)) #s(literal 17/9 binary64)) x) x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* -5/6 (pow x 2))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (.f64 #s(literal -5/6 binary64) (.f64 x x)))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (.f64 (.f64 (-.f64 (.f64 #s(literal -13/18 binary64) (.f64 x x)) #s(literal 5/6 binary64)) x) x))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -10/27 binary64) (.f64 x x)) #s(literal 13/18 binary64)) x) x) #s(literal 5/6 binary64)) (.f64 x x)))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))))
#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -373/1890 binary64) (.f64 x x)) #s(literal 10/27 binary64)) x) x) #s(literal 13/18 binary64)) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x)))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 1/3))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(literal 1/3 binary64))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
#s(approx (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))))
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#s(approx (+ eps x) eps)
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#s(approx (+ eps x) (+.f64 eps x))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) x)
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#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
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#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (/ x eps) eps) eps) eps)
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#s(approx (+ (* (/ x eps) eps) eps) (+.f64 eps x))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (+ eps x) x) eps)
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#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
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#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) eps)
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#s(approx (+ eps x) (+.f64 eps x))
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#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (sin x) 2) 1/6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))))
#s(approx (* (pow (sin x) 2) 1/6) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x) x))
#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))))
#s(approx (* (pow (sin x) 2) 1/6) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/135 binary64) (.f64 x x)) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) x))
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#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
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#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
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#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) (cos.f64 eps))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) #s(literal -1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
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#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) #s(hole binary64 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))))
#s(approx (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
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#s(approx (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
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#s(approx (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) #s(hole binary64 (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
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#s(approx (tan (+ x eps)) (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ eps x) x)
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ eps x) (fma.f64 (/.f64 eps x) x x))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan x) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 x))
#s(approx (+ (* (/ x eps) eps) eps) x)
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (/ x eps) eps) eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ eps x) (fma.f64 (/.f64 eps x) x x))
#s(approx (* (+ (* (+ (* (+ (* (sin x) (/ (sin x) (pow (cos x) 2))) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) #s(hole binary64 (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))))
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#s(approx (* (pow (sin x) 2) 1/6) #s(hole binary64 (* 1/6 (pow (sin x) 2))))
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#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 eps x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (tan (+ x eps)) (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
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#s(approx (+ eps x) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
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#s(approx (cos (+ eps x)) (cos.f64 (+.f64 eps x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps))
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#s(approx (tan (+ x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
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#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (sin eps) (cos eps)) eps)
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
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#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) (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))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
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#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (cos eps) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) eps)
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/2 binary64))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) (cos.f64 x))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (cos (+ eps 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)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ eps x) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin eps) (cos eps)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (/ x eps) eps) eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ eps x) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (tan (+ x eps)) (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (+ (* (/ x eps) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (/ x eps) eps) eps) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 eps x)))

rewrite114.0ms (0.9%)

Memory

-2.8MiB live, 185.7MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	296
0	84	290
1	330	248
0	2766	242

Stop Event

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

Counts

25 → 277

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
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(/.f64 (*.f64 eps (-.f64 (pow.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) #s(literal 1/36 binary64))) (-.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) #s(literal -1/6 binary64)))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) #s(literal 3 binary64)) #s(literal -1 binary64) #s(literal -1/216 binary64))) (fma.f64 #s(literal -1/6 binary64) (-.f64 #s(literal -1/6 binary64) (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) eps (*.f64 #s(literal -1/6 binary64) eps))
(fma.f64 eps (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) (*.f64 eps #s(literal -1/6 binary64)))
(fma.f64 eps #s(literal -1/6 binary64) (*.f64 eps (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) eps))
(+.f64 (.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) eps) (.f64 #s(literal -1/6 binary64) eps))
(+.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) eps))
(+.f64 (.f64 eps (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))) (.f64 eps #s(literal -1/6 binary64)))
(+.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 eps (neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))))
(.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (sin.f64 x))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) #s(literal 1/6 binary64)))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal -2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) x)) (sin.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 eps x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps x))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 eps x)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 eps x)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) (neg.f64 x))) (cos.f64 (-.f64 (+.f64 eps x) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (+.f64 eps x)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 eps x))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (+.f64 eps x)))) (cos.f64 (-.f64 x (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 2 binary64))
(+.f64 (/.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal -1 binary64)))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))

eval92.0ms (0.7%)

Memory: 7.2MiB live, 196.5MiB allocated; 19ms collecting garbage
Compiler: Compiled 28 501 to 2 911 computations (89.8% saved)

prune14.0ms (0.1%)

Memory

-8.5MiB live, 38.2MiB allocated; 3ms collecting garbage

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	475	9	484
Fresh	5	0	5
Picked	5	0	5
Done	0	1	1
Total	485	10	495

Accuracy

100.0%

Counts

495 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
▶	100.0%	(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.6%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	100.0%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) eps) (cos.f64 eps)))
▶	3.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))

Compiler

Compiled 303 to 218 computations (28.1% saved)

simplify195.0ms (1.6%)

Memory

44.9MiB live, 179.6MiB allocated; 59ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (+.f64 #s(literal 0 binary64) eps))
cost-diff	0	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
cost-diff	2	(+.f64 #s(literal 0 binary64) eps)
cost-diff	0	(cos.f64 x)
cost-diff	0	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
cost-diff	0	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
cost-diff	0	(PI.f64)
cost-diff	0	(+.f64 eps (PI.f64))
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
cost-diff	2	(tan.f64 (+.f64 eps (PI.f64)))
cost-diff	0	#s(approx (/ (sin eps) (cos eps)) eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	#s(approx (- (+ eps x) x) eps)
cost-diff	0	(sin.f64 #s(approx (- (+ eps x) x) eps))
cost-diff	0	(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	167
0	53	155
1	91	139
2	170	139
3	389	139
4	1645	139
5	6851	139
0	8066	139

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 #s(approx (- (+ eps x) x) eps))
#s(approx (- (+ eps x) x) 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)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin eps) (cos eps)) eps)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(tan.f64 (+.f64 eps (PI.f64)))
(+.f64 eps (PI.f64))
eps
(PI.f64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
eps
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
x
#s(literal 2 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
(cos.f64 x)
x
(cos.f64 (+.f64 eps x))
(+.f64 eps x)

Outputs
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(sin.f64 #s(approx (- (+ eps x) x) eps))
#s(approx (- (+ eps x) x) 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)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin eps) (cos eps)) eps)
eps
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 (+.f64 eps (PI.f64)))
(tan.f64 eps)
(+.f64 eps (PI.f64))
(+.f64 (PI.f64) eps)
eps
(PI.f64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
eps
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
x
#s(literal 2 binary64)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(sin.f64 eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
(cos.f64 x)
x
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)

localize527.0ms (4.3%)

Memory

-25.1MiB live, 547.0MiB allocated; 96ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.0078125	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
accuracy	0.0078125	(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
accuracy	0.0	(cos.f64 x)
accuracy	0.0078125	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.015625	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.2327861238982686	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.0	(PI.f64)
accuracy	0.00390625	(+.f64 eps (PI.f64))
accuracy	1.0258092658713123	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
accuracy	61.707756797920034	(tan.f64 (+.f64 eps (PI.f64)))
accuracy	0.01970466452874396	#s(approx (/ (sin eps) (cos eps)) eps)
accuracy	1.0258092658713123	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.0	#s(approx (- (+ eps x) x) eps)
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

Samples

362.0ms	106×	2	valid
131.0ms	150×	1	valid

Compiler

Compiled 141 to 29 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 458.0ms

ival-tan: 370.0ms (80.8% of total)

adjust: 37.0ms (8.1% of total)

ival-div: 13.0ms (2.8% of total)

ival-add: 9.0ms (2% of total)

ival-cos: 7.0ms (1.5% of total)

ival-sin: 6.0ms (1.3% of total)

ival-pow2: 5.0ms (1.1% of total)

ival-sub: 4.0ms (0.9% of total)

ival-mult: 3.0ms (0.7% of total)

ival-pi: 2.0ms (0.4% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory

26.3MiB live, 26.3MiB allocated; 0ms collecting garbage

Counts

19 → 110

Calls

Call 1

Inputs
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 #s(approx (- (+ eps x) x) eps))
#s(approx (- (+ eps x) x) eps)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin eps) (cos eps)) eps)
(tan.f64 (+.f64 eps (PI.f64)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(+.f64 eps (PI.f64))
(PI.f64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(cos.f64 (+.f64 eps x))

Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ (sin eps) (cos x))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (PI)) (cos (PI)))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (+ eps (PI)) #s(hole binary64 (PI)))
#s(approx (+ eps (PI)) #s(hole binary64 (+ eps (PI))))
#s(approx (+ 0 eps) #s(hole binary64 eps))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole 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))))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ eps (cos x))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 eps))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (+ eps (PI)) #s(hole binary64 eps))
#s(approx (+ eps (PI)) #s(hole binary64 (* eps (+ 1 (/ (PI) eps)))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))))
#s(approx (+ eps (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ (sin (neg (* -1 eps))) (cos x))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (tan (+ eps (PI))) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (cos (+ eps x)))
4.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (tan (+ eps (PI))) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (cos (+ eps x)))
3.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (tan (+ eps (PI))) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (cos (+ eps x)))
3.0ms	x	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (tan (+ eps (PI))) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (cos (+ eps x)))
2.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (* (cos (+ eps x)) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (tan (+ eps (PI))) (- (tan (+ x eps)) (tan x)) (+ eps (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (cos x) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) (/ (sin (+ 0 eps)) (cos x)) (sin (+ 0 eps)) (cos (+ eps x)))

simplify160.0ms (1.3%)

Memory

19.7MiB live, 151.7MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	547	2828
1	1618	2575
2	6763	2506
0	8149	2401

Stop Event

1×	iter limit
1×	node limit

Counts

110 → 110

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ (sin eps) (cos x))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* 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)))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (PI)) (cos (PI)))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (+ eps (PI)) #s(hole binary64 (PI)))
#s(approx (+ eps (PI)) #s(hole binary64 (+ eps (PI))))
#s(approx (+ 0 eps) #s(hole binary64 eps))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole 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))))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ eps (cos x))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 eps))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (+ eps (PI)) #s(hole binary64 eps))
#s(approx (+ eps (PI)) #s(hole binary64 (* eps (+ 1 (/ (PI) eps)))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))))
#s(approx (+ eps (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ (sin (neg (* -1 eps))) (cos x))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))

Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.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))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.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))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) 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))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (- (+ eps x) x) eps)
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (sin.f64 eps) x) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) (cos.f64 eps)) x (/.f64 (sin.f64 eps) (cos.f64 eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* 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)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (.f64 (neg.f64 x) (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) 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))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) eps)
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(literal 1 binary64))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.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))))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.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))) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) 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))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (sin.f64 eps))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal -5/24 binary64) (sin.f64 eps)) (.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (.f64 x x) (sin.f64 eps)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (fma.f64 (sin.f64 eps) #s(literal 7/360 binary64) (.f64 (sin.f64 eps) #s(literal -5/48 binary64)))) (.f64 #s(literal -5/24 binary64) (sin.f64 eps))) (.f64 x x) (.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) (cos.f64 eps))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
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#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 eps) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ eps (cos x))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) (cos.f64 x)))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)) (/.f64 eps (cos.f64 x))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x))))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (cos.f64 x)) (.f64 eps eps) (/.f64 #s(literal -1/6 binary64) (cos.f64 x))) (/.f64 eps (cos.f64 x))))
#s(approx (sin (+ 0 eps)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) eps)
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) (cos.f64 x))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (cos (+ eps 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)))
#s(approx (/ (sin eps) (cos eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin eps) (cos eps)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ eps (PI))) (/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps))))
#s(approx (+ eps (PI)) #s(hole binary64 eps))
#s(approx (+ eps (PI)) eps)
#s(approx (+ eps (PI)) #s(hole binary64 (* eps (+ 1 (/ (PI) eps)))))
#s(approx (+ eps (PI)) (fma.f64 (/.f64 (PI.f64) eps) eps eps))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))))
#s(approx (tan (+ eps (PI))) #s(hole binary64 (/ (sin (- (PI) (* -1 eps))) (cos (- (PI) (* -1 eps))))))
#s(approx (tan (+ eps (PI))) (/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps))))
#s(approx (+ eps (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))))
#s(approx (+ eps (PI)) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 eps)))
#s(approx (/ (/ (sin (+ 0 eps)) (cos x)) (cos (+ eps x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) #s(hole binary64 (/ (sin (neg (* -1 eps))) (cos x))))
#s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 (sin.f64 eps) (cos.f64 x)))
#s(approx (sin (+ 0 eps)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))

rewrite89.0ms (0.7%)

Memory

-54.1MiB live, 67.2MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	143
0	53	125
1	228	103
0	2010	103

Stop Event

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

Counts

19 → 165

Calls

Call 1

Inputs
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 #s(approx (- (+ eps x) x) eps))
#s(approx (- (+ eps x) x) eps)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin eps) (cos eps)) eps)
(tan.f64 (+.f64 eps (PI.f64)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(+.f64 eps (PI.f64))
(PI.f64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x))
(sin.f64 (+.f64 #s(literal 0 binary64) eps))
(cos.f64 (+.f64 eps x))

Outputs
(*.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))
(/.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 (sin.f64 #s(approx (- (+ eps x) x) eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 #s(approx (- (+ eps x) x) eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(sin.f64 #s(approx (- (+ eps x) x) eps))
#s(approx (- (+ eps x) x) eps)
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal -2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) x)) (sin.f64 (+.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 x (neg.f64 (+.f64 x eps))))) #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 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) (neg.f64 x))) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps)) #s(literal 2 binary64))
(+.f64 (/.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) #s(literal 2 binary64)) (/.f64 (cos.f64 eps) #s(literal 2 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin eps) (cos eps)) eps)
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (tan.f64 eps))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (neg.f64 (cos.f64 eps))))
(/.f64 (+.f64 (tan.f64 #s(literal 0 binary64)) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 #s(literal 0 binary64)) (tan.f64 eps))))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 #s(literal 0 binary64)))))
(/.f64 (sin.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64))) (cos.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64))))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 eps))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(neg.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)))
(neg.f64 (/.f64 (sin.f64 eps) (neg.f64 (cos.f64 eps))))
(tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) eps))
(tan.f64 eps)
(+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 eps)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 eps)))))
(+.f64 (/.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 eps)) (/.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(/.f64 (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 eps eps)) (-.f64 (PI.f64) eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (.f64 eps eps) (.f64 (PI.f64) eps))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 (PI.f64) eps) (-.f64 eps (PI.f64)))) (neg.f64 (-.f64 eps (PI.f64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (*.f64 eps eps))))
(/.f64 (*.f64 (+.f64 (PI.f64) eps) (-.f64 eps (PI.f64))) (-.f64 eps (PI.f64)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (PI.f64))) (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 eps (PI.f64))))
(-.f64 eps (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(-.f64 eps (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))
(+.f64 (+.f64 (PI.f64) #s(literal 0 binary64)) eps)
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (.f64 eps eps))) (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) eps) (.f64 eps eps))))
(+.f64 #s(literal 0 binary64) (+.f64 (PI.f64) eps))
(+.f64 (+.f64 (PI.f64) eps) #s(literal 0 binary64))
(+.f64 (PI.f64) eps)
(+.f64 eps (+.f64 #s(literal 0 binary64) (PI.f64)))
(+.f64 eps (PI.f64))
(PI.f64)
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (/.f64 eps (cos.f64 x)) (cos.f64 x))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 (.f64 eps (neg.f64 eps)) (.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (.f64 eps eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 eps (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (fabs.f64 (cos.f64 x)) (fabs.f64 (cos.f64 x)))
(*.f64 (exp.f64 (log.f64 (cos.f64 x))) (exp.f64 (log.f64 (cos.f64 x))))
(*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) (cos.f64 x))
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 2 binary64))
(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 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) x)) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) x)) (cos.f64 (-.f64 (neg.f64 x) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 x))) (cos.f64 (-.f64 x (neg.f64 x)))) #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 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (neg.f64 x)) (sin.f64 (neg.f64 x))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 x) (sin.f64 x)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
(+.f64 (cosh.f64 (.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
eps
(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))) (sin.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (fma.f64 (tan.f64 x) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (/.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 eps) (cos.f64 x))
(neg.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(+.f64 (/.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 x)) (/.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x))) (.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))))) (fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 0 binary64) (cos.f64 eps))) (.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps)))) (-.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps))) (.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps))))))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (sin.f64 eps) (*.f64 #s(literal 0 binary64) (cos.f64 eps)))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (cos.f64 eps)))
(fma.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(sin.f64 eps)
(-.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal -1 binary64) (sin.f64 eps)))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) (.f64 #s(literal 0 binary64) (cos.f64 eps)))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.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))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps))))
(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))

eval49.0ms (0.4%)

Memory: -1.1MiB live, 44.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 7 277 to 1 156 computations (84.1% saved)

prune12.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated; 0ms collecting garbage

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	285	10	295
Fresh	3	1	4
Picked	3	2	5
Done	0	1	1
Total	291	14	305

Accuracy

100.0%

Counts

305 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	100.0%	(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
	99.9%	(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))
▶	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	62.0%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	99.6%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶	99.6%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
▶	99.2%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	99.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
	99.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
▶	99.0%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
▶	98.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))

Compiler

Compiled 675 to 419 computations (37.9% saved)

simplify238.0ms (1.9%)

Memory

5.1MiB live, 146.8MiB allocated; 16ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	376
0	75	376
1	141	364
2	368	352
3	1304	352
4	5225	352
0	8113	345

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (1.9%)

Memory

-2.9MiB live, 228.5MiB allocated; 32ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0.0078125	(/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))
accuracy	0.021816259768442016	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
accuracy	0.2327861238982686	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
accuracy	0.0078125	(/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.0234375	(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.2327861238982686	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.35069341987624036	#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(neg.f64 x)
accuracy	0.07421875	(.f64 (.f64 (neg.f64 x) x) eps)
accuracy	0.2327861238982686	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
accuracy	0.4626842411576406	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps))
accuracy	0.0	(fma.f64 (*.f64 x x) eps eps)
accuracy	0.0	(*.f64 x x)
accuracy	0.2327861238982686	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
accuracy	0.6598863195773781	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.01171875	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.01596665172363414	#s(approx (sin (- (+ eps x) x)) eps)

Samples

155.0ms	147×	1	valid
35.0ms	109×	0	valid

Compiler

Compiled 257 to 41 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-add: 54.0ms (33% of total)

ival-mult: 50.0ms (30.5% of total)

adjust: 18.0ms (11% of total)

const: 17.0ms (10.4% of total)

ival-cos: 8.0ms (4.9% of total)

ival-div: 7.0ms (4.3% of total)

ival-pow2: 4.0ms (2.4% of total)

ival-sin: 3.0ms (1.8% of total)

ival-sub: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series28.0ms (0.2%)

Memory

26.0MiB live, 71.9MiB allocated; 5ms collecting garbage

Counts

24 → 105

Calls

Call 1

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

Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (+ eps (* 2/3 (* eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 eps))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* (neg x) x) eps) #s(hole binary64 (* -1 (* eps (pow x 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* 2/3 (* eps (pow x 2)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* 2/3 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* -2/45 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (+ 1 (pow x 2)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* eps (+ 1 (* 2/3 (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* -1 (* eps (- (* -2/3 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (+ (* (* (* (neg x) x) eps) -2/3) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (* 2 x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/2 (cos (* 2 x))) (cos x) (* (* (neg x) x) eps) (neg x) (cos (* 2 x)))
4.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (+ (* (* (* (neg x) x) eps) -2/3) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (* 2 x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/2 (cos (* 2 x))) (cos x) (* (* (neg x) x) eps) (neg x) (cos (* 2 x)))
4.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (+ (* (* (* (neg x) x) eps) -2/3) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (* 2 x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/2 (cos (* 2 x))) (cos x) (* (* (neg x) x) eps) (neg x) (cos (* 2 x)))
4.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (+ (* (* (* (neg x) x) eps) -2/3) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (* 2 x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/2 (cos (* 2 x))) (cos x) (* (* (neg x) x) eps) (neg x) (cos (* 2 x)))
4.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (+ (* (* (* (neg x) x) eps) -2/3) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (* 2 x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (* 1/2 (cos (* 2 x))) (cos x) (* (* (neg x) x) eps) (neg x) (cos (* 2 x)))

simplify190.0ms (1.6%)

Memory

-23.5MiB live, 165.6MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	431	2261
1	1168	2180
2	4223	2136
0	8720	1981

Stop Event

1×	iter limit
1×	node limit

Counts

105 → 105

Calls

Call 1

Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (+ eps (* 2/3 (* eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 eps))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* (neg x) x) eps) #s(hole binary64 (* -1 (* eps (pow x 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* 2/3 (* eps (pow x 2)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* 2/3 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* -2/45 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (+ 1 (pow x 2)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* eps (+ 1 (* 2/3 (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* -1 (* eps (- (* -2/3 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))))

Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) x) (cos.f64 eps)) (sin.f64 eps)) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (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))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* 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)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps)) (sin.f64 eps) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (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))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (cos.f64 eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) (cos.f64 eps))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 eps)) x) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64))) x) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) eps)
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)) eps eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (* x x) eps) eps) eps)
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* (* x x) eps) eps) (fma.f64 (*.f64 x x) eps eps))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) eps)
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (+ eps (* 2/3 (* eps (pow x 2))))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) eps)
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (fma.f64 (*.f64 x x) eps eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)) eps eps))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(literal 1 binary64))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -2/45 binary64) #s(literal -1 binary64))) (.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -2/45 binary64) #s(literal -1 binary64))) (.f64 x x) #s(literal 1 binary64)))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(literal 1 binary64))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -2/45 binary64) #s(literal -1 binary64))) (.f64 x x) #s(literal 1 binary64)))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 eps))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) eps)
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (fma.f64 (*.f64 x x) eps eps))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)) eps eps))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) (fma.f64 (neg.f64 x) x #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -2/45 binary64) #s(literal -1 binary64))) (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (* (* (neg x) x) eps) #s(hole binary64 (* -1 (* eps (pow x 2)))))
#s(approx (* (* (neg x) x) eps) (.f64 (.f64 (neg.f64 x) x) eps))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (neg x) (neg.f64 x))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(literal 1 binary64))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) (fma.f64 (fma.f64 #s(literal 2/3 binary64) (.f64 x x) #s(literal -2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (cos (* 2 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -4/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (+ eps x)))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (+ eps x))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ eps (pow (cos x) 2)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* (pow x 2) (+ eps (/ eps (pow x 2))))))
#s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 (+.f64 (/.f64 eps (*.f64 x x)) eps) x) x))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* 2/3 (* eps (pow x 2)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) eps)))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* (pow x 2) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 (.f64 (fma.f64 #s(literal 2/3 binary64) eps (/.f64 eps (*.f64 x x))) x) x))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* 2/3 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64)) eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 2/3 binary64) eps (/.f64 eps (.f64 x x)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* (pow x 4) (+ (* 2/3 eps) (+ (/ eps (pow x 2)) (/ eps (pow x 4)))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (.f64 (fma.f64 #s(literal 2/3 binary64) eps (+.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (/.f64 eps (.f64 x x)))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (pow (cos x) 2) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* -2/45 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -2/45 binary64)))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) 2/45))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 2/45 binary64)) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/3 (/ 1 (pow x 2))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 2/45 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/3 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 2/45 (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* (+ (* -2/45 (* x x)) 1/3) (* x x)) -1) (* x x)) 1) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/45 binary64))) (pow.f64 x #s(literal 6 binary64))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))))
#s(approx (/ eps (+ 1/2 (* 1/2 (cos (* 2 x))))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (* 1/2 (cos (* 2 x))) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (cos (* 2 x)) (cos.f64 (*.f64 #s(literal -2 binary64) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- eps (* -1 x))))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (fma.f64 (.f64 eps eps) (fma.f64 (fma.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (cos.f64 x))) (sin.f64 x) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 eps) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 eps))
#s(approx (sin (- (+ eps x) x)) eps)
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin (- (+ eps x) x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (- (+ eps x) x)) (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))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (*.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (sin.f64 x) (cos.f64 x)))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole 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))))
#s(approx (* (cos (+ eps x)) (cos x)) (fma.f64 (fma.f64 (neg.f64 (cos.f64 x)) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)) (sin.f64 x) (.f64 #s(literal -1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos x)))
#s(approx (cos (+ eps x)) (cos.f64 x))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (cos (+ eps 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)))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* eps (+ 1 (pow x 2)))))
#s(approx (+ (* (* x x) eps) eps) (fma.f64 (*.f64 x x) eps eps))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* eps (+ 1 (* 2/3 (pow x 2))))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/3 binary64) (*.f64 x x)) eps eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ eps x)) (cos.f64 (+.f64 x eps)))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (* (* x x) eps) eps) (fma.f64 (*.f64 x x) eps eps))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) #s(hole binary64 (* -1 (* eps (- (* -2/3 (pow x 2)) 1)))))
#s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)))))
#s(approx (+ (* (+ (* (* (* (neg x) x) eps) -2/3) eps) (* x x)) eps) (.f64 (fma.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal -1 binary64)) (neg.f64 eps)))

rewrite91.0ms (0.7%)

Memory

-2.3MiB live, 58.8MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	326
0	75	314
1	281	302
0	2134	302

Stop Event

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

Counts

24 → 247

Calls

Call 1

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

Outputs
(*.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) eps))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
#s(approx (sin (- (+ eps x) x)) eps)
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(/.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 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 x) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 x (neg.f64 (+.f64 x eps))))) #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 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (+.f64 x eps)) x)) (cos.f64 (-.f64 (neg.f64 (+.f64 x eps)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 x eps) (neg.f64 x))) (cos.f64 (-.f64 (+.f64 x eps) (neg.f64 x)))) #s(literal 2 binary64))
(/.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)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.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))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps))))
(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)
(*.f64 eps (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64))) (-.f64 eps (.f64 (*.f64 x x) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (-.f64 (.f64 (*.f64 x x) eps) eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 x x) eps)) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps eps)) (-.f64 (.f64 (*.f64 x x) eps) eps))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 x x) eps) eps))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps (.f64 (.f64 x x) eps)) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64))))
(fma.f64 (*.f64 eps (fabs.f64 x)) (fabs.f64 x) eps)
(fma.f64 (*.f64 eps (neg.f64 x)) (neg.f64 x) eps)
(fma.f64 (*.f64 x eps) x eps)
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) eps) eps)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) eps) eps)
(fma.f64 (*.f64 x x) eps eps)
(fma.f64 x (*.f64 x eps) eps)
(fma.f64 eps (*.f64 x x) eps)
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) eps) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 x x) eps) eps)))
(-.f64 eps (.f64 (neg.f64 eps) (.f64 x x)))
(-.f64 eps (.f64 (.f64 (neg.f64 x) x) eps))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (.f64 (.f64 x x) eps)) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (.f64 (.f64 x x) eps)) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 x x) eps) eps)
(+.f64 eps (.f64 (.f64 x x) eps))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)))) (-.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 (neg.f64 eps) eps))) (neg.f64 (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)) eps)))
(/.f64 (neg.f64 (fma.f64 #s(literal -8/27 binary64) (pow.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)))))))
(/.f64 (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 (neg.f64 eps) eps)) (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)) eps))
(/.f64 (fma.f64 #s(literal -8/27 binary64) (pow.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64))) (.f64 (.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps)) eps))))
(/.f64 (fma.f64 #s(literal -8/27 binary64) (pow.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps))))))
(fma.f64 (.f64 #s(literal -2/3 binary64) (.f64 (neg.f64 x) x)) eps eps)
(fma.f64 (.f64 #s(literal -2/3 binary64) (neg.f64 x)) (.f64 x eps) eps)
(fma.f64 (.f64 #s(literal -2/3 binary64) eps) (.f64 (neg.f64 x) x) eps)
(fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps)
(fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps)
(fma.f64 (.f64 (neg.f64 x) x) (.f64 #s(literal -2/3 binary64) eps) eps)
(fma.f64 (neg.f64 x) (.f64 (.f64 x eps) #s(literal -2/3 binary64)) eps)
(fma.f64 (neg.f64 x) (.f64 x (.f64 #s(literal -2/3 binary64) eps)) eps)
(fma.f64 x (.f64 (neg.f64 x) (.f64 #s(literal -2/3 binary64) eps)) eps)
(fma.f64 eps (.f64 (.f64 (neg.f64 x) x) #s(literal -2/3 binary64)) eps)
(-.f64 (/.f64 (.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)) eps)))
(-.f64 eps (.f64 (.f64 x x) (*.f64 #s(literal -2/3 binary64) eps)))
(-.f64 eps (.f64 #s(literal 2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps)))
(-.f64 eps (.f64 (neg.f64 (.f64 (*.f64 (neg.f64 x) x) eps)) #s(literal -2/3 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)) #s(literal 3 binary64)) (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps)))))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 4/9 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 2 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps)))))))
(+.f64 (.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps)) eps)
(+.f64 eps (.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) (*.f64 x x) eps)))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) (*.f64 x x) eps))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64))) (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps) eps) x) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps) eps) x) x) eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64)) (.f64 eps eps)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (*.f64 (neg.f64 x) x) eps) eps) x) x) eps))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) (*.f64 x eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x)) (pow.f64 (.f64 (.f64 (fma.f64 #s(literal -2/3 binary64) (.f64 (.f64 (neg.f64 x) x) eps) eps) x) x) #s(literal 2 binary64))))
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(+.f64 (cosh.f64 (.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 eps (.f64 (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 2 binary64)))
(.f64 (/.f64 eps (fma.f64 (pow.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 eps (cos.f64 x)) (cos.f64 x))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 eps) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 eps (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal -2 binary64) x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(.f64 (.f64 eps (neg.f64 x)) x)
(.f64 (.f64 x eps) (neg.f64 x))
(.f64 (.f64 (neg.f64 x) x) eps)
(.f64 (neg.f64 x) (.f64 x eps))
(.f64 x (.f64 (neg.f64 x) eps))
(.f64 eps (.f64 (neg.f64 x) x))
(neg.f64 (.f64 (.f64 x x) eps))
(neg.f64 x)
(*.f64 (+.f64 (cos.f64 x) (sin.f64 x)) (-.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (-.f64 (.f64 (pow.f64 (cos.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 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (cos.f64 x) (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))))
(fma.f64 (+.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(fma.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(fma.f64 (fabs.f64 (cos.f64 x)) (fabs.f64 (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(fma.f64 (exp.f64 (log.f64 (cos.f64 x))) (exp.f64 (log.f64 (cos.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(fma.f64 (sin.f64 (.f64 #s(literal 2 binary64) x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) (-.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(fma.f64 (cos.f64 x) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(sin.f64 (fma.f64 #s(literal -2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (*.f64 #s(literal -2 binary64) x)))
(cos.f64 (*.f64 #s(literal -2 binary64) x))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 2 binary64) x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(+.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))

eval47.0ms (0.4%)

Memory: 13.5MiB live, 59.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 14 434 to 1 870 computations (87% saved)

prune22.0ms (0.2%)

Memory

-5.2MiB live, 40.8MiB allocated; 4ms collecting garbage

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	387	10	397
Fresh	4	2	6
Picked	2	3	5
Done	1	2	3
Total	394	17	411

Accuracy

100.0%

Counts

411 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
	99.4%	(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
✓	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.4%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	99.1%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
	99.6%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
✓	99.6%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	99.2%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	99.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
	99.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
✓	98.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
	99.0%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)) (*.f64 x x) eps)))
	98.4%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) eps))) (.f64 x x) eps)))
	6.4%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
✓	98.4%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))

Compiler

Compiled 1 483 to 526 computations (64.5% saved)

regimes33.0ms (0.3%)

Memory

-6.7MiB live, 39.0MiB allocated; 4ms collecting garbage

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) eps))) (.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 #s(approx (+ x eps) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) eps) (PI.f64)) (PI.f64))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(-.f64 (tan.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (tan.f64 x))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 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 #s(literal 0 binary64) eps)) (cos.f64 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))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (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) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))

Outputs

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

Calls

3 calls:

12.0ms	eps
9.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes57.0ms (0.5%)

Memory

-20.2MiB live, 30.0MiB allocated; 8ms collecting garbage

Counts

39 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) eps))) (.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 #s(approx (+ x eps) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) eps) (PI.f64)) (PI.f64))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(-.f64 (tan.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (tan.f64 x))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 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 #s(literal 0 binary64) eps)) (cos.f64 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))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (.f64 (/.f64 (+.f64 (/.f64 (.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))

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

Calls

3 calls:

38.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory

21.1MiB live, 21.1MiB allocated; 0ms collecting garbage

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) eps))) (.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 #s(approx (+ x eps) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) eps) (PI.f64)) (PI.f64))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))) (tan.f64 x))
(/.f64 #s(approx (/ (sin (+ 0 eps)) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) eps) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(-.f64 (tan.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (tan.f64 x))
(/.f64 (sin.f64 #s(approx (- (+ eps x) x) eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-22.7MiB live, 23.2MiB allocated; 3ms collecting garbage

Counts

25 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (.f64 (.f64 x x) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) eps))) (.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (.f64 x x) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) x) eps) #s(literal -2/3 binary64) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 17/45 binary64)) (.f64 x x) (.f64 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 x) x) (.f64 eps #s(literal -17/45 binary64)) (.f64 (neg.f64 eps) #s(literal -2/3 binary64))) (.f64 x x) eps) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (tan.f64 #s(approx (+ x eps) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) eps) (PI.f64)) (PI.f64))) (tan.f64 x))

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

Calls

3 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

33.1MiB live, 33.1MiB allocated; 0ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

-26.3MiB live, 18.3MiB allocated; 5ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

Calls

3 calls:

7.0ms	x
3.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

Outputs

#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 #s(approx (+ (* (* (* (neg x) x) eps) -2/3) eps) (fma.f64 (*.f64 #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))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

-28.0MiB live, 15.5MiB allocated; 6ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Accuracy

Total -58.9b remaining (-5740.2%)

Threshold costs -58.9b (-5740.2%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) eps))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify61.0ms (0.5%)

Memory

-17.0MiB live, 40.6MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	342
1	138	325
2	233	309
3	497	309
4	1435	309

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations538.0ms (4.4%)

Memory

-17.8MiB live, 376.7MiB allocated; 62ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 342 to 101 computations (70.5% saved)

preprocess57.0ms (0.5%)

Memory: 32.2MiB live, 78.5MiB allocated; 5ms collecting garbage
Compiler: Compiled 716 to 226 computations (68.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze131.0ms (1.1%)

sample6.8s (55.8%)

explain115.0ms (0.9%)

preprocess198.0ms (1.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify147.0ms (1.2%)

localize52.0ms (0.4%)

series18.0ms (0.1%)

simplify160.0ms (1.3%)

rewrite720.0ms (5.9%)

eval35.0ms (0.3%)

prune10.0ms (0.1%)

simplify236.0ms (1.9%)

localize315.0ms (2.6%)

series83.0ms (0.7%)

simplify216.0ms (1.8%)

rewrite114.0ms (0.9%)

eval92.0ms (0.7%)

prune14.0ms (0.1%)

simplify195.0ms (1.6%)

localize527.0ms (4.3%)

series27.0ms (0.2%)

simplify160.0ms (1.3%)

rewrite89.0ms (0.7%)

eval49.0ms (0.4%)

prune12.0ms (0.1%)

simplify238.0ms (1.9%)

localize235.0ms (1.9%)

series28.0ms (0.2%)

simplify190.0ms (1.6%)

rewrite91.0ms (0.7%)

eval47.0ms (0.4%)

prune22.0ms (0.2%)

regimes33.0ms (0.3%)

regimes57.0ms (0.5%)

regimes23.0ms (0.2%)

regimes21.0ms (0.2%)

regimes13.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes11.0ms (0.1%)

regimes4.0ms (0%)

simplify61.0ms (0.5%)

derivations538.0ms (4.4%)

preprocess57.0ms (0.5%)

end0.0ms (0%)

Profiling