Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

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

analyze49.0ms (0.4%)

Memory

21.5MiB live, 66.0MiB allocated; 23ms 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)

sample6.9s (53.1%)

Memory

-169.5MiB live, 7 973.6MiB allocated; 2.7s collecting garbage

Samples

3.6s	26 314×	0	invalid
1.3s	5 111×	1	valid
427.0ms	3 145×	0	valid

Precisions

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

const: 716.0ms (18.3% of total)

ival-tan: 676.0ms (17.3% of total)

ival-fabs: 665.0ms (17% of total)

ival-mult: 367.0ms (9.4% of total)

adjust: 316.0ms (8.1% of total)

ival-<=: 272.0ms (6.9% of total)

ival-add: 269.0ms (6.9% of total)

ival-<: 247.0ms (6.3% of total)

ival-sub: 234.0ms (6% of total)

ival-and: 101.0ms (2.6% of total)

exact: 42.0ms (1.1% of total)

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

Bogosity

explain140.0ms (1.1%)

Memory

-0.2MiB live, 190.0MiB allocated; 32ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
226	2	(-2.149671592621115e-192 1.8925975972374645e-194)	6	(-7.931845447766479e-63 1.1558208663394699e-64)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
1	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	222	12
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	220	6
-	2	28

Precision

0.990990990990991

Recall

0.9734513274336283

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	220	6	0
-	2	6	22

Precision?

0.9658119658119658

Recall?

1.0

Freqs

test

number	freq
0	34
1	221
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms	322×	1	valid
9.0ms	188×	0	valid
6.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

adjust: 42.0ms (62.9% of total)

ival-tan: 17.0ms (25.5% of total)

ival-add: 4.0ms (6% of total)

ival-sub: 4.0ms (6% of total)

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

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

preprocess259.0ms (2%)

Memory

11.9MiB live, 247.5MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

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	654	43
7	1492	43
8	3439	43
9	4340	43
10	6665	43
11	7416	43
12	7872	43
0	6	7
0	10	7
1	16	7
2	25	7
3	41	7
4	66	7
5	117	7
6	211	7
7	474	7
8	1311	7
9	2274	7
10	3303	7
11	3588	7
12	3771	7
13	3850	7
14	3868	7
15	3874	7
16	3880	7
17	3886	7
18	3892	7
19	3898	7
20	3904	7
21	3910	7
22	3916	7
23	3922	7
24	3928	7
25	7779	7
0	8041	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

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify229.0ms (1.8%)

Memory

-25.3MiB live, 165.4MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	16	18
2	25	18
3	41	18
4	66	18
5	117	18
6	211	18
7	474	18
8	1311	18
9	2274	18
10	3303	18
11	3588	18
12	3771	18
13	3850	18
14	3868	18
15	3874	18
16	3880	18
17	3886	18
18	3892	18
19	3898	18
20	3904	18
21	3910	18
22	3916	18
23	3922	18
24	3928	18
25	7779	18
0	8041	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)

localize32.0ms (0.2%)

Memory

27.4MiB live, 27.4MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(tan.f64 x)
accuracy	0.038309980164287515	(tan.f64 (+.f64 x eps))
accuracy	24.72515387721605	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

20.0ms	161×	1	valid
4.0ms	94×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-tan: 7.0ms (40.7% of total)

adjust: 6.0ms (34.9% of total)

ival-add: 2.0ms (11.6% of total)

ival-sub: 2.0ms (11.6% of total)

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

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

series11.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

Counts

4 → 31

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

Calls

6 calls:

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

simplify175.0ms (1.3%)

Memory

-31.3MiB live, 297.5MiB allocated; 48ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	970
1	488	910
2	1845	849
0	8454	797

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

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

rewrite223.0ms (1.7%)

Memory

37.6MiB live, 221.0MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	440	16
3	6608	16
0	8588	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)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (/.f64 (-.f64 (.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)) (sin.f64 x))) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
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(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)))))

eval27.0ms (0.2%)

Memory: -8.9MiB live, 35.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 5 935 to 840 computations (85.8% saved)

prune10.0ms (0.1%)

Memory

21.6MiB live, 21.6MiB allocated; 0ms collecting garbage

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	172	11	183
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	12	184

Accuracy

100.0%

Counts

184 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.2%	(/.f64 (-.f64 (.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (tan.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (+.f64 #s(literal 0 binary64) (tan.f64 x)))) (.f64 (cos.f64 (+.f64 eps x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (tan.f64 x)))))
▶	61.3%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	61.4%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
	61.4%	(-.f64 (+.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (/.f64 (tan.f64 eps) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))) (tan.f64 x))
▶	51.0%	(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (tan.f64 x))
	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	60.7%	(-.f64 (tan.f64 #s(approx (+ x eps) (fma.f64 (/.f64 x eps) 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 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #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))
	99.8%	#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))
	99.3%	#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))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 573 to 306 computations (46.6% saved)

simplify235.0ms (1.8%)

Memory

-58.2MiB live, 302.1MiB allocated; 88ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(tan.f64 eps)
cost-diff	0	(+.f64 (tan.f64 eps) (tan.f64 x))
cost-diff	0	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(sin.f64 (-.f64 (+.f64 eps x) x))
cost-diff	0	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
cost-diff	4	(-.f64 (+.f64 eps x) x)
cost-diff	0	(/.f64 x (-.f64 x eps))
cost-diff	0	(tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))))
cost-diff	0	(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (tan.f64 x))
cost-diff	4	(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x 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	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 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #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 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #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	59	745
0	115	737
1	205	694
2	504	663
3	2071	590
0	8812	589

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

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

localize354.0ms (2.7%)

Memory

23.0MiB live, 256.7MiB allocated; 22ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(neg.f64 (tan.f64 x))
accuracy	0.0078125	(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))
accuracy	0.0078125	(+.f64 (tan.f64 eps) (tan.f64 x))
accuracy	24.7121775955954	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.01171875	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	24.75281217211249	(-.f64 (+.f64 eps x) x)
accuracy	0.234375	(/.f64 x (-.f64 x eps))
accuracy	0.23828125	(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
accuracy	24.7121775955954	(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (tan.f64 x))
accuracy	25.775073919250104	(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))
accuracy	0.0	(sin.f64 eps)
accuracy	0.0	(cos.f64 eps)
accuracy	0.0078125	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	1.204428561574053	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.1953125	(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	0.21484375	(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
accuracy	0.33984375	(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #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	0.9772262695368841	(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #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

218.0ms	169×	1	valid
37.0ms	85×	0	valid
18.0ms	2×	5	exit

Compiler

Compiled 712 to 69 computations (90.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-mult: 50.0ms (22.5% of total)

adjust: 46.0ms (20.7% of total)

ival-tan: 24.0ms (10.8% of total)

ival-div: 24.0ms (10.8% of total)

ival-add: 24.0ms (10.8% of total)

ival-pow2: 23.0ms (10.4% of total)

ival-sub: 8.0ms (3.6% of total)

ival-cos: 7.0ms (3.2% of total)

const: 6.0ms (2.7% of total)

ival-sin: 6.0ms (2.7% of total)

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

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

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

exact: 0.0ms (0% of total)

series83.0ms (0.6%)

Memory

15.9MiB live, 59.3MiB allocated; 9ms collecting garbage

Counts

26 → 160

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	x	@	-inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (pow (cos x) 2)) (sin x)) 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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps))) (- (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (tan x)) (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (/ x (- x eps)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (/ (* (neg eps) eps) (- x eps)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (neg (tan x)))
16.0ms	eps	@	0	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (pow (cos x) 2)) (sin x)) 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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps))) (- (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (tan x)) (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (/ x (- x eps)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (/ (* (neg eps) eps) (- x eps)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (neg (tan x)))
15.0ms	x	@	inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (pow (cos x) 2)) (sin x)) 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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps))) (- (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (tan x)) (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (/ x (- x eps)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (/ (* (neg eps) eps) (- x eps)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (neg (tan x)))
11.0ms	eps	@	-inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (pow (cos x) 2)) (sin x)) 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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps))) (- (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (tan x)) (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (/ x (- x eps)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (/ (* (neg eps) eps) (- x eps)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (neg (tan x)))
9.0ms	eps	@	inf	((+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (pow (cos x) 2)) (sin x)) 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)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps))) (- (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (tan x)) (tan (+ (* x (/ x (- x eps))) (/ (* (neg eps) eps) (- x eps)))) (/ x (- x eps)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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) (/ (* (neg eps) eps) (- x eps)) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (neg (tan x)))

simplify148.0ms (1.1%)

Memory

-4.1MiB live, 91.3MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	792	3690
1	2407	3440
0	8252	3291

Stop Event

1×	iter limit
1×	node limit

Counts

160 → 158

Calls

Call 1

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

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* -4/3 (pow x 2)) 1/2)
(-.f64 (.f64 (.f64 x x) #s(literal -4/3 binary64)) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(-.f64 (.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))
(* -5/6 (pow x 2))
(.f64 #s(literal -5/6 binary64) (.f64 x x))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(.f64 (.f64 (-.f64 (.f64 #s(literal -13/18 binary64) (.f64 x x)) #s(literal 5/6 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(.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))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
(.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))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 #s(literal 4/3 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -2/3 binary64) (.f64 x x)) #s(literal 1 binary64)) x) x) #s(literal 1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(-.f64 (.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -17/45 binary64) (.f64 x x)) #s(literal 2/3 binary64)) x) x) #s(literal 1 binary64)) (.f64 x x)) #s(literal 1 binary64))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (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))) (+.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)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (.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) (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)))
eps
(+ eps x)
(+.f64 eps x)
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (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))) (+.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)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (.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) (cos.f64 eps)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (/ x eps))
(/.f64 (neg.f64 x) eps)
(* x (- (* -1 (/ x (pow eps 2))) (/ 1 eps)))
(.f64 (-.f64 (/.f64 (neg.f64 x) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) eps)) x)
(* x (- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps)))
(.f64 (-.f64 (.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) x) (/.f64 #s(literal 1 binary64) eps)) x)
(* x (- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)))
(.f64 (-.f64 (.f64 (-.f64 (*.f64 (-.f64 (/.f64 (neg.f64 x) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) x) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) x) (/.f64 #s(literal 1 binary64) eps)) x)
(+ (* 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)))
(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)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.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))) (/.f64 (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)))
(sin eps)
(sin.f64 eps)
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (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)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64))) (pow.f64 (cos.f64 eps) #s(literal 4 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))) (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)))
(+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 (fma.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)) (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (.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) (cos.f64 eps)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ x (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x)
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
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(/.f64 (-.f64 x (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) eps) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps)) (*.f64 x x)) eps)) (neg.f64 eps))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* -1 (* eps (- (* -1 (/ (- (/ (pow x 2) eps) (* -1 x)) eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) (neg.f64 eps)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) eps)) (pow x 2)) eps)) (* -1 x)) eps)) 1)))
(.f64 (neg.f64 eps) (-.f64 (/.f64 (-.f64 x (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 eps)) (.f64 x x)) eps)) (neg.f64 eps)) #s(literal 1 binary64)))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))

rewrite235.0ms (1.8%)

Memory

1.7MiB live, 145.3MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	335
0	96	352
1	390	233
2	3438	233
0	8220	227

Stop Event

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

Counts

26 → 559

Calls

Call 1

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

eval90.0ms (0.7%)

Memory: 22.2MiB live, 158.6MiB allocated; 10ms collecting garbage
Compiler: Compiled 25 826 to 3 262 computations (87.4% saved)

prune17.0ms (0.1%)

Memory

-10.9MiB live, 38.2MiB allocated; 7ms collecting garbage

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	537	9	546
Fresh	5	1	6
Picked	4	1	5
Done	0	1	1
Total	546	12	558

Accuracy

100.0%

Counts

558 → 12

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 (+.f64 eps x))) (cos.f64 x))
▶	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓	51.0%	(-.f64 (tan.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (tan.f64 x))
	4.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)) (+.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (tan.f64 x))
✓	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.3%	#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 (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 #s(approx (+ ( (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 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)) 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))
	99.8%	#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))
	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
▶	3.5%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64))))
	3.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
▶	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 526 to 329 computations (37.5% saved)

simplify104.0ms (0.8%)

Memory

-28.9MiB live, 110.2MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

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 (+.f64 eps x)))
cost-diff	0	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 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	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64))))
cost-diff	1	(+.f64 (+.f64 (PI.f64) eps) (PI.f64))
cost-diff	2	(+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64))
cost-diff	3	(tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64)))
cost-diff	0	(tan.f64 eps)
cost-diff	0	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
cost-diff	0	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
cost-diff	0	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	176
0	55	156
1	94	144
2	168	142
3	388	142
4	1255	142
5	3637	142
6	6720	142
0	8090	140

Stop Event

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

Calls

Call 1

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

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

localize471.0ms (3.6%)

Memory

30.9MiB live, 392.1MiB allocated; 70ms 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 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x)))
accuracy	0.015625	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
accuracy	0.0	(cos.f64 x)
accuracy	0.015625	(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01953125	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.44238934093737486	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.01953125	(+.f64 (+.f64 (PI.f64) eps) (PI.f64))
accuracy	0.01953125	(+.f64 (PI.f64) eps)
accuracy	1.204428561574053	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64))))
accuracy	61.48120543032467	(tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) eps) (PI.f64)) (PI.f64)))
accuracy	0.0	(tan.f64 eps)
accuracy	1.204428561574053	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
accuracy	0.0	#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
accuracy	0.00390625	(cos.f64 (+.f64 eps x))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	0.01171875	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

Samples

278.0ms	91×	2	valid
165.0ms	164×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 153 to 30 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 412.0ms

ival-tan: 299.0ms (72.6% of total)

adjust: 50.0ms (12.1% of total)

ival-add: 23.0ms (5.6% of total)

ival-div: 10.0ms (2.4% of total)

ival-sub: 6.0ms (1.5% of total)

ival-cos: 6.0ms (1.5% of total)

ival-sin: 6.0ms (1.5% of total)

ival-pow2: 5.0ms (1.2% of total)

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

ival-pi: 2.0ms (0.5% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated; 0ms collecting garbage

Counts

20 → 86

Calls

Call 1

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

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ 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))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(cos x)
(/ (sin eps) (cos (+ eps x)))
(cos (+ eps x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI)))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (+ (PI) (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2)))))) (cos (+ (PI) (* 2 (PI)))))) (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ (PI) (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (pow (cos (+ (PI) (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ (PI) (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (cos (+ (PI) (* 2 (PI))))))))) (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (PI) (* 2 (PI)))
(+ eps (+ (PI) (* 2 (PI))))
(* 2 (PI))
(+ eps (* 2 (PI)))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(PI)
(+ eps (PI))
(/ (sin (+ eps (+ (PI) (* 2 (PI))))) (cos (+ eps (+ (PI) (* 2 (PI))))))
(* eps (+ 1 (+ (* 2 (/ (PI) eps)) (/ (PI) eps))))
(* eps (+ 1 (* 2 (/ (PI) eps))))
(* eps (+ 1 (/ (PI) eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (+ (PI) (* 2 (PI))) (* -1 eps))) (cos (- (+ (PI) (* 2 (PI))) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ (+ (PI) (* 2 (PI))) eps)) 1)))
(* -1 (* eps (- (* -2 (/ (PI) eps)) 1)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))

Calls

6 calls:

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

simplify186.0ms (1.4%)

Memory

7.7MiB live, 143.5MiB allocated; 66ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	451	1917
1	1485	1820
2	5503	1761
0	8066	1667

Stop Event

1×	iter limit
1×	node limit

Counts

86 → 85

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ 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))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(/ eps (pow (cos x) 2))
(pow (cos x) 2)
(cos x)
(/ (sin eps) (cos (+ eps x)))
(cos (+ eps x))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI)))))
(+ (* eps (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin (+ (PI) (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2)))))) (cos (+ (PI) (* 2 (PI)))))) (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ (PI) (* 2 (PI)))) 2) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (pow (cos (+ (PI) (* 2 (PI)))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (* 1/6 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2)))))))) (* -1 (/ (* (sin (+ (PI) (* 2 (PI)))) (- 1 (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (cos (+ (PI) (* 2 (PI))))))))) (* -1 (/ (pow (sin (+ (PI) (* 2 (PI)))) 2) (pow (cos (+ (PI) (* 2 (PI)))) 2))))) (/ (sin (+ (PI) (* 2 (PI)))) (cos (+ (PI) (* 2 (PI))))))
(+ (PI) (* 2 (PI)))
(+ eps (+ (PI) (* 2 (PI))))
(* 2 (PI))
(+ eps (* 2 (PI)))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(PI)
(+ eps (PI))
(/ (sin (+ eps (+ (PI) (* 2 (PI))))) (cos (+ eps (+ (PI) (* 2 (PI))))))
(* eps (+ 1 (+ (* 2 (/ (PI) eps)) (/ (PI) eps))))
(* eps (+ 1 (* 2 (/ (PI) eps))))
(* eps (+ 1 (/ (PI) eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin (- (+ (PI) (* 2 (PI))) (* -1 eps))) (cos (- (+ (PI) (* 2 (PI))) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ (+ (PI) (* 2 (PI))) eps)) 1)))
(* -1 (* eps (- (* -2 (/ (PI) eps)) 1)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (PI) eps)) 1)))

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

rewrite225.0ms (1.7%)

Memory

20.3MiB live, 201.2MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	151
0	55	131
1	251	113
2	2223	113
0	11675	111

Stop Event

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

Counts

20 → 605

Calls

Call 1

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

Outputs
(*.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (+.f64 (cos.f64 eps) (cos.f64 (+.f64 (+.f64 x eps) x)))) #s(literal 2 binary64))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(neg.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps))
(/.f64 (-.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x eps) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 x eps) (neg.f64 x)))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (+.f64 (sin.f64 eps) (sin.f64 (+.f64 (+.f64 x eps) x))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 x eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 x eps) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) #s(literal 0 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 2 binary64))) (neg.f64 (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))) (+.f64 (pow.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) #s(literal 0 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) #s(literal 0 binary64)) (.f64 #s(literal 1 binary64) (sin.f64 eps))))))
(neg.f64 (neg.f64 (sin.f64 eps)))
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (cos.f64 eps) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps)))
(fma.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)))))))
(fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64))) (*.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64)))))
(fma.f64 (neg.f64 (sin.f64 eps)) #s(literal -1 binary64) (*.f64 (neg.f64 (cos.f64 eps)) #s(literal 0 binary64)))
(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 (cos.f64 eps) #s(literal 0 binary64)))
(fma.f64 (cos.f64 eps) #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 x) (cos.f64 (-.f64 x eps)) (*.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(fma.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 eps)) (*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps))))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (sin.f64 (+.f64 x eps)) (*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) (sin.f64 x)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(sin.f64 (+.f64 (neg.f64 eps) (PI.f64)))
(sin.f64 (neg.f64 (neg.f64 eps)))
(sin.f64 (neg.f64 (+.f64 (PI.f64) eps)))
(sin.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (+.f64 (PI.f64) eps))))
(sin.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (+.f64 (PI.f64) eps)) (PI.f64)))
(sin.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) eps))
(sin.f64 eps)
(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (cos.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x eps) x)))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (+.f64 (+.f64 x eps) x))) (sin.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x eps) x)))))
(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (+.f64 x eps) x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 eps)) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (sin.f64 eps))))
(-.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (cos.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64))))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (sin.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (+.f64 (PI.f64) eps) (PI.f64))))))
(-.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))))
(-.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))))
(-.f64 (.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (.f64 (cos.f64 eps) #s(literal 0 binary64)) (.f64 #s(literal -1 binary64) (sin.f64 eps)))
(cos.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (PI.f64)))
(cos.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (+.f64 (PI.f64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (+.f64 (PI.f64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (cos.f64 eps)) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (sin.f64 eps)))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (-.f64 x eps))) (.f64 (cos.f64 x) (sin.f64 (-.f64 eps x))))
(+.f64 (.f64 (sin.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)))))) (.f64 (cos.f64 (/.f64 (pow.f64 (+.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (+.f64 (PI.f64) eps)) (pow.f64 (+.f64 (PI.f64) eps) #s(literal 2 binary64)))))))
(+.f64 (.f64 (neg.f64 (sin.f64 eps)) #s(literal -1 binary64)) (.f64 (neg.f64 (cos.f64 eps)) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 eps))) (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64)))) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 (fma.f64 #s(literal 2 binary64) (PI.f64) (PI.f64)))))
(+.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 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (.f64 (cos.f64 eps) #s(literal 0 binary64)) (.f64 #s(literal 1 binary64) (sin.f64 eps)))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(/.f64 (fma.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 eps))) #s(literal 4 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps)))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps))))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.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)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.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)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (+.f64 x eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 (+.f64 x eps))))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 (+.f64 x eps)))))) #s(literal 2 binary64))
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(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) eps)
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))) eps)
(fma.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))) eps)
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) eps)
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))) eps)
(fma.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))) eps)
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) eps)
(fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) eps)
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)) eps)
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) eps)
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) eps)
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) eps)
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) eps)
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) eps)
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) eps)
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) eps)
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) eps)
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) eps)
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) eps)
(-.f64 (/.f64 (.f64 (PI.f64) (PI.f64)) (-.f64 (PI.f64) eps)) (/.f64 (.f64 eps eps) (-.f64 (PI.f64) eps)))
(-.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 (PI.f64) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (PI.f64)) (.f64 (PI.f64) (PI.f64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (PI.f64)) (.f64 (PI.f64) (PI.f64)))))
(+.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))

eval113.0ms (0.9%)

Memory: -9.3MiB live, 135.2MiB allocated; 20ms collecting garbage
Compiler: Compiled 21 306 to 3 360 computations (84.2% saved)

prune439.0ms (3.4%)

Memory

-85.9MiB live, 83.7MiB allocated; 992ms collecting garbage

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	682	17	699
Fresh	4	1	5
Picked	3	2	5
Done	1	1	2
Total	690	21	711

Accuracy

100.0%

Counts

711 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.2%	(/.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (.f64 eps eps)) (.f64 (.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (neg.f64 (.f64 eps eps))))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
✓	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.1%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 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)))))
▶	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
	4.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)) (+.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (tan.f64 x))
✓	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	36.9%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 2 binary64))))
▶	57.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
	99.3%	#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) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
▶	99.3%	#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 x x))))))
	99.3%	#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) (+.f64 (PI.f64) x)))))))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) x) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
▶	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	98.5%	#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)))))
	98.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	98.7%	#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 #s(literal 2/3 binary64) eps)) (.f64 x x) eps) (*.f64 x x) eps)))
	98.7%	#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)))
▶	98.5%	#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)))
	3.5%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ (+ (PI) eps) (PI)) (PI)) (fma.f64 (PI.f64) #s(literal 3 binary64) eps))))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 1 056 to 674 computations (36.2% saved)

simplify109.0ms (0.8%)

Memory

-27.1MiB live, 92.4MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	354
0	74	354
1	140	342
2	330	322
3	1061	318
4	3492	318
0	8362	315

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (1.2%)

Memory

24.3MiB live, 170.6MiB allocated; 31ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
accuracy	0.01953125	(pow.f64 (cos.f64 x) #s(literal 2 binary64))
accuracy	0.44238934093737486	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
accuracy	26.65776713506687	(/.f64 (neg.f64 (.f64 eps eps)) (.f64 (neg.f64 eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
accuracy	0.0	(cos.f64 (+.f64 x x))
accuracy	0.015625	(/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
accuracy	0.01953125	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))
accuracy	0.44238934093737486	#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 x x))))))
accuracy	0.015625	(/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.20703125	(.f64 #s(literal 1/3 binary64) (.f64 x x))
accuracy	0.44238934093737486	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.5801502244086066	#s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 (*.f64 x x) eps eps)
accuracy	0.0	(*.f64 x x)
accuracy	0.44238934093737486	#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	0.8436071101064821	#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
accuracy	0.00390625	(fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))
accuracy	0.0078125	(*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x))
accuracy	0.01171875	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
accuracy	0.13310045437105483	#s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))

Samples

88.0ms	152×	1	valid
25.0ms	104×	0	valid

Compiler

Compiled 238 to 38 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

adjust: 23.0ms (26.4% of total)

ival-mult: 15.0ms (17.2% of total)

ival-cos: 13.0ms (14.9% of total)

ival-div: 9.0ms (10.3% of total)

ival-add: 9.0ms (10.3% of total)

ival-sin: 5.0ms (5.7% of total)

const: 4.0ms (4.6% of total)

ival-sub: 3.0ms (3.4% of total)

ival-pow2: 3.0ms (3.4% of total)

ival-neg: 2.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.4%)

Memory

17.8MiB live, 60.4MiB allocated; 23ms collecting garbage

Counts

26 → 81

Calls

Call 1

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

Outputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ 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))))
(pow x 2)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
1/2
(+ 1/2 (* -1 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ 1 (* -1 (* eps x)))
(+ 1 (* x (+ (* -1 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1 eps) (* x (- (* 1/6 (* eps x)) 1/2)))))
(* 1/3 (pow x 2))
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))
(* -1 eps)
(+ (* -1 eps) (* eps (pow x 2)))
(+ (* -1 eps) (* (pow x 2) (+ eps (* -1/3 (* eps (pow x 2))))))
(+ (* -1 eps) (* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* 2/45 (* eps (pow x 2))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(/ eps (pow (cos x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(pow (cos x) 2)
(* 1/3 (pow x 4))
(* (pow x 4) (- 1/3 (/ 1 (pow x 2))))
(* (pow x 4) (- (+ 1/3 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(* 1/2 (cos (* 2 x)))
(cos (+ eps x))
(+ (cos x) (* -1 (* eps (sin x))))
(cos (* 2 x))
(* -1 (* eps (pow (cos x) 2)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
(* 1/2 (cos (neg (* -2 x))))
(cos (- eps (* -1 x)))
(cos (neg (* -2 x)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (pow x 2)))
(* -1 (pow eps 2))
(pow eps 2)
(cos x)
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (/ (cos x) eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(cos (- x (* -1 eps)))
(* -1 (* eps (+ (sin x) (* -1 (/ (cos x) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (- (* 1/3 (* x x)) 1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (+ x x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (+ x x))))) (* 1/2 (cos (+ x x))) (/ (neg (* eps eps)) (* (neg eps) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (neg (* eps eps)) (* eps eps) (cos (+ eps x)) (+ (* (sin x) (neg eps)) (cos x)) (* 1/3 (* x x)) (cos (+ x x)) (pow (cos x) 2) (* (neg eps) (pow (cos x) 2)))
15.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (- (* 1/3 (* x x)) 1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (+ x x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (+ x x))))) (* 1/2 (cos (+ x x))) (/ (neg (* eps eps)) (* (neg eps) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (neg (* eps eps)) (* eps eps) (cos (+ eps x)) (+ (* (sin x) (neg eps)) (cos x)) (* 1/3 (* x x)) (cos (+ x x)) (pow (cos x) 2) (* (neg eps) (pow (cos x) 2)))
5.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (- (* 1/3 (* x x)) 1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (+ x x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (+ x x))))) (* 1/2 (cos (+ x x))) (/ (neg (* eps eps)) (* (neg eps) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (neg (* eps eps)) (* eps eps) (cos (+ eps x)) (+ (* (sin x) (neg eps)) (cos x)) (* 1/3 (* x x)) (cos (+ x x)) (pow (cos x) 2) (* (neg eps) (pow (cos x) 2)))
4.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (- (* 1/3 (* x x)) 1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (+ x x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (+ x x))))) (* 1/2 (cos (+ x x))) (/ (neg (* eps eps)) (* (neg eps) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (neg (* eps eps)) (* eps eps) (cos (+ eps x)) (+ (* (sin x) (neg eps)) (cos x)) (* 1/3 (* x x)) (cos (+ x x)) (pow (cos x) 2) (* (neg eps) (pow (cos x) 2)))
4.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) (* (cos (+ eps x)) (cos x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (+ (* (- (* 1/3 (* x x)) 1) (* x x)) 1) (+ 1/2 (* 1/2 (cos (+ x x)))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (+ 1/2 (* 1/2 (cos (+ x x))))) (* 1/2 (cos (+ x x))) (/ (neg (* eps eps)) (* (neg eps) (pow (cos x) 2))) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (neg (* eps eps)) (* eps eps) (cos (+ eps x)) (+ (* (sin x) (neg eps)) (cos x)) (* 1/3 (* x x)) (cos (+ x x)) (pow (cos x) 2) (* (neg eps) (pow (cos x) 2)))

simplify187.0ms (1.4%)

Memory

-22.9MiB live, 166.5MiB allocated; 89ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	299	1033
1	1003	1004
2	3394	952
0	8369	894

Stop Event

1×	iter limit
1×	node limit

Counts

81 → 80

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))
(+ 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))))
(pow x 2)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
1/2
(+ 1/2 (* -1 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+ 1 (* -1 (* eps x)))
(+ 1 (* x (+ (* -1 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1 eps) (* x (- (* 1/6 (* eps x)) 1/2)))))
(* 1/3 (pow x 2))
(+ 1 (* -2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))
(* -1 eps)
(+ (* -1 eps) (* eps (pow x 2)))
(+ (* -1 eps) (* (pow x 2) (+ eps (* -1/3 (* eps (pow x 2))))))
(+ (* -1 eps) (* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* 2/45 (* eps (pow x 2))))))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(/ eps (pow (cos x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(pow (cos x) 2)
(* 1/3 (pow x 4))
(* (pow x 4) (- 1/3 (/ 1 (pow x 2))))
(* (pow x 4) (- (+ 1/3 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(/ eps (+ 1/2 (* 1/2 (cos (* 2 x)))))
(* 1/2 (cos (* 2 x)))
(cos (+ eps x))
(+ (cos x) (* -1 (* eps (sin x))))
(cos (* 2 x))
(* -1 (* eps (pow (cos x) 2)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(+ 1/2 (* 1/2 (cos (neg (* -2 x)))))
(/ eps (+ 1/2 (* 1/2 (cos (neg (* -2 x))))))
(* 1/2 (cos (neg (* -2 x))))
(cos (- eps (* -1 x)))
(cos (neg (* -2 x)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (+ 1 (pow x 2)))
(* -1 (pow eps 2))
(pow eps 2)
(cos x)
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (/ (cos x) eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (pow x 2)) 1)))
(cos (- x (* -1 eps)))
(* -1 (* eps (+ (sin x) (* -1 (/ (cos x) eps)))))

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

rewrite170.0ms (1.3%)

Memory

-6.9MiB live, 186.4MiB allocated; 43ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	317
0	74	321
1	262	289
2	1858	289
0	8916	289

Stop Event

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

Counts

26 → 415

Calls

Call 1

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

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

eval69.0ms (0.5%)

Memory: 1.3MiB live, 89.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 17 479 to 2 390 computations (86.3% saved)

prune37.0ms (0.3%)

Memory

-7.9MiB live, 49.4MiB allocated; 12ms collecting garbage

Pruning

22 alts after pruning (15 fresh and 7 done)

	Pruned	Kept	Total
New	456	5	461
Fresh	3	10	13
Picked	1	4	5
Done	0	3	3
Total	460	22	482

Accuracy

100.0%

Counts

482 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.2%	(/.f64 (/.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (.f64 eps eps)) (.f64 (.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (neg.f64 (.f64 eps eps))))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
✓	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.1%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	98.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 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)))))
✓	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x))) (cos.f64 x)))
	4.1%	(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64)) (+.f64 (+.f64 (PI.f64) eps) (PI.f64)))) (tan.f64 x))
✓	61.3%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	57.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (.f64 eps eps) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))
	57.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (*.f64 (neg.f64 eps) (cos.f64 x)) (cos.f64 x))))
	99.3%	#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) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
✓	99.3%	#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 x x))))))
	99.3%	#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) (+.f64 (PI.f64) x)))))))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) x) x) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
✓	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	98.5%	#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)))))
	98.1%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) #s(literal 1 binary64))))
	98.7%	#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)))
	98.7%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))
✓	98.5%	#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)))
	6.2%	#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))))
	3.5%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 #s(approx (+ (+ (+ (PI) eps) (PI)) (PI)) (fma.f64 (PI.f64) #s(literal 3 binary64) eps))))
✓	98.1%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))

Compiler

Compiled 1 744 to 645 computations (63% saved)

regimes37.0ms (0.3%)

Memory

14.8MiB live, 58.5MiB allocated; 8ms collecting garbage

Counts

43 → 1

Calls

Call 1

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

15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps
10.0ms	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)

regimes36.0ms (0.3%)

Memory

1.2MiB live, 46.8MiB allocated; 5ms collecting garbage

Counts

42 → 1

Calls

Call 1

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

Calls

3 calls:

14.0ms	x
10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms	eps

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)

regimes24.0ms (0.2%)

Memory

27.5MiB live, 27.5MiB allocated; 0ms collecting garbage

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.3%)

Memory

-18.4MiB live, 29.1MiB allocated; 2ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

Outputs

#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) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))))))

Calls

3 calls:

21.0ms	eps
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes55.0ms (0.4%)

Memory

-44.7MiB live, 44.2MiB allocated; 16ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

Outputs
#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 x x))))))

Calls

3 calls:

14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	x
4.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

21.0MiB live, 21.0MiB allocated; 0ms collecting garbage

Counts

15 → 1

Calls

Call 1

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

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:

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

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

-31.0MiB live, 15.3MiB allocated; 5ms collecting garbage

Counts

7 → 1

Calls

Call 1

Inputs
#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) #s(literal 1 binary64))))
#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 (fma.f64 (.f64 (.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 (.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 (-.f64 (.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 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`eps`
98.7%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#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) #s(literal 1 binary64))))
#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 (fma.f64 (.f64 (.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 (.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 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#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) #s(literal 1 binary64))))
#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)))))

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:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#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 (/ (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))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.2%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
6.2%	1	`x`
6.2%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify52.0ms (0.4%)

Memory

-0.9MiB live, 45.0MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	351
1	142	333
2	229	315
3	414	315
4	978	315
5	4449	315

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

derivations1.0s (7.8%)

Memory

7.9MiB live, 578.2MiB allocated; 56ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	151
0	55	131
1	251	113
2	2223	113
0	11675	111
0	6	16
0	10	16
1	53	16
2	440	16
3	6608	16
0	8588	16
0	792	3690
1	2407	3440
0	8252	3291
0	299	1033
1	1003	1004
2	3394	952
0	8369	894
0	157	970
1	488	910
2	1845	849
0	8454	797
0	451	1917
1	1485	1820
2	5503	1761
0	8066	1667

Stop Event

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

Compiler

Compiled 351 to 100 computations (71.5% saved)

preprocess137.0ms (1.1%)

Memory: -5.0MiB live, 136.9MiB allocated; 30ms collecting garbage
Compiler: Compiled 734 to 224 computations (69.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze49.0ms (0.4%)

sample6.9s (53.1%)

explain140.0ms (1.1%)

preprocess259.0ms (2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify229.0ms (1.8%)

localize32.0ms (0.2%)

series11.0ms (0.1%)

simplify175.0ms (1.3%)

rewrite223.0ms (1.7%)

eval27.0ms (0.2%)

prune10.0ms (0.1%)

simplify235.0ms (1.8%)

localize354.0ms (2.7%)

series83.0ms (0.6%)

simplify148.0ms (1.1%)

rewrite235.0ms (1.8%)

eval90.0ms (0.7%)

prune17.0ms (0.1%)

simplify104.0ms (0.8%)

localize471.0ms (3.6%)

series20.0ms (0.2%)

simplify186.0ms (1.4%)

rewrite225.0ms (1.7%)

eval113.0ms (0.9%)

prune439.0ms (3.4%)

simplify109.0ms (0.8%)

localize159.0ms (1.2%)

series50.0ms (0.4%)

simplify187.0ms (1.4%)

rewrite170.0ms (1.3%)

eval69.0ms (0.5%)

prune37.0ms (0.3%)

regimes37.0ms (0.3%)

regimes36.0ms (0.3%)

regimes24.0ms (0.2%)

regimes33.0ms (0.3%)

regimes55.0ms (0.4%)

regimes13.0ms (0.1%)

regimes18.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0%)

regimes3.0ms (0%)

simplify52.0ms (0.4%)

derivations1.0s (7.8%)

preprocess137.0ms (1.1%)

end0.0ms (0%)

Profiling