Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze54.0ms (0.5%)

Memory

1.0MiB live, 53.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.3s (55.2%)

Memory

127.7MiB live, 6 865.7MiB allocated

Samples

3.1s	25 720×	0	invalid
743.0ms	5 522×	0	valid
569.0ms	2 734×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.1s

const: 718.0ms (22.9% of total)

ival-tan: 641.0ms (20.4% of total)

ival-add: 358.0ms (11.4% of total)

ival-mult: 289.0ms (9.2% of total)

ival-<=: 274.0ms (8.7% of total)

ival-fabs: 232.0ms (7.4% of total)

ival-<: 212.0ms (6.7% of total)

ival-sub: 179.0ms (5.7% of total)

ival-and: 104.0ms (3.3% of total)

adjust: 74.0ms (2.4% of total)

exact: 46.0ms (1.5% of total)

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

Bogosity

explain89.0ms (0.8%)

Memory

21.6MiB live, 180.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
227	3	(7.223973763198391e-129 3.2580342723061734e-131)	2	(1.8380107909096626e-38 5.7732116707539e-40)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	228	4

Confusion

	Predicted +	Predicted -
+	225	2
-	3	26

Precision

0.9868421052631579

Recall

0.9911894273127754

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	225	2	0
-	3	2	24

Precision?

0.978448275862069

Recall?

1.0

Freqs

test

number	freq
0	28
1	228

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms	198×	1	valid
15.0ms	308×	0	valid
2.0ms	4×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-tan: 12.0ms (44.3% of total)

adjust: 8.0ms (29.5% of total)

ival-add: 3.0ms (11.1% of total)

ival-sub: 3.0ms (11.1% of total)

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

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

preprocess290.0ms (2.6%)

Memory

-21.0MiB live, 250.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	51	35
2	150	35
3	492	35
4	1175	35
5	2398	35
6	3552	35
7	4149	35
8	4809	35
9	5866	35
10	6992	35
0	6	7
0	10	7
1	18	7
2	44	7
3	137	7
4	378	7
5	951	7
6	1902	7
7	2646	7
8	3696	7
9	4531	7
10	5320	7
11	6346	7
12	7721	7
0	8155	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: 0.5MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify201.0ms (1.8%)

Memory

12.7MiB live, 165.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	18	18
2	44	18
3	137	18
4	378	18
5	951	18
6	1902	18
7	2646	18
8	3696	18
9	4531	18
10	5320	18
11	6346	18
12	7721	18
0	8155	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)

localize46.0ms (0.4%)

Memory

20.9MiB live, 67.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(tan.f64 x)
accuracy	0.0234375	(tan.f64 (+.f64 x eps))
accuracy	26.15141397970812	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Samples

27.0ms	99×	1	valid
12.0ms	154×	0	valid
1.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-tan: 22.0ms (78.5% of total)

adjust: 2.0ms (7.1% of total)

ival-add: 2.0ms (7.1% of total)

ival-sub: 2.0ms (7.1% of total)

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

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

series15.0ms (0.1%)

Memory

-12.7MiB live, 25.1MiB allocated

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
5.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
3.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x))
2.0ms	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))

simplify162.0ms (1.4%)

Memory

19.6MiB live, 170.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	966
1	518	897
2	2004	844
0	8109	790

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

rewrite345.0ms (3%)

Memory

-360.1MiB live, 238.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	55	16
2	509	16
0	8306	16

Stop Event

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

Counts

4 → 253

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 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (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 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 eps) (tan.f64 x))) (cos.f64 x))))
(.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(.f64 (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 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (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))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (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))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (pow.f64 (.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (pow.f64 (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))) #s(literal -1 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) (pow.f64 (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))) #s(literal -1 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal 3 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal 1 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))))
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(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 (tan.f64 x) #s(literal 0 binary64)))) (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) #s(literal 0 binary64)))))

eval37.0ms (0.3%)

Memory: 4.2MiB live, 49.3MiB allocated
Compiler: Compiled 7 608 to 1 068 computations (86% saved)

prune9.0ms (0.1%)

Memory

-20.1MiB live, 17.4MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	270	6	276
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	270	7	277

Accuracy

100.0%

Counts

277 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.1%	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
▶	59.2%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	59.2%	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
✓	59.2%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 221 to 144 computations (34.8% saved)

simplify159.0ms (1.4%)

Memory

26.1MiB live, 140.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	290
0	68	282
1	131	278
2	301	271
3	1048	271
4	5978	267
0	8034	263

Stop Event

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

Calls

Call 1

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

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

localize161.0ms (1.4%)

Memory

10.0MiB live, 196.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
accuracy	0.0078125	(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
accuracy	26.125253310028008	(-.f64 (+.f64 eps x) x)
accuracy	0.0	(cos.f64 x)
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
accuracy	0.0234375	(tan.f64 (+.f64 eps x))
accuracy	26.129969319410293	(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x)))
accuracy	0.0	(cos.f64 (+.f64 eps x))
accuracy	0.01171875	(sin.f64 (+.f64 eps x))
accuracy	0.04296875	(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
accuracy	26.15141397970812	(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
accuracy	0.0	(/.f64 (sin.f64 eps) (cos.f64 eps))
accuracy	0.0	(sin.f64 eps)
accuracy	0.0	(cos.f64 eps)
accuracy	0.42198766592996806	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
accuracy	0.0078125	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
accuracy	0.01171875	(/.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))
accuracy	0.021816259768442016	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
accuracy	0.1328125	(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)))

Samples

64.0ms	101×	1	valid
52.0ms	149×	0	valid
7.0ms	4×	3	valid
2.0ms	2×	2	valid

Compiler

Compiled 556 to 77 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-div: 22.0ms (25.1% of total)

adjust: 10.0ms (11.4% of total)

ival-mult: 10.0ms (11.4% of total)

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

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

ival-tan: 7.0ms (8% of total)

ival-cos: 7.0ms (8% of total)

ival-pow2: 7.0ms (8% of total)

ival-sub: 4.0ms (4.6% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series46.0ms (0.4%)

Memory

12.5MiB live, 49.4MiB allocated

Counts

25 → 139

Calls

Call 1

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

Outputs
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* x (+ eps (* -1/6 eps)))))))
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* -1/6 eps) (* 1/6 x))))))))
(/ (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 (* (pow eps 2) x))
(+ eps (* x (+ (* eps x) (pow eps 2))))
(+ eps (* x (+ (* x (+ eps (* x (- (* eps (+ eps (* -1/6 eps))) (* -1/2 (pow eps 2)))))) (pow eps 2))))
(* x (+ eps (* x (+ 1 (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))
(* x (+ eps (* x (+ 1 (* x (- (+ eps (+ (* -1/6 eps) (* 2/3 x))) (* -1/2 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)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+ eps x)
-1
(- (* -1/2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(+ (* 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)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(* (pow x 2) (+ 1 (* 1/6 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2))))))))
(cos eps)
(+ (cos eps) (* -1 (* x (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
(+ 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)))
(+ (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)))))))))
(+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x)))) (cos x)))
(/ (+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x))) (cos x))
(/ (sin (+ eps x)) (cos (+ eps x)))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(/ -1 (cos x))
(sin x)
(* -1 (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(pow (sin x) 2)
(/ (pow (sin x) 2) (cos x))
(cos (+ eps x))
(cos x)
(* (cos x) (cos (+ eps x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(+ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ 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)))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (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))))
(+ (* -1 (/ (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 (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))))
(+ (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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (pow (sin x) 2) (* eps (cos x)))))
(/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))))
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (cos x)))) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (/ (* (pow eps 2) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps))))
(* -1 (/ (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(cos (- x (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	((+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (pow (sin x) 2) (/ (pow (sin x) 2) (cos x)) (cos (+ eps x)) (tan (+ eps x)) (cos x) (* (cos (+ eps x)) (cos x)))
9.0ms	x	@	-inf	((+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (pow (sin x) 2) (/ (pow (sin x) 2) (cos x)) (cos (+ eps x)) (tan (+ eps x)) (cos x) (* (cos (+ eps x)) (cos x)))
6.0ms	x	@	0	((+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (pow (sin x) 2) (/ (pow (sin x) 2) (cos x)) (cos (+ eps x)) (tan (+ eps x)) (cos x) (* (cos (+ eps x)) (cos x)))
5.0ms	eps	@	-inf	((+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (pow (sin x) 2) (/ (pow (sin x) 2) (cos x)) (cos (+ eps x)) (tan (+ eps x)) (cos x) (* (cos (+ eps x)) (cos x)))
5.0ms	eps	@	0	((+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (pow (sin x) 2) (/ (pow (sin x) 2) (cos x)) (cos (+ eps x)) (tan (+ eps x)) (cos x) (* (cos (+ eps x)) (cos x)))

simplify242.0ms (2.1%)

Memory

-24.5MiB live, 222.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	547	2825
1	1939	2667
2	7359	2548
0	8778	2389

Stop Event

1×	iter limit
1×	node limit

Counts

139 → 137

Calls

Call 1

Inputs
(* eps x)
(* x (+ eps x))
(* x (+ eps (* x (+ 1 (* x (+ eps (* -1/6 eps)))))))
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* -1/6 eps) (* 1/6 x))))))))
(/ (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 (* (pow eps 2) x))
(+ eps (* x (+ (* eps x) (pow eps 2))))
(+ eps (* x (+ (* x (+ eps (* x (- (* eps (+ eps (* -1/6 eps))) (* -1/2 (pow eps 2)))))) (pow eps 2))))
(* x (+ eps (* x (+ 1 (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))
(* x (+ eps (* x (+ 1 (* x (- (+ eps (+ (* -1/6 eps) (* 2/3 x))) (* -1/2 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)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+ eps x)
-1
(- (* -1/2 (pow x 2)) 1)
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(+ (* 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)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(* (pow x 2) (+ 1 (* 1/6 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2))))))))
(cos eps)
(+ (cos eps) (* -1 (* x (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
(+ 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)))
(+ (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)))))))))
(+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (/ (* eps (+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x)))) (cos x)))
(/ (+ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (/ (pow (sin x) 2) (cos x))) (cos x))
(/ (sin (+ eps x)) (cos (+ eps x)))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(/ -1 (cos x))
(sin x)
(* -1 (cos x))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(pow (sin x) 2)
(/ (pow (sin x) 2) (cos x))
(cos (+ eps x))
(cos x)
(* (cos x) (cos (+ eps x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(cos (- eps (* -1 x)))
(* (cos x) (cos (- eps (* -1 x))))
(+ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ 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)))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x)))
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(+ (* -1 (/ (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))))
(+ (* -1 (/ (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 (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))))
(+ (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))))
(pow (cos x) 2)
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (pow (sin x) 2) (* eps (cos x)))))
(/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))
(* eps (+ 1 (/ x eps)))
(* -1 (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))))
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (cos x)))) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (/ (* (pow eps 2) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps))))
(* -1 (/ (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(cos (- x (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))

Outputs
(* eps x)
(*.f64 eps x)
(* x (+ eps x))
(*.f64 (+.f64 eps x) x)
(* x (+ eps (* x (+ 1 (* x (+ eps (* -1/6 eps)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 5/6 binary64) (.f64 eps x) #s(literal 1 binary64)) x eps) x)
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* -1/6 eps) (* 1/6 x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/6 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(/ (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 (- (/ (* 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 (*.f64 (sin.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)) (/.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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 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 (* (pow eps 2) x))
(fma.f64 (*.f64 eps eps) x eps)
(+ eps (* x (+ (* eps x) (pow eps 2))))
(fma.f64 (*.f64 eps (+.f64 eps x)) x eps)
(+ eps (* x (+ (* x (+ eps (* x (- (* eps (+ eps (* -1/6 eps))) (* -1/2 (pow eps 2)))))) (pow eps 2))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (.f64 #s(literal 5/6 binary64) (.f64 eps eps))) x eps) x (.f64 eps eps)) x eps)
(* x (+ eps (* x (+ 1 (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))
(.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 4/3 binary64)) x #s(literal 1 binary64)) x eps) x)
(* x (+ eps (* x (+ 1 (* x (- (+ eps (+ (* -1/6 eps) (* 2/3 x))) (* -1/2 eps)))))))
(.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 eps #s(literal 1/3 binary64))) eps) x #s(literal 1 binary64)) x 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 (+.f64 (/.f64 (fma.f64 (*.f64 (sin.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)) (/.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 (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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 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 1/6 binary64)))) 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)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
(+ eps x)
(+.f64 eps x)
-1
#s(literal -1 binary64)
(- (* -1/2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)
(fma.f64 (fma.f64 #s(literal -5/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)
(fma.f64 (fma.f64 (fma.f64 #s(literal -61/720 binary64) (.f64 x x) #s(literal -5/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(- (* 1/2 (pow x 2)) 1)
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))
(+ (* 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)))
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#s(literal 0 binary64)
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))))
(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps #s(literal 0 binary64))
(+ (* -1 (/ (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))))
(+.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (/.f64 eps (cos.f64 x)) eps))
(+ (* -1 (/ (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))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64) (neg.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (sin.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps #s(literal 0 binary64))
(/ eps (pow (cos x) 2))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(.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))))
(fma.f64 (*.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps (cos.f64 x))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(fma.f64 (neg.f64 eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(fma.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) eps (.f64 (neg.f64 (cos.f64 x)) (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 (neg.f64 (sin.f64 x)) (cos.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) eps) (.f64 (cos.f64 x) (sin.f64 x)) (.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) eps)
(* eps (+ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (pow (sin x) 2) (* eps (cos x)))))
(*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))) eps)
(/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (.f64 eps eps))
(* (pow eps 2) (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(.f64 (+.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (.f64 eps eps))
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)))
(* eps (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))
(*.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))) (cos.f64 x)) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* -1 (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) eps)
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (cos x)))) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (neg.f64 (cos.f64 x))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))))
(- (/ (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)))
(* -1 (/ (* (pow eps 2) (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps))))
(.f64 (+.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (.f64 eps eps))
(* -1 (/ (* eps (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (cos x)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)))
(* -1 (* eps (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x)))))
(*.f64 (-.f64 (/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (neg.f64 eps))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps)
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))

rewrite189.0ms (1.7%)

Memory

-5.9MiB live, 185.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	236
0	68	208
1	313	164
2	2977	164
0	8169	161

Stop Event

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

Counts

25 → 729

Calls

Call 1

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

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

eval150.0ms (1.3%)

Memory: 25.6MiB live, 219.8MiB allocated
Compiler: Compiled 30 970 to 4 229 computations (86.3% saved)

prune16.0ms (0.1%)

Memory

11.5MiB live, 48.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1 042	4	1 046
Fresh	1	0	1
Picked	5	0	5
Done	1	0	1
Total	1 049	4	1 053

Accuracy

100.0%

Counts

1 053 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 eps #s(literal 1/3 binary64))) eps) x #s(literal 1 binary64)) x eps) x)) eps eps))
▶	99.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
▶	99.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps eps) x eps)))
▶	5.4%	#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 164 to 92 computations (43.9% saved)

simplify187.0ms (1.6%)

Memory

-46.9MiB live, 92.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	426
0	67	426
1	148	417
2	424	402
3	1609	402
4	6488	388
0	8079	370

Stop Event

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

Calls

Call 1

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

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

localize178.0ms (1.6%)

Memory

41.9MiB live, 192.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 eps #s(literal 1/3 binary64))) eps) x #s(literal 1 binary64)) x eps) x)
accuracy	0.3046875	(*.f64 eps #s(literal 1/3 binary64))
accuracy	0.34375	(fma.f64 #s(literal 2/3 binary64) x (*.f64 eps #s(literal 1/3 binary64)))
accuracy	0.3671875	(+.f64 (fma.f64 #s(literal 2/3 binary64) x (*.f64 eps #s(literal 1/3 binary64))) eps)
accuracy	0.0	(+.f64 eps x)
accuracy	0.0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
accuracy	0.04838648533329809	#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps))
accuracy	0.11328125	(*.f64 eps (+.f64 eps x))
accuracy	0.0	(fma.f64 (*.f64 eps eps) x eps)
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps eps) x eps)))
accuracy	0.42198766592996806	#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps eps) x eps))
accuracy	59.853570663353196	#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Samples

76.0ms	151×	0	valid
70.0ms	100×	1	valid
4.0ms	3×	5	exit
1.0ms	1×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 687 to 96 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-add: 39.0ms (31% of total)

ival-mult: 27.0ms (21.5% of total)

ival-tan: 17.0ms (13.5% of total)

adjust: 11.0ms (8.7% of total)

const: 8.0ms (6.4% of total)

ival-div: 8.0ms (6.4% of total)

ival-pow2: 6.0ms (4.8% of total)

ival-cos: 3.0ms (2.4% of total)

ival-sin: 3.0ms (2.4% of total)

ival-sub: 2.0ms (1.6% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series55.0ms (0.5%)

Memory

-6.2MiB live, 31.4MiB allocated

Counts

17 → 94

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	0	((+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* eps eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* eps (+ eps x)) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ eps x) (+ (* 2/3 x) (* eps 1/3)) (* eps 1/3) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x))
10.0ms	eps	@	0	((+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* eps eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* eps (+ eps x)) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ eps x) (+ (* 2/3 x) (* eps 1/3)) (* eps 1/3) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x))
5.0ms	eps	@	-inf	((+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* eps eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* eps (+ eps x)) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ eps x) (+ (* 2/3 x) (* eps 1/3)) (* eps 1/3) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x))
5.0ms	eps	@	inf	((+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* eps eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* eps (+ eps x)) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ eps x) (+ (* 2/3 x) (* eps 1/3)) (* eps 1/3) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x))
4.0ms	x	@	-inf	((+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps eps) x) eps) (* eps eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* eps (+ eps x)) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ eps x) (+ (* 2/3 x) (* eps 1/3)) (* eps 1/3) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x))

simplify147.0ms (1.3%)

Memory

-16.8MiB live, 143.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	358	1738
1	1290	1636
2	4799	1533
0	8201	1438

Stop Event

1×	iter limit
1×	node limit

Counts

94 → 92

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

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 (- (/ (* 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 (*.f64 (sin.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)) (/.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 (* (pow eps 2) x))
(fma.f64 (*.f64 eps eps) x eps)
(+ eps (* x (+ (* eps x) (pow eps 2))))
(*.f64 (fma.f64 (+.f64 eps x) x #s(literal 1 binary64)) eps)
(+ eps (* x (+ (* x (+ eps (* x (- (* eps (+ eps (* -1/6 eps))) (* -1/2 (pow eps 2)))))) (pow eps 2))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (.f64 #s(literal 5/6 binary64) (.f64 eps eps))) x eps) x (.f64 eps eps)) x eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* eps x) (pow eps 2))
(*.f64 (+.f64 eps x) eps)
(+ eps (* 1/3 eps))
(*.f64 #s(literal 4/3 binary64) eps)
(+ eps (+ (* 1/3 eps) (* 2/3 x)))
(fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
(* eps x)
(*.f64 eps x)
(* x (+ eps x))
(*.f64 (+.f64 eps x) x)
(* x (+ eps (* x (+ 1 (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps x) #s(literal 1 binary64)) x eps) x)
(* x (+ eps (* x (+ 1 (* x (- (+ eps (+ (* -1/6 eps) (* 2/3 x))) (* -1/2 eps)))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(+ eps x)
(+.f64 eps x)
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* 2/3 x))
(fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal 1/3 binary64) eps))
(* x (+ eps (* x (+ 1 (* x (+ eps (* 1/3 eps)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps x) #s(literal 1 binary64)) x eps) x)
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* 1/3 eps) (* 2/3 x))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x))))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
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rewrite218.0ms (1.9%)

Memory

18.2MiB live, 137.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	391
0	67	389
1	356	303
2	3312	303
0	8213	280

Stop Event

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

Counts

17 → 236

Calls

Call 1

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

Outputs
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps eps) x eps)))
#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps eps) x eps))
(.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (neg.f64 eps))) (pow.f64 (fma.f64 (.f64 eps x) eps (neg.f64 eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (*.f64 eps eps) x)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (.f64 eps x) eps (neg.f64 eps)) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (*.f64 eps (neg.f64 eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x)))) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 eps eps) x) #s(literal 2 binary64))) (-.f64 eps (.f64 (*.f64 eps eps) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (neg.f64 eps)))) (neg.f64 (fma.f64 (*.f64 eps x) eps (neg.f64 eps))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x))))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (neg.f64 eps))) (fma.f64 (*.f64 eps x) eps (neg.f64 eps)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 eps eps) x) #s(literal 2 binary64)) (*.f64 x (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps x) eps (neg.f64 eps)) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (*.f64 eps (neg.f64 eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x)))) (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(fma.f64 (*.f64 x (neg.f64 eps)) (neg.f64 eps) eps)
(fma.f64 (*.f64 x (fabs.f64 eps)) (fabs.f64 eps) eps)
(fma.f64 (*.f64 eps x) eps eps)
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) x) eps)
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) x) eps)
(fma.f64 (*.f64 eps eps) x eps)
(fma.f64 eps (*.f64 eps x) eps)
(fma.f64 x (*.f64 eps eps) eps)
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 eps eps) x) #s(literal 2 binary64)) (fma.f64 (.f64 eps x) eps (neg.f64 eps))) (/.f64 (.f64 eps eps) (fma.f64 (*.f64 eps x) eps (neg.f64 eps))))
(-.f64 eps (.f64 (neg.f64 (.f64 eps eps)) x))
(-.f64 eps (.f64 (neg.f64 eps) (.f64 eps x)))
(-.f64 eps (.f64 (neg.f64 x) (.f64 eps eps)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 eps eps) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x))))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 x x) (.f64 eps (-.f64 eps (.f64 (.f64 eps eps) x))))))
(+.f64 (.f64 (.f64 eps eps) x) eps)
(+.f64 eps (.f64 (.f64 eps eps) x))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)))
(*.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 eps eps)
(.f64 #s(literal 1 binary64) (.f64 eps eps))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (fabs.f64 eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(neg.f64 (*.f64 eps (neg.f64 eps)))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(sqrt.f64 (pow.f64 eps #s(literal 4 binary64)))
(fabs.f64 (neg.f64 (*.f64 eps eps)))
(fabs.f64 (*.f64 eps eps))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fabs.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 (+.f64 eps x) eps) x eps)))
#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 (+.f64 eps x) eps) x eps))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 eps eps)) (pow.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) x (neg.f64 eps)) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (.f64 (+.f64 eps x) eps) x (neg.f64 eps)) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64))) (-.f64 eps (.f64 (*.f64 (+.f64 eps x) eps) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (fma.f64 (.f64 (+.f64 eps x) eps) x (neg.f64 eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 eps eps)) (fma.f64 (.f64 (+.f64 eps x) eps) x (neg.f64 eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 (+.f64 eps x) eps) x) eps))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (+.f64 eps x) eps) x (neg.f64 eps)) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(fma.f64 (*.f64 (+.f64 eps x) x) eps eps)
(fma.f64 (*.f64 eps x) (+.f64 eps x) eps)
(fma.f64 (*.f64 (+.f64 eps x) eps) x eps)
(fma.f64 (+.f64 eps x) (*.f64 eps x) eps)
(fma.f64 eps (*.f64 (+.f64 eps x) x) eps)
(fma.f64 x (*.f64 (+.f64 eps x) eps) eps)
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)) (fma.f64 (.f64 (+.f64 eps x) eps) x (neg.f64 eps))) (/.f64 (.f64 eps eps) (fma.f64 (*.f64 (+.f64 eps x) eps) x (neg.f64 eps))))
(-.f64 eps (.f64 (neg.f64 (.f64 (+.f64 eps x) eps)) x))
(-.f64 eps (.f64 (neg.f64 eps) (.f64 (+.f64 eps x) x)))
(-.f64 eps (.f64 (neg.f64 x) (.f64 (+.f64 eps x) eps)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x)) (pow.f64 (.f64 (.f64 (+.f64 eps x) eps) x) #s(literal 2 binary64)))))
(+.f64 (.f64 (.f64 (+.f64 eps x) eps) x) eps)
(+.f64 eps (.f64 (.f64 (+.f64 eps x) eps) x))
(*.f64 (+.f64 eps x) eps)
(*.f64 eps (+.f64 eps x))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) eps) (-.f64 eps x))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) eps) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) eps) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (.f64 eps (.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 eps (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 eps (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x eps) (.f64 eps eps)))
(/.f64 (.f64 eps (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 eps x) #s(literal 2 binary64))) (.f64 eps (-.f64 eps x)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (*.f64 x (pow.f64 eps #s(literal 3 binary64))))))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 eps x))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (*.f64 eps x))
(fma.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)) (*.f64 eps x))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 eps x))
(fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 eps x))
(fma.f64 eps eps (*.f64 eps x))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 eps x))
(fma.f64 x eps (*.f64 eps eps))
(-.f64 (.f64 eps eps) (.f64 (neg.f64 eps) x))
(-.f64 (.f64 eps eps) (.f64 (neg.f64 x) eps))
(+.f64 (.f64 eps x) (.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 eps x))
(.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64)) (.f64 eps eps)) (pow.f64 (-.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) eps) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps))) (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) eps) (-.f64 (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64)) (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps))) (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal 1/3 binary64) eps)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 4/3 binary64) eps) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 #s(literal 4/3 binary64) eps)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64))) (-.f64 eps (fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal 1/3 binary64) eps))))
(/.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 64/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (-.f64 (pow.f64 (.f64 #s(literal 4/3 binary64) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 #s(literal 4/3 binary64) eps)))))
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#s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
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(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
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(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 eps x) (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
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(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 eps x)
(+.f64 x eps)
(.f64 (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 eps eps))) (pow.f64 (fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal -1/3 binary64) eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (*.f64 #s(literal 2/3 binary64) x)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal -1/3 binary64) eps)) (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 eps eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x)))) (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (.f64 eps eps)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (*.f64 #s(literal 2/3 binary64) x)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 eps) #s(literal 1/3 binary64)) #s(literal 3 binary64))) (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (fma.f64 #s(literal 1/9 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal 2/3 binary64) x) (*.f64 (neg.f64 eps) #s(literal 1/3 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 eps eps)))) (neg.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal -1/3 binary64) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 eps eps))) (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal -1/3 binary64) eps)))
(/.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (.f64 eps eps) (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 1/3 binary64)) eps))))
(/.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal -1/3 binary64) eps)) (-.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x)))) (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64)))))
(fma.f64 #s(literal 1/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x))
(fma.f64 #s(literal 2/3 binary64) x (*.f64 (neg.f64 (neg.f64 eps)) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 2/3 binary64) x (neg.f64 (*.f64 (neg.f64 eps) #s(literal 1/3 binary64))))
(fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal 1/3 binary64) eps))
(fma.f64 eps #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) x))
(fma.f64 x #s(literal 2/3 binary64) (*.f64 (neg.f64 (neg.f64 eps)) #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 2/3 binary64) (neg.f64 (*.f64 (neg.f64 eps) #s(literal 1/3 binary64))))
(fma.f64 x #s(literal 2/3 binary64) (*.f64 #s(literal 1/3 binary64) eps))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 2/3 binary64) x (.f64 #s(literal -1/3 binary64) eps))) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) x (*.f64 #s(literal -1/3 binary64) eps))))
(-.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 #s(literal -1/3 binary64) eps))
(-.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 (neg.f64 eps) #s(literal 1/3 binary64)))
(-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal -2/3 binary64) x))
(-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 (neg.f64 x) #s(literal 2/3 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 2/3 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x))))) (/.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 4/9 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/3 binary64) eps) (-.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x))))))
(+.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 (neg.f64 (neg.f64 eps)) #s(literal 1/3 binary64)))
(+.f64 (.f64 #s(literal 2/3 binary64) x) (neg.f64 (.f64 (neg.f64 eps) #s(literal 1/3 binary64))))
(+.f64 (.f64 #s(literal 2/3 binary64) x) (.f64 #s(literal 1/3 binary64) eps))
(+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) x))
(*.f64 #s(literal 1/3 binary64) eps)
(*.f64 eps #s(literal 1/3 binary64))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(.f64 x (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps)) x) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x (neg.f64 eps)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) x) (fma.f64 eps (-.f64 eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x (neg.f64 eps)))
(/.f64 (.f64 x (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x (*.f64 eps x))
(fma.f64 eps x (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(fma.f64 eps x (.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))
(fma.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) (*.f64 eps x))
(fma.f64 x eps (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(fma.f64 x eps (.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))
(+.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x) (.f64 eps x))
(+.f64 (.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (.f64 eps x))
(+.f64 (.f64 eps x) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(+.f64 (.f64 eps x) (.f64 x (.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) eps (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))

eval122.0ms (1.1%)

Memory: -10.7MiB live, 81.6MiB allocated
Compiler: Compiled 19 115 to 1 763 computations (90.8% saved)

prune45.0ms (0.4%)

Memory

-17.3MiB live, 21.0MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	303	5	308

Accuracy

100.0%

Counts

308 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
✓	99.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
▶	99.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps))))
▶	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))))
✓	5.4%	#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 234 to 131 computations (44% saved)

simplify152.0ms (1.3%)

Memory

24.3MiB live, 142.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	497
0	61	497
1	133	483
2	371	469
3	1302	469
4	5796	455
0	8255	431

Stop Event

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

Calls

Call 1

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

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

localize223.0ms (2%)

Memory

-30.0MiB live, 166.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.044484442520879436	#s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
accuracy	0.12890625	(.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
accuracy	0.31640625	(*.f64 #s(literal 2/3 binary64) x)
accuracy	25.188418030541033	#s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x))
accuracy	0.0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps))))
accuracy	0.0	#s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps))
accuracy	0.01171875	(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)
accuracy	0.04838648533329809	#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
accuracy	0.0	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))))
accuracy	0.04838648533329809	#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps)))
accuracy	0.10546875	(.f64 (.f64 x x) eps)
accuracy	59.97674820476788	#s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))

Samples

135.0ms	154×	0	valid
57.0ms	99×	1	valid
2.0ms	2×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 748 to 91 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-mult: 22.0ms (22.7% of total)

ival-pow2: 21.0ms (21.7% of total)

ival-add: 18.0ms (18.6% of total)

adjust: 9.0ms (9.3% of total)

const: 7.0ms (7.2% of total)

ival-div: 6.0ms (6.2% of total)

ival-tan: 5.0ms (5.2% of total)

ival-sin: 5.0ms (5.2% of total)

ival-sub: 2.0ms (2.1% of total)

ival-cos: 2.0ms (2.1% 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

32.6MiB live, 32.6MiB allocated

Counts

14 → 67

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (+ (* x x) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (* 2/3 x))
3.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (+ (* x x) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (* 2/3 x))
3.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (+ (* x x) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (* 2/3 x))
3.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (+ (* x x) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (* 2/3 x))
3.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (* x x) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (+ (* (* eps (+ eps x)) x) eps) (* (+ (* x x) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (* (+ (* (+ (* (+ (+ (* 2/3 x) (* eps 1/3)) eps) x) 1) x) eps) x) (+ (+ (* 2/3 x) (* eps 1/3)) eps) (* 2/3 x))

simplify135.0ms (1.2%)

Memory

-10.6MiB live, 109.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	313	1411
1	1131	1317
2	4325	1224
0	8379	1150

Stop Event

1×	iter limit
1×	node limit

Counts

67 → 66

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

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

rewrite295.0ms (2.6%)

Memory

-4.3MiB live, 157.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	446
0	61	446
1	308	359
2	2819	359
0	10500	330

Stop Event

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

Counts

14 → 83

Calls

Call 1

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

Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))))
#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps)))
#s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))
(.f64 (.f64 eps (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 eps x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) eps))
(.f64 (.f64 x x) eps)
(.f64 eps (.f64 x x))
(.f64 x (.f64 eps x))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps))))
#s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) 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 x #s(literal 4 binary64)) #s(literal 1 binary64)) eps) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) eps) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))
(/.f64 (*.f64 eps (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 eps (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))
(fma.f64 (.f64 eps (neg.f64 x)) (neg.f64 x) (.f64 #s(literal 1 binary64) eps))
(fma.f64 (.f64 eps (neg.f64 x)) (neg.f64 x) (.f64 eps #s(literal 1 binary64)))
(fma.f64 (.f64 eps x) x (.f64 #s(literal 1 binary64) eps))
(fma.f64 (.f64 eps x) x (.f64 eps #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) eps) (.f64 #s(literal 1 binary64) eps))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) eps) (.f64 eps #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 x x) eps))
(fma.f64 (.f64 x x) eps (.f64 #s(literal 1 binary64) eps))
(fma.f64 (.f64 x x) eps (.f64 eps #s(literal 1 binary64)))
(fma.f64 eps #s(literal 1 binary64) (.f64 (.f64 x x) eps))
(fma.f64 eps (.f64 x x) (.f64 #s(literal 1 binary64) eps))
(fma.f64 eps (.f64 x x) (.f64 eps #s(literal 1 binary64)))
(fma.f64 x (.f64 eps x) (.f64 #s(literal 1 binary64) eps))
(fma.f64 x (.f64 eps x) (.f64 eps #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (*.f64 x x) eps))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 (*.f64 x x) eps))
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(+.f64 eps (.f64 #s(approx (/ (+ ( (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps))
#s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x))
(.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)
(.f64 x (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps)) x) (fma.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x (neg.f64 eps)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) x) (fma.f64 eps (-.f64 eps (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps))) (fma.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x (neg.f64 eps)))
(/.f64 (.f64 x (+.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x (.f64 eps x))
(fma.f64 eps x (.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(fma.f64 eps x (.f64 x (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))
(fma.f64 x (.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) (.f64 eps x))
(fma.f64 x eps (.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(fma.f64 x eps (.f64 x (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))
(+.f64 (.f64 (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x) (.f64 eps x))
(+.f64 (.f64 x (.f64 (fma.f64 #s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)) (.f64 eps x))
(+.f64 (.f64 eps x) (.f64 (.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x) x))
(+.f64 (.f64 eps x) (.f64 x (.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x)))
#s(approx (+ (+ (* 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x))
(*.f64 #s(literal 2/3 binary64) x)
(*.f64 x #s(literal 2/3 binary64))
(sqrt.f64 (.f64 #s(literal 4/9 binary64) (.f64 x x)))
(fabs.f64 (neg.f64 (*.f64 #s(literal 2/3 binary64) x)))
(fabs.f64 (*.f64 #s(literal 2/3 binary64) x))

eval17.0ms (0.2%)

Memory: 18.4MiB live, 18.4MiB allocated
Compiler: Compiled 9 755 to 675 computations (93.1% saved)

prune17.0ms (0.1%)

Memory

-11.4MiB live, 25.5MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	129	6	135

Accuracy

100.0%

Counts

135 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (.f64 (fma.f64 (fma.f64 #s(approx (+ (+ ( 2/3 x) (* eps 1/3)) eps) (*.f64 #s(literal 2/3 binary64) x)) x #s(literal 1 binary64)) x eps) x)) eps eps))
✓	99.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) (fma.f64 (*.f64 eps (+.f64 eps x)) x eps)))
✓	99.9%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps))))
✓	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 x x) eps))))
	6.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (+ (* (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) eps) eps) #s(approx (+ (* (* eps (+ eps x)) x) eps) (.f64 (.f64 eps x) x))))
✓	5.4%	#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Compiler

Compiled 793 to 275 computations (65.3% saved)

regimes18.0ms (0.2%)

Memory

-10.1MiB live, 26.8MiB allocated

Counts

15 → 1

Calls

Call 1

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

Calls

3 calls:

8.0ms	eps
5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

-20.0MiB live, 15.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

5.0ms	x
2.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms	eps

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

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

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.3%	1	`x`
6.3%	1	`eps`
6.3%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

10.8MiB live, 10.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
5.4%	1	`x`
5.4%	1	`eps`
5.4%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify57.0ms (0.5%)

Memory

-16.1MiB live, 32.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	234
1	127	232
2	331	223
3	1236	223
4	6014	215

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness882.0ms (7.8%)

Memory

9.8MiB live, 525.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	55	16
2	509	16
0	8306	16
0	157	966
1	518	897
2	2004	844
0	8109	790
0	49	446
0	61	446
1	308	359
2	2819	359
0	10500	330
0	547	2825
1	1939	2667
2	7359	2548
0	8778	2389
0	358	1738
1	1290	1636
2	4799	1533
0	8201	1438

Stop Event

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

Compiler

Compiled 321 to 132 computations (58.9% saved)

preprocess65.0ms (0.6%)

Memory: -11.6MiB live, 66.2MiB allocated
Compiler: Compiled 500 to 150 computations (70% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze54.0ms (0.5%)

sample6.3s (55.2%)

explain89.0ms (0.8%)

preprocess290.0ms (2.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify201.0ms (1.8%)

localize46.0ms (0.4%)

series15.0ms (0.1%)

simplify162.0ms (1.4%)

rewrite345.0ms (3%)

eval37.0ms (0.3%)

prune9.0ms (0.1%)

simplify159.0ms (1.4%)

localize161.0ms (1.4%)

series46.0ms (0.4%)

simplify242.0ms (2.1%)

rewrite189.0ms (1.7%)

eval150.0ms (1.3%)

prune16.0ms (0.1%)

simplify187.0ms (1.6%)

localize178.0ms (1.6%)

series55.0ms (0.5%)

simplify147.0ms (1.3%)

rewrite218.0ms (1.9%)

eval122.0ms (1.1%)

prune45.0ms (0.4%)

simplify152.0ms (1.3%)

localize223.0ms (2%)

series20.0ms (0.2%)

simplify135.0ms (1.2%)

rewrite295.0ms (2.6%)

eval17.0ms (0.2%)

prune17.0ms (0.1%)

regimes18.0ms (0.2%)

regimes8.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

simplify57.0ms (0.5%)

soundness882.0ms (7.8%)

preprocess65.0ms (0.6%)

end0.0ms (0%)

Profiling