Metrics for 2tan (problem 3.3.2)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze108.0ms (0.9%)

Memory

-8.4MiB live, 46.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.0s (56.4%)

Memory

176.7MiB live, 7 864.7MiB allocated

Samples

3.6s	26 315×	0	invalid
723.0ms	5 532×	0	valid
469.0ms	2 724×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

const: 857.0ms (25.3% of total)

ival-tan: 705.0ms (20.9% of total)

ival-<=: 321.0ms (9.5% of total)

ival-add: 313.0ms (9.3% of total)

ival-mult: 273.0ms (8.1% of total)

ival-fabs: 271.0ms (8% of total)

ival-sub: 224.0ms (6.6% of total)

ival-<: 181.0ms (5.4% of total)

ival-and: 101.0ms (3% of total)

adjust: 79.0ms (2.3% of total)

exact: 44.0ms (1.3% of total)

ival-assert: 12.0ms (0.4% of total)

Bogosity

explain118.0ms (0.9%)

Memory

13.8MiB live, 289.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
232	1	(8.577321065122259e-61 7.987462559932218e-63)	1	(2.2283401437009445e-88 3.4489924662191003e-90)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
2	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`	cancellation	232	4
`tan.f64`	`(tan.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	232	1
-	1	22

Precision

0.9957081545064378

Recall

0.9957081545064378

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	232	1	0
-	1	3	19

Precision?

0.9831223628691983

Recall?

1.0

Freqs

test

number	freq
0	23
1	232
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms	182×	1	valid
20.0ms	326×	0	valid
1.0ms	4×	2	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-tan: 10.0ms (40.4% of total)

adjust: 8.0ms (32.4% of total)

ival-add: 3.0ms (12.1% of total)

ival-sub: 3.0ms (12.1% of total)

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

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

preprocess272.0ms (2.2%)

Memory

-9.5MiB live, 175.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	35	43
2	62	43
3	109	43
4	184	43
5	328	43
6	654	43
7	1492	43
8	3439	43
9	4340	43
10	6665	43
11	7416	43
12	7872	43
0	6	7
0	10	7
1	16	7
2	25	7
3	41	7
4	66	7
5	117	7
6	211	7
7	474	7
8	1311	7
9	2274	7
10	3303	7
11	3588	7
12	3771	7
13	3850	7
14	3868	7
15	3874	7
16	3880	7
17	3886	7
18	3892	7
19	3898	7
20	3904	7
21	3910	7
22	3916	7
23	3922	7
24	3928	7
25	7779	7
0	8041	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

series12.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

6 → 31

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
(/ (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
2.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	eps	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))

simplify652.0ms (5.3%)

Memory

-344.0MiB live, 252.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

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

rewrite189.0ms (1.5%)

Memory

0.2MiB live, 241.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	53	18
2	440	18
3	6608	18
0	8588	18

Stop Event

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

Counts

6 → 160

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

eval27.0ms (0.2%)

Memory: -3.1MiB live, 41.1MiB allocated
Compiler: Compiled 5 956 to 840 computations (85.9% saved)

prune15.0ms (0.1%)

Memory

-21.6MiB live, 23.8MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	174	12	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	174	13	187

Accuracy

100.0%

Counts

187 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.8%	(fma.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (-.f64 (/.f64 (tan.f64 eps) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x)))
▶	60.7%	(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	60.8%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
	60.8%	(-.f64 (+.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (/.f64 (tan.f64 eps) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))) (tan.f64 x))
	60.8%	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
	3.8%	(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
▶	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
✓	60.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	99.8%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
	99.7%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
	99.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

Compiler

Compiled 593 to 328 computations (44.7% saved)

simplify0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated

series132.0ms (1.1%)

Memory

13.8MiB live, 155.4MiB allocated

Counts

53 → 233

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))
(fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps)
(fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64))
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(sin.f64 x)
x
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(literal -1 binary64)
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
#s(literal -1/6 binary64)
eps
(/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
(tan.f64 (+.f64 (PI.f64) x))
(+.f64 (PI.f64) x)
(PI.f64)
#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 (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)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(tan.f64 eps)
(tan.f64 x)
(fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))
(neg.f64 (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)))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
x
(* x (+ 1 (* 5/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))
(* 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 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(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))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
(* eps x)
(* 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 (* -1/6 eps)))))))
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* -1/6 eps) (* 1/6 x))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(* (pow x 2) (+ 1 (* 1/6 (pow x 2))))
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(/ (sin x) (pow (cos x) 2))
(sin x)
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(cos x)
(/ (+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (pow (cos x) 2))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
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(/ 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))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
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(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ eps (/ (sin x) (cos x)))
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(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
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(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(* (pow eps 3) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))) 1/6))
(* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))) 1/6))
(/ (* 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 (* (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)))))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (* -1 (/ (+ (* -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))) eps)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) eps))) 1/6))
(* -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 (* (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)))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))

Calls

6 calls:

Time	Variable		Point	Expression
43.0ms	eps	@	inf	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan (+ (PI) x))) (tan (+ x eps)) (+ x eps) (tan (+ (PI) x)) (+ (PI) x) (PI) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (tan x) (+ (* (neg (tan x)) (tan eps)) 1) (neg (tan x)))
28.0ms	x	@	-inf	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan (+ (PI) x))) (tan (+ x eps)) (+ x eps) (tan (+ (PI) x)) (+ (PI) x) (PI) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (tan x) (+ (* (neg (tan x)) (tan eps)) 1) (neg (tan x)))
16.0ms	x	@	inf	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan (+ (PI) x))) (tan (+ x eps)) (+ x eps) (tan (+ (PI) x)) (+ (PI) x) (PI) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (tan x) (+ (* (neg (tan x)) (tan eps)) 1) (neg (tan x)))
15.0ms	eps	@	-inf	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan (+ (PI) x))) (tan (+ x eps)) (+ x eps) (tan (+ (PI) x)) (+ (PI) x) (PI) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (tan x) (+ (* (neg (tan x)) (tan eps)) 1) (neg (tan x)))
14.0ms	x	@	0	((- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (sin x) (pow (cos x) 2)) (sin x) x (pow (cos x) 2) (cos x) 2 1 -1/2 (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2)) (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2) (/ -1 (pow (cos x) 2)) -1 (* (pow (sin x) 2) 1/6) 1/6 -1/6 eps (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x)) (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 2) (cos x)) (- (tan (+ x eps)) (tan (+ (PI) x))) (tan (+ x eps)) (+ x eps) (tan (+ (PI) x)) (+ (PI) x) (PI) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan x)) (tan eps)) 1)) (+ (tan eps) (tan x)) (tan eps) (tan x) (+ (* (neg (tan x)) (tan eps)) 1) (neg (tan x)))

simplify164.0ms (1.3%)

Memory

36.2MiB live, 312.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	979	5605
1	3315	5331
0	8880	5043

Stop Event

1×	iter limit
1×	node limit

Counts

233 → 231

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 (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
x
(* x (+ 1 (* 5/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))
(* 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 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 1)
(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))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
(* eps x)
(* 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 (* -1/6 eps)))))))
(* x (+ eps (* x (+ 1 (* x (+ eps (+ (* -1/6 eps) (* 1/6 x))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(* (pow x 2) (+ 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))))))))
(- (/ (sin eps) (cos eps)) (/ (sin (PI)) (cos (PI))))
(- (+ (* x (- (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (/ (sin (PI)) (cos (PI))))
(- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* -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 (PI)) (cos (PI))))
(- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (+ (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* x (- (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (+ (* -1 (/ (* (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 (PI)) (cos (PI))))
(+ (* 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 x)
(/ (sin (PI)) (cos (PI)))
(+ (* x (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* x (- (+ 1 (/ (* x (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))
(PI)
(+ x (PI))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(sin eps)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))
(+ (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))))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(* 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))))))))
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))))))
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))))))))
(* -1 x)
(* x (- (* -1/3 (pow x 2)) 1))
(* x (- (* (pow x 2) (- (* -2/15 (pow x 2)) 1/3)) 1))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/315 (pow x 2)) 2/15)) 1/3)) 1))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(+ eps (* eps (+ (* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (+ (/ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (+ (/ (* (sin x) (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)
(+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (sin x) (pow (cos x) 2))
(sin x)
(pow (cos x) 2)
(cos x)
(/ (+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) (pow (cos x) 2))
(+ (* 1/6 (pow (sin x) 2)) (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)
(pow (sin x) 2)
(/ -1 (pow (cos x) 2))
(* 1/6 (pow (sin x) 2))
(/ (+ (* (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)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (cos x))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(* x (+ 1 (/ eps x)))
(/ (sin (+ x (PI))) (cos (+ x (PI))))
(* x (+ 1 (/ (PI) x)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(* (cos x) (cos (+ eps x)))
(cos (+ eps x))
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(* -1 (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin (- (PI) (* -1 x))) (cos (- (PI) (* -1 x)))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(/ (sin (- (PI) (* -1 x))) (cos (- (PI) (* -1 x))))
(* -1 (* x (- (* -1 (/ (PI) x)) 1)))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(* (cos x) (cos (- eps (* -1 x))))
(cos (- eps (* -1 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (cos x)))
(- (/ (sin x) (cos x)) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(- (+ (* 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))) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(- (+ (* 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 (PI))) (cos (+ x (PI)))))
(+ (* 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 (* 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)))
(/ 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))))
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2))
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x))))))
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x))))))))
(* (pow eps 3) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))) 1/6))
(* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))) 1/6))
(/ (* 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 (* (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)))))
(* eps (+ 1 (/ x eps)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (* -1 (/ (+ (* -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))) eps)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) eps))) 1/6))
(* -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 (* (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)))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin (+ x (PI))) (cos (+ x (PI)))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (cos (- x (* -1 eps))))
(cos (- x (* -1 eps)))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (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 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) #s(literal 1/2 binary64)) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ eps (* 1/3 (pow eps 3)))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(+.f64 (fma.f64 (.f64 eps eps) x (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(+.f64 (fma.f64 (.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps)) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(+.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)))) x (.f64 eps eps)) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64))) eps)
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 4/3 binary64) eps) x (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal 4/3 binary64) (*.f64 #s(literal 1/3 binary64) eps))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 4/3 binary64) eps)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) eps))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 17/9 binary64) eps)) (.f64 x x) (.f64 #s(literal 4/3 binary64) eps)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) eps))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (.f64 x x) #s(literal 4/3 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (.f64 x x) #s(literal 17/9 binary64)) (.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* -4/3 (pow x 2)) 1/2)
(-.f64 (.f64 #s(literal -4/3 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(-.f64 (.f64 (-.f64 (.f64 #s(literal -17/9 binary64) (.f64 x x)) #s(literal 4/3 binary64)) (.f64 x x)) #s(literal 1/2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(-.f64 (.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -248/135 binary64) (.f64 x x)) #s(literal 17/9 binary64)) (.f64 x x)) #s(literal 4/3 binary64)) (.f64 x x)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* 5/6 (pow x 2))))
(.f64 (fma.f64 #s(literal 5/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 61/120 binary64) (.f64 x x) #s(literal 5/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 277/1008 binary64) (.f64 x x) #s(literal 61/120 binary64)) (.f64 x x) #s(literal 5/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (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))
(* -5/6 (pow x 2))
(.f64 #s(literal -5/6 binary64) (.f64 x x))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(.f64 (-.f64 (.f64 #s(literal -14/9 binary64) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -89/54 binary64) (.f64 x x)) #s(literal 14/9 binary64)) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(.f64 (-.f64 (.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1289/945 binary64) (.f64 x x)) #s(literal 89/54 binary64)) (.f64 x x)) #s(literal 14/9 binary64)) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* -13/18 (pow x 2)) 5/6))
(.f64 (-.f64 (.f64 #s(literal -13/18 binary64) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* -10/27 (pow x 2)) 13/18)) 5/6))
(.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -10/27 binary64) (.f64 x x)) #s(literal 13/18 binary64)) (.f64 x x)) #s(literal 5/6 binary64)) (.f64 x x))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -373/1890 (pow x 2)) 10/27)) 13/18)) 5/6))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (+ 1 (* -1/6 (pow eps 2))))
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(+ 1 (* -1/2 (pow eps 2)))
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(/ eps (pow (cos x) 2))
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(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
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(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2))
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(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (/ x eps)))
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(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (* -1 (/ (+ (* -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))) eps)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))) 1/6))
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(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(sin (neg (* -1 eps)))
(sin.f64 eps)
(* (cos x) (cos (- x (* -1 eps))))
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))

rewrite230.0ms (1.9%)

Memory

13.0MiB live, 293.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	685
0	110	650
1	471	518
2	4094	518
0	8561	492

Stop Event

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

Counts

53 → 803

Calls

Call 1

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

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

eval393.0ms (3.2%)

Memory: 15.2MiB live, 729.1MiB allocated
Compiler: Compiled 112 534 to 9 852 computations (91.2% saved)

prune43.0ms (0.3%)

Memory

-32.6MiB live, 106.5MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 440	15	1 455
Fresh	5	2	7
Picked	4	1	5
Done	0	1	1
Total	1 449	19	1 468

Accuracy

100.0%

Counts

1 468 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(fma.f64 (/.f64 (tan.f64 eps) (-.f64 (pow.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 1 binary64)) (-.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x)))
	99.9%	(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
▶	56.4%	(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
▶	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	60.8%	(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 (+.f64 (neg.f64 x) (PI.f64))) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
▶	3.8%	(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
✓	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
✓	60.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.5%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	99.8%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	3.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))

Compiler

Compiled 1 092 to 640 computations (41.4% saved)

simplify0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated

series68.0ms (0.6%)

Memory

3.4MiB live, 163.3MiB allocated

Counts

37 → 161

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* eps eps) 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (tan x) (/ (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (* (cos (+ eps x)) (cos x))) (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x)) (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x) (+ 0 eps) 0)
12.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* eps eps) 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (tan x) (/ (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (* (cos (+ eps x)) (cos x))) (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x)) (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x) (+ 0 eps) 0)
6.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* eps eps) 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (tan x) (/ (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (* (cos (+ eps x)) (cos x))) (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x)) (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x) (+ 0 eps) 0)
6.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* eps eps) 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (tan x) (/ (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (* (cos (+ eps x)) (cos x))) (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x)) (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x) (+ 0 eps) 0)
6.0ms	x	@	0	((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (+ eps x) x (cos x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* eps eps) 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (- (tan (+ (+ (PI) x) eps)) (tan x)) (tan (+ (+ (PI) x) eps)) (+ (+ (PI) x) eps) (+ (PI) x) (PI) (tan x) (/ (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (* (cos (+ eps x)) (cos x))) (sin (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x))) (/ (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x)) (* (+ (+ eps x) x) (+ 0 eps)) (+ (+ eps x) x) (+ 0 eps) 0)

simplify174.0ms (1.4%)

Memory

-13.0MiB live, 218.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	663	4058
1	2299	3757
0	8899	3540

Stop Event

1×	iter limit
1×	node limit

Counts

161 → 159

Calls

Call 1

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

rewrite330.0ms (2.7%)

Memory

-1.5MiB live, 333.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	545
0	111	483
1	537	406
2	5264	406
0	8450	383

Stop Event

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

Counts

37 → 715

Calls

Call 1

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

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

eval311.0ms (2.5%)

Memory: 34.2MiB live, 320.4MiB allocated
Compiler: Compiled 99 525 to 6 858 computations (93.1% saved)

prune50.0ms (0.4%)

Memory

2.6MiB live, 136.7MiB allocated

Pruning

26 alts after pruning (21 fresh and 5 done)

	Pruned	Kept	Total
New	1 626	12	1 638
Fresh	3	9	12
Picked	2	3	5
Done	0	2	2
Total	1 631	26	1 657

Accuracy

100.0%

Counts

1 657 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(fma.f64 (/.f64 (tan.f64 eps) (-.f64 (pow.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 1 binary64)) (-.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x)))
	99.9%	(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
	56.4%	(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
	56.4%	(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
▶	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
▶	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
✓	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.2%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
✓	3.8%	(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
✓	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
✓	60.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.5%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶	35.3%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
▶	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	3.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
▶	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
	60.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
✓	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))

Compiler

Compiled 1 926 to 1 072 computations (44.3% saved)

simplify0.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated

series69.0ms (0.6%)

Memory

-28.3MiB live, 76.3MiB allocated

Counts

46 → 193

Calls

Call 1

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

Outputs
(/ (sin eps) (sin (+ eps (* 1/2 (PI)))))
(+ (* -1 (/ (* x (* (cos (+ eps (* 1/2 (PI)))) (sin eps))) (pow (sin (+ eps (* 1/2 (PI)))) 2))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos (+ eps (* 1/2 (PI)))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3))))) (sin (+ eps (* 1/2 (PI)))))) (+ (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)) (/ (* (sin eps) (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))) (pow (sin (+ eps (* 1/2 (PI)))) 2)))))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(sin eps)
(sin (+ eps (* 1/2 (PI))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1 (sin (+ eps (* 1/2 (PI))))) (* x (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(+ eps (* 1/2 (PI)))
(+ eps (+ x (* 1/2 (PI))))
x
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)))
(/ (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)))
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(pow x 2)
eps
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(/ (sin eps) (* (cos x) (sin (+ eps (+ x (* 1/2 (PI)))))))
(* (cos x) (sin (+ eps (+ x (* 1/2 (PI))))))
(sin (+ eps (+ x (* 1/2 (PI)))))
(* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))
(cos x)
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(/ (sin eps) (* (cos x) (sin (- (* 1/2 (PI)) (+ eps x)))))
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(* (cos x) (sin (- (+ eps (* 1/2 (PI))) (* -1 x))))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(sin (- (+ (* -1 x) (* 1/2 (PI))) eps))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2)))) (+ (* 1/2 (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2)))) (/ (* (cos (+ x (* 1/2 (PI)))) (- (* 1/2 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI))))))) (+ (* -1 (/ (pow (cos (+ x (* 1/2 (PI)))) 2) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))))) (sin (+ x (* 1/2 (PI))))))))) (* 1/2 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))) (+ (* -1 (/ (pow (cos (+ x (* 1/2 (PI)))) 2) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))))) (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2))))) (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI))))))))
(* 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))))
(* (cos x) (sin (+ x (* 1/2 (PI)))))
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(sin (+ x (* 1/2 (PI))))
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(+ x (* 1/2 (PI)))
(* 1/2 (PI))
(* 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 (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (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 (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow 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))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))
(+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))
1/3
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(+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))
2/15
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(pow eps 2)
(+ x (* eps (+ 1 (* 4/3 (* eps x)))))
(+ 1 (* 4/3 (pow eps 2)))
(pow eps 3)
(/ eps (* (cos x) (sin (- (* 1/2 (PI)) x))))
(* eps (+ (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))) (/ (* eps (cos (- (* 1/2 (PI)) x))) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (* -1 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))) (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos (- (* 1/2 (PI)) x)) (- (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (sin (- (* 1/2 (PI)) x)))) (+ (* -1/2 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))) (* 1/6 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))))) (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (* -1 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))) (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))))
(* (cos x) (sin (- (* 1/2 (PI)) x)))
(+ (* -1 (* eps (* (cos x) (cos (- (* 1/2 (PI)) x))))) (* (cos x) (sin (- (* 1/2 (PI)) x))))
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(+ (* eps (+ (* -1 (* (cos x) (cos (- (* 1/2 (PI)) x)))) (* eps (+ (* -1/2 (* (cos x) (sin (- (* 1/2 (PI)) x)))) (* 1/6 (* eps (* (cos x) (cos (- (* 1/2 (PI)) x))))))))) (* (cos x) (sin (- (* 1/2 (PI)) x))))
(sin (- (* 1/2 (PI)) x))
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(+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* -1/2 (* eps (sin (- (* 1/2 (PI)) x)))))))
(+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) x))) (* 1/6 (* eps (cos (- (* 1/2 (PI)) x)))))))))
(- (* 1/2 (PI)) x)
(- (+ (* -1 eps) (* 1/2 (PI))) x)
(- (* -1 eps) x)
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
(* eps (+ 1 (* 1/2 (/ (PI) eps))))
(* (pow eps 3) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))) 1/6))
(* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* 17/315 (pow eps 7))
(* (pow eps 7) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 7) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* (pow eps 7) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (+ (* 2/15 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(* 17/315 (pow eps 6))
(* (pow eps 6) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 6) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* (pow eps 6) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (+ (* 2/15 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(* 17/315 (pow eps 4))
(* (pow eps 4) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 4) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* 17/315 (pow eps 2))
(* (pow eps 2) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(* 4/3 (pow eps 2))
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))
(* eps (- (* 1/2 (/ (PI) eps)) (+ 1 (/ x eps))))
(* eps (- (* -1 (/ x eps)) 1))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (sin (- (+ x (* 1/2 (PI))) (* -1 eps))))
(sin (- (+ x (* 1/2 (PI))) (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))
(* -1 (* eps (- (* -1/2 (/ (PI) eps)) 1)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (* -1 (/ (+ (* -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))) eps)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) eps))) 1/6))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* -1 (* (pow eps 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))) (pow eps 2))) 17/315)))
(* -1 (* (pow eps 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 4))) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))
(/ (sin (neg (* -1 eps))) (* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x))))
(* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x)))
(sin (- (+ (* -1 eps) (* 1/2 (PI))) x))
(* -1 (* eps (+ 1 (* -1 (/ (- (* 1/2 (PI)) x) eps)))))
(* -1 (* eps (+ 1 (/ x eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	eps	@	-inf	((/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x)) (sin (+ x (+ (/ (PI) 2) eps))) (+ x (+ (/ (PI) 2) eps)) x (+ (/ (PI) 2) eps) (/ (PI) 2) (PI) 2 (cos x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (* x x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (+ (* 17/315 (* eps eps)) 2/15) 17/315 (* eps eps) 2/15 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) (/ (pow eps 3) (* eps eps))) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (/ (pow eps 3) (* eps eps)) (pow eps 3) 3 (/ (sin (- (+ eps x) x)) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x))) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x)) (sin (+ (neg (+ x eps)) (/ (PI) 2))) (+ (neg (+ x eps)) (/ (PI) 2)) (neg (+ x eps)) (+ x eps))
11.0ms	x	@	inf	((/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x)) (sin (+ x (+ (/ (PI) 2) eps))) (+ x (+ (/ (PI) 2) eps)) x (+ (/ (PI) 2) eps) (/ (PI) 2) (PI) 2 (cos x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (* x x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (+ (* 17/315 (* eps eps)) 2/15) 17/315 (* eps eps) 2/15 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) (/ (pow eps 3) (* eps eps))) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (/ (pow eps 3) (* eps eps)) (pow eps 3) 3 (/ (sin (- (+ eps x) x)) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x))) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x)) (sin (+ (neg (+ x eps)) (/ (PI) 2))) (+ (neg (+ x eps)) (/ (PI) 2)) (neg (+ x eps)) (+ x eps))
8.0ms	x	@	-inf	((/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x)) (sin (+ x (+ (/ (PI) 2) eps))) (+ x (+ (/ (PI) 2) eps)) x (+ (/ (PI) 2) eps) (/ (PI) 2) (PI) 2 (cos x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (* x x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (+ (* 17/315 (* eps eps)) 2/15) 17/315 (* eps eps) 2/15 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) (/ (pow eps 3) (* eps eps))) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (/ (pow eps 3) (* eps eps)) (pow eps 3) 3 (/ (sin (- (+ eps x) x)) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x))) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x)) (sin (+ (neg (+ x eps)) (/ (PI) 2))) (+ (neg (+ x eps)) (/ (PI) 2)) (neg (+ x eps)) (+ x eps))
7.0ms	eps	@	inf	((/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x)) (sin (+ x (+ (/ (PI) 2) eps))) (+ x (+ (/ (PI) 2) eps)) x (+ (/ (PI) 2) eps) (/ (PI) 2) (PI) 2 (cos x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (* x x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (+ (* 17/315 (* eps eps)) 2/15) 17/315 (* eps eps) 2/15 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) (/ (pow eps 3) (* eps eps))) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (/ (pow eps 3) (* eps eps)) (pow eps 3) 3 (/ (sin (- (+ eps x) x)) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x))) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x)) (sin (+ (neg (+ x eps)) (/ (PI) 2))) (+ (neg (+ x eps)) (/ (PI) 2)) (neg (+ x eps)) (+ x eps))
7.0ms	eps	@	0	((/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (sin (- (+ eps x) x)) (sin eps) eps (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x)) (sin (+ x (+ (/ (PI) 2) eps))) (+ x (+ (/ (PI) 2) eps)) x (+ (/ (PI) 2) eps) (/ (PI) 2) (PI) 2 (cos x) (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) eps) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (* x x) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) eps) (+ (* (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (* eps eps)) 1) (+ (* (+ (* 17/315 (* eps eps)) 2/15) (* eps eps)) 1/3) (+ (* 17/315 (* eps eps)) 2/15) 17/315 (* eps eps) 2/15 1/3 1 (- (tan (+ x eps)) (tan x)) (+ (* (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) eps) (/ (pow eps 3) (* eps eps))) (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) (+ (* 4/3 (* eps eps)) 1) 4/3 (* (* eps eps) 1/3) (/ (pow eps 3) (* eps eps)) (pow eps 3) 3 (/ (sin (- (+ eps x) x)) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x))) (* (sin (+ (neg (+ x eps)) (/ (PI) 2))) (cos x)) (sin (+ (neg (+ x eps)) (/ (PI) 2))) (+ (neg (+ x eps)) (/ (PI) 2)) (neg (+ x eps)) (+ x eps))

simplify174.0ms (1.4%)

Memory

-1.7MiB live, 186.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	4884
1	2692	4678
0	9061	4351

Stop Event

1×	iter limit
1×	node limit

Counts

193 → 191

Calls

Call 1

Inputs
(/ (sin eps) (sin (+ eps (* 1/2 (PI)))))
(+ (* -1 (/ (* x (* (cos (+ eps (* 1/2 (PI)))) (sin eps))) (pow (sin (+ eps (* 1/2 (PI)))) 2))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos (+ eps (* 1/2 (PI)))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3))))) (sin (+ eps (* 1/2 (PI)))))) (+ (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)) (/ (* (sin eps) (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))) (pow (sin (+ eps (* 1/2 (PI)))) 2)))))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(sin eps)
(sin (+ eps (* 1/2 (PI))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1 (sin (+ eps (* 1/2 (PI))))) (* x (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(+ eps (* 1/2 (PI)))
(+ eps (+ x (* 1/2 (PI))))
x
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)))
(/ (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)))
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(pow x 2)
eps
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(/ (sin eps) (* (cos x) (sin (+ eps (+ x (* 1/2 (PI)))))))
(* (cos x) (sin (+ eps (+ x (* 1/2 (PI))))))
(sin (+ eps (+ x (* 1/2 (PI)))))
(* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))
(cos x)
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(/ (sin eps) (* (cos x) (sin (- (* 1/2 (PI)) (+ eps x)))))
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(* (cos x) (sin (- (+ eps (* 1/2 (PI))) (* -1 x))))
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(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
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(sin (- (+ (* -1 x) (* 1/2 (PI))) eps))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2)))) (+ (* 1/2 (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2)))) (/ (* (cos (+ x (* 1/2 (PI)))) (- (* 1/2 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI))))))) (+ (* -1 (/ (pow (cos (+ x (* 1/2 (PI)))) 2) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))))) (sin (+ x (* 1/2 (PI))))))))) (* 1/2 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))) (+ (* -1 (/ (pow (cos (+ x (* 1/2 (PI)))) 2) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI)))))))))) (/ (cos (+ x (* 1/2 (PI)))) (* (cos x) (pow (sin (+ x (* 1/2 (PI)))) 2))))) (/ 1 (* (cos x) (sin (+ x (* 1/2 (PI))))))))
(* 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))))
(* (cos x) (sin (+ x (* 1/2 (PI)))))
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(sin (+ x (* 1/2 (PI))))
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(+ x (* 1/2 (PI)))
(* 1/2 (PI))
(* 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 (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (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 (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps x) (pow x 2))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow 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))))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))
(+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))
1/3
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(+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))
2/15
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(pow eps 2)
(+ x (* eps (+ 1 (* 4/3 (* eps x)))))
(+ 1 (* 4/3 (pow eps 2)))
(pow eps 3)
(/ eps (* (cos x) (sin (- (* 1/2 (PI)) x))))
(* eps (+ (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))) (/ (* eps (cos (- (* 1/2 (PI)) x))) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (* -1 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))) (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos (- (* 1/2 (PI)) x)) (- (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (sin (- (* 1/2 (PI)) x)))) (+ (* -1/2 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))) (* 1/6 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))))) (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (* -1 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))) (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))))
(* (cos x) (sin (- (* 1/2 (PI)) x)))
(+ (* -1 (* eps (* (cos x) (cos (- (* 1/2 (PI)) x))))) (* (cos x) (sin (- (* 1/2 (PI)) x))))
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(+ (* eps (+ (* -1 (* (cos x) (cos (- (* 1/2 (PI)) x)))) (* eps (+ (* -1/2 (* (cos x) (sin (- (* 1/2 (PI)) x)))) (* 1/6 (* eps (* (cos x) (cos (- (* 1/2 (PI)) x))))))))) (* (cos x) (sin (- (* 1/2 (PI)) x))))
(sin (- (* 1/2 (PI)) x))
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(+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* -1/2 (* eps (sin (- (* 1/2 (PI)) x)))))))
(+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) x))) (* 1/6 (* eps (cos (- (* 1/2 (PI)) x)))))))))
(- (* 1/2 (PI)) x)
(- (+ (* -1 eps) (* 1/2 (PI))) x)
(- (* -1 eps) x)
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
(* eps (+ 1 (* 1/2 (/ (PI) eps))))
(* (pow eps 3) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2)))))) 1/6))
(* (pow eps 2) (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))))) 1/6))
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))))
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))
(* 17/315 (pow eps 7))
(* (pow eps 7) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 7) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* (pow eps 7) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (+ (* 2/15 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(* 17/315 (pow eps 6))
(* (pow eps 6) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 6) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* (pow eps 6) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (+ (* 2/15 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(* 17/315 (pow eps 4))
(* (pow eps 4) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* (pow eps 4) (+ 17/315 (+ (/ 1/3 (pow eps 4)) (* 2/15 (/ 1 (pow eps 2))))))
(* 17/315 (pow eps 2))
(* (pow eps 2) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))
(* 4/3 (* (pow eps 2) x))
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps)))
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2)))))
(* 4/3 (pow eps 2))
(* (pow eps 2) (+ 4/3 (/ 1 (pow eps 2))))
(* eps (- (* 1/2 (/ (PI) eps)) (+ 1 (/ x eps))))
(* eps (- (* -1 (/ x eps)) 1))
(* eps (+ 1 (/ x eps)))
(/ (sin (neg (* -1 eps))) (* (cos x) (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
(sin (neg (* -1 eps)))
(* (cos x) (sin (- (+ x (* 1/2 (PI))) (* -1 eps))))
(sin (- (+ x (* 1/2 (PI))) (* -1 eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))
(* -1 (* eps (- (* -1/2 (/ (PI) eps)) 1)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (* -1 (/ (+ (* -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))) eps)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (* eps (cos x))))) 1/6))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (cos x))) eps))) 1/6))
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) eps))) eps)) (* 4/3 (pow x 2)))))
(* -1 (* (pow eps 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))) (pow eps 2))) 17/315)))
(* -1 (* (pow eps 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 4))) (+ 17/315 (* 2/15 (/ 1 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)))
(/ (sin (neg (* -1 eps))) (* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x))))
(* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x)))
(sin (- (+ (* -1 eps) (* 1/2 (PI))) x))
(* -1 (* eps (+ 1 (* -1 (/ (- (* 1/2 (PI)) x) eps)))))
(* -1 (* eps (+ 1 (/ x eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Outputs
(/ (sin eps) (sin (+ eps (* 1/2 (PI)))))
(/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (* -1 (/ (* x (* (cos (+ eps (* 1/2 (PI)))) (sin eps))) (pow (sin (+ eps (* 1/2 (PI)))) 2))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(fma.f64 (neg.f64 x) (/.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (sin.f64 eps)) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(fma.f64 (fma.f64 (neg.f64 x) (neg.f64 (fma.f64 (pow.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))) (*.f64 (neg.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos (+ eps (* 1/2 (PI)))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3))))) (sin (+ eps (* 1/2 (PI)))))) (+ (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)) (/ (* (sin eps) (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))) (pow (sin (+ eps (* 1/2 (PI)))) 2)))))) (+ (* -1 (/ (sin eps) (sin (+ eps (* 1/2 (PI)))))) (* -1 (/ (* (pow (cos (+ eps (* 1/2 (PI)))) 2) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 3)))))) (/ (* (cos (+ eps (* 1/2 (PI)))) (sin eps)) (pow (sin (+ eps (* 1/2 (PI)))) 2)))) (/ (sin eps) (sin (+ eps (* 1/2 (PI))))))
(fma.f64 (fma.f64 (-.f64 (.f64 (neg.f64 x) (fma.f64 (neg.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) (/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) (/.f64 (.f64 (sin.f64 eps) (+.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -2/3 binary64)))) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) (neg.f64 (fma.f64 (pow.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))))) x (.f64 (neg.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) x (/.f64 (sin.f64 eps) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))))
(sin eps)
(sin.f64 eps)
(sin (+ eps (* 1/2 (PI))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1 (* x (sin (+ eps (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (neg.f64 x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1 (sin (+ eps (* 1/2 (PI))))) (* x (+ (* -1/2 (cos (+ eps (* 1/2 (PI))))) (* -1/6 (cos (+ eps (* 1/2 (PI))))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x) #s(literal -2/3 binary64) (neg.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 x #s(literal -1/6 binary64)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ eps (* 1/2 (PI)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)
(+ eps (+ x (* 1/2 (PI))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps))
x
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (*.f64 x (sin.f64 eps)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ eps (* 1/3 (pow eps 3)))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x)))
(fma.f64 (*.f64 eps eps) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))))
(fma.f64 (.f64 eps (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps #s(literal 4/3 binary64)) x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps)) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))
(* 1/3 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(+ (* 1/3 (pow eps 2)) (* eps x))
(fma.f64 (.f64 #s(literal 1/3 binary64) eps) eps (.f64 x eps))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))
(+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps #s(literal 4/3 binary64)) x (fma.f64 (.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))
(pow x 2)
(*.f64 x x)
eps
(+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)
(/ (sin eps) (sin (- (* 1/2 (PI)) eps)))
(/.f64 (sin.f64 eps) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))
(+ (/ (sin eps) (sin (- (* 1/2 (PI)) eps))) (/ (* x (* (cos (- (* 1/2 (PI)) eps)) (sin eps))) (pow (sin (- (* 1/2 (PI)) eps)) 2)))
(fma.f64 x (/.f64 (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) (sin.f64 eps)) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps))))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (sin (- (* 1/2 (PI)) eps)))) (* -1 (/ (* (pow (cos (- (* 1/2 (PI)) eps)) 2) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 3)))))) (* -1 (/ (* (cos (- (* 1/2 (PI)) eps)) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 2))))) (/ (sin eps) (sin (- (* 1/2 (PI)) eps))))
(fma.f64 (fma.f64 (neg.f64 x) (neg.f64 (fma.f64 (pow.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps))))) (/.f64 (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) (sin.f64 eps)) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps))))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos (- (* 1/2 (PI)) eps)) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 2))) (+ (/ (* (cos (- (* 1/2 (PI)) eps)) (+ (* -1 (/ (sin eps) (sin (- (* 1/2 (PI)) eps)))) (* -1 (/ (* (pow (cos (- (* 1/2 (PI)) eps)) 2) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 3))))) (sin (- (* 1/2 (PI)) eps))) (/ (* (sin eps) (+ (* 1/6 (cos (- (* 1/2 (PI)) eps))) (* 1/2 (cos (- (* 1/2 (PI)) eps))))) (pow (sin (- (* 1/2 (PI)) eps)) 2)))))) (+ (* -1 (/ (sin eps) (sin (- (* 1/2 (PI)) eps)))) (* -1 (/ (* (pow (cos (- (* 1/2 (PI)) eps)) 2) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 3)))))) (* -1 (/ (* (cos (- (* 1/2 (PI)) eps)) (sin eps)) (pow (sin (- (* 1/2 (PI)) eps)) 2))))) (/ (sin eps) (sin (- (* 1/2 (PI)) eps))))
(fma.f64 (fma.f64 (-.f64 (.f64 (neg.f64 x) (fma.f64 (neg.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps))) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) (fma.f64 (sin.f64 eps) (/.f64 (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2/3 binary64)) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) (/.f64 (.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps))))) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))))) (neg.f64 (fma.f64 (pow.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))))) x (/.f64 (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) (sin.f64 eps)) (pow.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps))))
(sin (- (* 1/2 (PI)) eps))
(sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps))
(+ (sin (- (* 1/2 (PI)) eps)) (* -1 (* x (cos (- (* 1/2 (PI)) eps)))))
(fma.f64 (neg.f64 x) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))
(+ (sin (- (* 1/2 (PI)) eps)) (* x (+ (* -1 (cos (- (* 1/2 (PI)) eps))) (* -1 (* x (sin (- (* 1/2 (PI)) eps)))))))
(fma.f64 (neg.f64 (fma.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)) x (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))) x (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps)))
(+ (sin (- (* 1/2 (PI)) eps)) (* x (+ (* -1 (cos (- (* 1/2 (PI)) eps))) (* x (+ (* -1 (sin (- (* 1/2 (PI)) eps))) (* x (+ (* 1/6 (cos (- (* 1/2 (PI)) eps))) (* 1/2 (cos (- (* 1/2 (PI)) eps))))))))))
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)) (pow (cos x) 2))))) 1/6)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
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(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 x eps))
(+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
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(+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))
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1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/15 (pow eps 2)))
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(+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))
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2/15
#s(literal 2/15 binary64)
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(pow eps 2)
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(+ 1 (* 4/3 (pow eps 2)))
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(pow eps 3)
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(/ eps (* (cos x) (sin (- (* 1/2 (PI)) x))))
(/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
(* eps (+ (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))) (/ (* eps (cos (- (* 1/2 (PI)) x))) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (cos (- (* 1/2 (PI)) x)) (- (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (sin (- (* 1/2 (PI)) x)))) (+ (* -1/2 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))) (* 1/6 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))))) (* 1/2 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))) (+ (* -1 (/ (pow (cos (- (* 1/2 (PI)) x)) 2) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 3)))) (* 1/6 (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x)))))))) (* -1 (/ (cos (- (* 1/2 (PI)) x)) (* (cos x) (pow (sin (- (* 1/2 (PI)) x)) 2)))))) (/ 1 (* (cos x) (sin (- (* 1/2 (PI)) x))))))
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(* (cos x) (sin (- (* 1/2 (PI)) x)))
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(sin (- (* 1/2 (PI)) x))
(sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(+ (sin (- (* 1/2 (PI)) x)) (* -1 (* eps (cos (- (* 1/2 (PI)) x)))))
(fma.f64 (neg.f64 eps) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
(+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* -1/2 (* eps (sin (- (* 1/2 (PI)) x)))))))
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(- (* 1/2 (PI)) x)
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
(- (+ (* -1 eps) (* 1/2 (PI))) x)
(-.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x)
(- (* -1 eps) x)
(-.f64 (neg.f64 eps) x)
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
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(.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)) (neg.f64 eps))) (.f64 eps eps))
(/ (sin (neg (* -1 eps))) (* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x))))
(/.f64 (sin.f64 eps) (.f64 (sin.f64 (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x)) (cos.f64 x)))
(* (cos x) (sin (- (+ (* -1 eps) (* 1/2 (PI))) x)))
(.f64 (sin.f64 (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x)) (cos.f64 x))
(sin (- (+ (* -1 eps) (* 1/2 (PI))) x))
(sin.f64 (-.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x))
(* -1 (* eps (+ 1 (* -1 (/ (- (* 1/2 (PI)) x) eps)))))
(.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x) eps)))
(* -1 (* eps (+ 1 (/ x eps))))
(neg.f64 (fma.f64 (/.f64 x eps) eps eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite250.0ms (2%)

Memory

24.6MiB live, 218.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	955
0	136	940
1	607	760
2	5145	760
0	8053	718

Stop Event

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

Counts

46 → 648

Calls

Call 1

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

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

eval180.0ms (1.5%)

Memory: -13.3MiB live, 265.9MiB allocated
Compiler: Compiled 66 480 to 4 750 computations (92.9% saved)

prune60.0ms (0.5%)

Memory

16.9MiB live, 161.7MiB allocated

Pruning

26 alts after pruning (19 fresh and 7 done)

	Pruned	Kept	Total
New	935	8	943
Fresh	5	11	16
Picked	3	2	5
Done	0	5	5
Total	943	26	969

Accuracy

100.0%

Counts

969 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (fma.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x) (.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x))))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (sin.f64 #s(approx (+ (neg (+ x eps)) (/ (PI) 2)) (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x))) (cos.f64 x)))
	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 #s(approx (+ x (+ (/ (PI) 2) eps)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps)))) (cos.f64 x)))
✓	99.9%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
	99.2%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
	99.8%	(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
✓	3.8%	(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
✓	6.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
✓	60.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.5%	#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
	99.5%	#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
	35.4%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
	98.5%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
✓	99.2%	#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
	3.4%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
✓	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
	60.3%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
✓	98.6%	#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))

Compiler

Compiled 2 824 to 916 computations (67.6% saved)

regimes38.0ms (0.3%)

Memory

15.9MiB live, 59.7MiB allocated

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 #s(approx (+ x (+ (/ (PI) 2) eps)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps)))) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (sin.f64 #s(approx (+ (neg (+ x eps)) (/ (PI) 2)) (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 (+.f64 (neg.f64 x) (PI.f64))) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (fma.f64 (.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x) (.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x))))
(-.f64 (+.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (/.f64 (tan.f64 eps) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64)))) (tan.f64 x))
(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x)) eps eps))
(fma.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (-.f64 (/.f64 (tan.f64 eps) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x)))
(fma.f64 (/.f64 (tan.f64 eps) (-.f64 (pow.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps)) #s(literal 1 binary64)) (-.f64 (/.f64 (tan.f64 x) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64) #s(literal -1/6 binary64)) eps) eps (/.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) (cos.f64 x))) eps eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes57.0ms (0.5%)

Memory

-33.7MiB live, 22.9MiB allocated

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 #s(approx (+ x (+ (/ (PI) 2) eps)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps)))) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (sin.f64 #s(approx (+ (neg (+ x eps)) (/ (PI) 2)) (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
(/.f64 (sin.f64 (/.f64 (.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (+.f64 eps x) x))) (.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 (+.f64 (neg.f64 x) (PI.f64))) (tan.f64 eps) #s(literal 1 binary64))) (tan.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x))) (cos.f64 x)))

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

Calls

3 calls:

37.0ms	x
9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 #s(approx (+ x (+ (/ (PI) 2) eps)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps)))) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (sin.f64 #s(approx (+ (neg (+ x eps)) (/ (PI) 2)) (-.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) eps) x))) (cos.f64 x)))
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 x (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 x)))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (cos.f64 x)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

-9.5MiB live, 35.0MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))

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

Calls

3 calls:

9.0ms	x
6.0ms	eps
6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.2%)

Memory

-10.0MiB live, 33.5MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) #s(approx (+ (* (+ (* (+ (* 4/3 (* eps eps)) 1) x) eps) x) (* (* eps eps) 1/3)) (*.f64 x (+.f64 x eps)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (-.f64 (+.f64 x eps) x))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) (.f64 eps x))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 #s(approx (+ ( 17/315 (* eps eps)) 2/15) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (.f64 eps eps) #s(literal 2/15 binary64)) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 #s(approx (+ (* 4/3 (* eps eps)) 1) (.f64 #s(literal 4/3 binary64) (.f64 eps eps))) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) eps eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (.f64 (.f64 eps eps) eps) (.f64 eps eps))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (+ (* (* (+ (* (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/2) (/ (+ (* (+ (* (pow (sin x) 2) (/ -1 (pow (cos x) 2))) -1) (pow (sin x) 2)) (* (pow (sin x) 2) 1/6)) (pow (cos x) 2))) -1) -1/6) eps) eps) (/ (+ (* (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (sin x)) (/ (pow (sin x) 2) (cos x))) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 eps eps) #s(literal 1 binary64)) x eps) x (.f64 (.f64 eps eps) #s(literal 1/3 binary64)))) eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (PI.f64) x)))
(-.f64 (tan.f64 (+.f64 (+.f64 (PI.f64) x) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 (PI.f64) x) (PI.f64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (sin (+ x (+ (/ (PI) 2) eps))) (cos x))) (/.f64 (/.f64 eps (cos.f64 x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))))

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

Calls

3 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

31.6MiB live, 31.6MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify89.0ms (0.7%)

Memory

-66.6MiB live, 57.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	350
1	189	328
2	504	312
3	2195	288

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness985.0ms (7.9%)

Memory

18.5MiB live, 680.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	4884
1	2692	4678
0	9061	4351
0	979	5605
1	3315	5331
0	8880	5043
0	663	4058
1	2299	3757
0	8899	3540
0	96	955
0	136	940
1	607	760
2	5145	760
0	8053	718
0	6	18
0	10	18
1	53	18
2	440	18
3	6608	18
0	8588	18
0	157	970
1	488	910
2	1845	849
0	8454	797
0	80	545
0	111	483
1	537	406
2	5264	406
0	8450	383

Stop Event

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

Compiler

Compiled 704 to 327 computations (53.6% saved)

preprocess120.0ms (1%)

Memory: 32.2MiB live, 77.6MiB allocated
Compiler: Compiled 736 to 234 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze108.0ms (0.9%)

sample7.0s (56.4%)

explain118.0ms (0.9%)

preprocess272.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series12.0ms (0.1%)

simplify652.0ms (5.3%)

rewrite189.0ms (1.5%)

eval27.0ms (0.2%)

prune15.0ms (0.1%)

simplify0.0ms (0%)

series132.0ms (1.1%)

simplify164.0ms (1.3%)

rewrite230.0ms (1.9%)

eval393.0ms (3.2%)

prune43.0ms (0.3%)

simplify0.0ms (0%)

series68.0ms (0.6%)

simplify174.0ms (1.4%)

rewrite330.0ms (2.7%)

eval311.0ms (2.5%)

prune50.0ms (0.4%)

simplify0.0ms (0%)

series69.0ms (0.6%)

simplify174.0ms (1.4%)

rewrite250.0ms (2%)

eval180.0ms (1.5%)

prune60.0ms (0.5%)

regimes38.0ms (0.3%)

regimes57.0ms (0.5%)

regimes24.0ms (0.2%)

regimes22.0ms (0.2%)

regimes21.0ms (0.2%)

regimes16.0ms (0.1%)

regimes3.0ms (0%)

simplify89.0ms (0.7%)

soundness985.0ms (7.9%)

preprocess120.0ms (1%)

end0.0ms (0%)

Profiling