Details

analyze302.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 96 to 69 computations (28.1% saved)

sample110.0ms (0.6%)

Algorithm

1×

intervals

Results

59.0ms	256×	body	128	valid
16.0ms	256×	pre	128	true

Compiler

Compiled 173 to 125 computations (27.7% saved)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

493×	`associate--l+_binary32`
415×	`unsub-neg_binary32`
384×	`associate--l-_binary32`
362×	`distribute-rgt-in_binary32`
356×	`distribute-neg-in_binary32`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	101
1	66	101
2	189	72
3	606	72
4	1602	72
5	2259	72
6	4869	72
7	4951	72

prune19.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))

Status

Error

Program

▶

0.4b

(+.f32 (*.f32 (sqrt.f32 (-.f32 1 (*.f32 (*.f32 ux (*.f32 (-.f32 1 ux) maxCos)) (*.f32 ux (*.f32 (-.f32 1 ux) maxCos))))) (+.f32 (*.f32 (cos.f32 (*.f32 (*.f32 uy 2) PI.f32)) xi) (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) yi))) (*.f32 (*.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))

Compiler

Compiled 156 to 111 computations (28.8% saved)

localize82.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 ux (.f32 (-.f32 1 ux) maxCos))
0.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite313.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

21×	`pow1_binary32` `add-exp-log_binary32` `add-cbrt-cube_binary32`
11×	`add-sqr-sqrt_binary32`
10×	`pow-prod-down_binary32` `prod-exp_binary32` `cbrt-unprod_binary32` `associate-r_binary32`
9×	`add-cube-cbrt_binary32` `*-un-lft-identity_binary32`
8×	`associate-l_binary32`

Counts

4 → 74

Calls

4 calls:

8.0ms	(.f32 ux (.f32 (-.f32 1 ux) maxCos))
7.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)

Compiler

Compiled 3439 to 2256 computations (34.4% saved)

series227.0ms (1.2%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

69.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
59.0ms	(.f32 ux (.f32 (-.f32 1 ux) maxCos))
29.0ms	(.f32 (.f32 uy 2) PI.f32)
24.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 2786 to 1950 computations (30% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

391×	`unsub-neg_binary32`
309×	`neg-mul-1_binary32`
299×	`neg-sub0_binary32`
258×	`associate-l_binary32`
253×	`+-commutative_binary32`

Counts

98 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1431
1	379	1230
2	1300	1215
3	2321	1206
4	4186	1206
5	5106	1206

prune288.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	66	11	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Error

0.1b

Counts

78 → 11

Alt Table

Status	Error	Program
▶	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	2.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 2 (.f32 uy (.f32 PI.f32 yi))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))) zi))
	18.6b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 yi)) (sqrt.f32 yi)))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (sqrt.f32 PI.f32)) (sqrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	1.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (-.f32 (.f32 2 (.f32 uy (.f32 PI.f32 yi))) (.f32 4/3 (.f32 yi (pow.f32 (.f32 uy PI.f32) 3)))))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (.f32 (cbrt.f32 ux) (cbrt.f32 ux)) (.f32 (-.f32 maxCos (*.f32 maxCos ux)) (cbrt.f32 ux))) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux)) zi))

Compiler

Compiled 3897 to 2495 computations (36% saved)

localize104.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
0.3b	(.f32 (.f32 (+.f32 uy uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.6b	(.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))

rewrite503.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`pow1_binary32` `add-exp-log_binary32`
18×	`add-cbrt-cube_binary32`
17×	`add-sqr-sqrt_binary32` `associate-l_binary32`
16×	`*-un-lft-identity_binary32`
14×	`add-cube-cbrt_binary32`

Counts

4 → 92

Calls

4 calls:

15.0ms	(.f32 (.f32 (+.f32 uy uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))
12.0ms	(.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))
6.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)

Compiler

Compiled 4783 to 2404 computations (49.7% saved)

series199.0ms (1.1%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

66.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
40.0ms	(.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)))
24.0ms	(.f32 (.f32 uy 2) PI.f32)
23.0ms	(.f32 (.f32 (+.f32 uy uy) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))

Compiler

Compiled 2352 to 1557 computations (33.8% saved)

simplify154.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

386×	`associate-l_binary32`
358×	`distribute-rgt-out_binary32`
315×	`associate-r_binary32`
245×	`count-2_binary32`
189×	`unswap-sqr_binary32`

Counts

110 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	1798
1	421	1566
2	1561	1482
3	2646	1476
4	4838	1476
5	4880	1476
6	5000	1476
7	4916	1476

prune389.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	90	11	101

Error

0.1b

Counts

101 → 11

Alt Table

Status	Error	Program
	2.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 2 (.f32 uy (.f32 PI.f32 yi))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))) zi))
	18.6b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 yi)) (sqrt.f32 yi)))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (sqrt.f32 PI.f32)) (sqrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	1.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (-.f32 (.f32 2 (.f32 uy (.f32 PI.f32 yi))) (.f32 4/3 (.f32 yi (pow.f32 (.f32 uy PI.f32) 3)))))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 (sqrt.f32 (+.f32 uy uy)) (.f32 (cbrt.f32 (pow.f32 PI.f32 2)) (sqrt.f32 (+.f32 uy uy)))) (cbrt.f32 PI.f32))) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (.f32 (cbrt.f32 ux) (cbrt.f32 ux)) (.f32 (-.f32 maxCos (*.f32 maxCos ux)) (cbrt.f32 ux))) zi))
▶	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux)) zi))

Compiler

Compiled 4655 to 2772 computations (40.5% saved)

localize102.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
0.3b	(/.f32 (*.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite526.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

21×	`add-exp-log_binary32` `add-cbrt-cube_binary32`
16×	`pow1_binary32`
14×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`add-cube-cbrt_binary32`

Counts

4 → 81

Calls

4 calls:

15.0ms	(/.f32 (*.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux))
9.0ms	(.f32 (.f32 uy 2) PI.f32)
6.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)

Compiler

Compiled 4202 to 2801 computations (33.3% saved)

series241.0ms (1.3%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

71.0ms	(/.f32 (*.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux))
67.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) yi)
24.0ms	(.f32 (.f32 uy 2) PI.f32)
23.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 2896 to 2038 computations (29.6% saved)

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

617×	`times-frac_binary32`
506×	`*-commutative_binary32`
430×	`associate-/l*_binary32`
315×	`div-sub_binary32`
221×	`associate-l_binary32`

Counts

105 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	1748
1	453	1506
2	1571	1492
3	4279	1489
4	5086	1489

prune437.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	83	11	94

Error

0.1b

Counts

94 → 11

Alt Table

Status	Error	Program
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 (pow.f32 ux 3) (pow.f32 (pow.f32 ux 3) 3))) (.f32 (+.f32 ux 1) (+.f32 (.f32 ux ux) (+.f32 (pow.f32 ux 6) (pow.f32 ux 4))))) zi))
	2.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 2 (.f32 uy (.f32 PI.f32 yi))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
▶	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))) zi))
	18.6b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 yi)) (sqrt.f32 yi)))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (sqrt.f32 PI.f32)) (sqrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	1.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (-.f32 (.f32 2 (.f32 uy (.f32 PI.f32 yi))) (.f32 4/3 (.f32 yi (pow.f32 (.f32 uy PI.f32) 3)))))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 (sqrt.f32 (+.f32 uy uy)) (.f32 (cbrt.f32 (pow.f32 PI.f32 2)) (sqrt.f32 (+.f32 uy uy)))) (cbrt.f32 PI.f32))) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
✓	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux)) zi))

Compiler

Compiled 4530 to 3007 computations (33.6% saved)

localize100.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (*.f32 maxCos ux)) (sqrt.f32 ux)))
0.3b	(.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite485.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

21×	`pow1_binary32` `add-exp-log_binary32` `add-cbrt-cube_binary32`
15×	`add-sqr-sqrt_binary32`
13×	`associate-r_binary32`
11×	`add-cube-cbrt_binary32` `-un-lft-identity_binary32` `associate-l*_binary32`
10×	`pow-prod-down_binary32` `prod-exp_binary32` `cbrt-unprod_binary32`

Counts

4 → 83

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (*.f32 maxCos ux)) (sqrt.f32 ux)))
7.0ms	(.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))
5.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 4104 to 2081 computations (49.3% saved)

series202.0ms (1.1%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

55.0ms	(.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (*.f32 maxCos ux)) (sqrt.f32 ux)))
50.0ms	(.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))
23.0ms	(.f32 (.f32 uy 2) PI.f32)
22.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 2661 to 1825 computations (31.4% saved)

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

492×	`*-commutative_binary32`
230×	`associate-l_binary32`
219×	`exp-prod_binary32`
209×	`distribute-rgt-neg-in_binary32`
208×	`distribute-lft-neg-out_binary32` `distribute-rgt-in_binary32`

Counts

103 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1521
1	347	1234
2	1163	1222
3	2264	1222
4	4401	1210
5	4942	1210
6	4950	1210

prune349.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	83	11	94

Error

0.1b

Counts

94 → 11

Alt Table

Status	Error	Program
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 (pow.f32 ux 3) (pow.f32 (pow.f32 ux 3) 3))) (.f32 (+.f32 ux 1) (+.f32 (.f32 ux ux) (+.f32 (pow.f32 ux 6) (pow.f32 ux 4))))) zi))
	2.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 2 (.f32 uy (.f32 PI.f32 yi))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 (sqrt.f32 ux) (.f32 (-.f32 maxCos (.f32 maxCos ux)) (sqrt.f32 ux))) zi))
	18.6b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 yi)) (sqrt.f32 yi)))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (sqrt.f32 PI.f32)) (sqrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.5b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	1.8b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (-.f32 (.f32 2 (.f32 uy (.f32 PI.f32 yi))) (.f32 4/3 (.f32 yi (pow.f32 (.f32 uy PI.f32) 3)))))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy PI.f32)))))))) (.f32 (.f32 ux (*.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 (sqrt.f32 (+.f32 uy uy)) (.f32 (cbrt.f32 (pow.f32 PI.f32 2)) (sqrt.f32 (+.f32 uy uy)))) (cbrt.f32 PI.f32))) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) yi))) (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) zi))
	0.4b	(+.f32 (.f32 (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) (.f32 ux (.f32 (-.f32 1 ux) maxCos))))) (+.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) PI.f32)) xi) (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) yi))) (.f32 (/.f32 (.f32 maxCos (-.f32 ux (pow.f32 ux 3))) (+.f32 1 ux)) zi))

Compiler

Compiled 3524 to 2095 computations (40.6% saved)

regimes8.8s (47.7%)

Accuracy

Total 0.2b remaining (52.2%)

Threshold costs 0.2b (52.2%)

Compiler

Compiled 129696 to 89922 computations (30.7% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`distribute-rgt-neg-in_binary32`
26×	`distribute-lft-neg-in_binary32`
25×	`cancel-sign-sub-inv_binary32`
19×	`neg-mul-1_binary32` `neg-sub0_binary32` `*-commutative_binary32`
18×	`distribute-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	94
1	54	94
2	68	94
3	82	94
4	95	94
5	110	94
6	119	94
7	135	94
8	161	94
9	187	94
10	199	94
11	206	94
12	208	94
13	204	94

end4.0ms (0%)

Compiler: Compiled 65 to 46 computations (29.2% saved)

sample4.2s (22.5%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
475.0ms	8000×	pre	128	true

Compiler

Compiled 830 to 579 computations (30.2% saved)

Iter	Nodes	Cost
0	32	94
1	54	94
2	68	94
3	82	94
4	95	94
5	110	94
6	119	94
7	135	94
8	161	94
9	187	94
10	199	94
11	206	94
12	208	94
13	204	94

Iter	Nodes	Cost
0	32	94
1	54	94
2	68	94
3	82	94
4	95	94
5	110	94
6	119	94
7	135	94
8	161	94
9	187	94
10	199	94
11	206	94
12	208	94
13	204	94

Details

analyze302.0ms (1.6%)

sample110.0ms (0.6%)

simplify72.0ms (0.4%)

prune19.0ms (0.1%)

localize82.0ms (0.4%)

rewrite313.0ms (1.7%)

series227.0ms (1.2%)

simplify91.0ms (0.5%)

prune288.0ms (1.6%)

localize104.0ms (0.6%)

rewrite503.0ms (2.7%)

series199.0ms (1.1%)

simplify154.0ms (0.8%)

prune389.0ms (2.1%)

localize102.0ms (0.5%)

rewrite526.0ms (2.8%)

series241.0ms (1.3%)

simplify87.0ms (0.5%)

prune437.0ms (2.4%)

localize100.0ms (0.5%)

rewrite485.0ms (2.6%)

series202.0ms (1.1%)

simplify120.0ms (0.6%)

prune349.0ms (1.9%)

regimes8.8s (47.7%)

simplify12.0ms (0.1%)

end4.0ms (0%)

sample4.2s (22.5%)

Profiling

Iter	Nodes	Cost
0	32	94
1	54	94
2	68	94
3	82	94
4	95	94
5	110	94
6	119	94
7	135	94
8	161	94
9	187	94
10	199	94
11	206	94
12	208	94
13	204	94