Details

analyze741.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	99.9%	4
0%	0%	99.9%	5
0%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample65.0ms (0.3%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 72 to 53 computations (26.4% saved)

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-+l-_binary32`
416×	`associate-+r-_binary32`
386×	`associate--l-_binary32`
320×	`neg-mul-1_binary32`
316×	`distribute-rgt-in_binary32`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	39
2	113	39
3	402	39
4	1502	36
5	4687	36
6	4944	36
7	5024	36

prune14.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))

Status

Error

Program

▶

0.6b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (*.f32 (-.f32 ux (*.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))))

12.9b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

Compiler

Compiled 134 to 94 computations (29.9% saved)

localize61.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.3b	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

rewrite258.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`pow1_binary32` `add-exp-log_binary32` `add-log-exp_binary32` `add-cbrt-cube_binary32` `add-sqr-sqrt_binary32` `*-un-lft-identity_binary32`
12×	`associate-*r/_binary32`
11×	`associate-r_binary32`
9×	`add-cube-cbrt_binary32`
8×	`frac-times_binary32` `sqrt-div_binary32`

Counts

4 → 90

Calls

4 calls:

18.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
14.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
9.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
5.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3166 to 1687 computations (46.7% saved)

series336.0ms (1.4%)

Error

0.4b

Counts

4 → 41

Calls

4 calls:

148.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
52.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))
36.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
15.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3546 to 2467 computations (30.4% saved)

simplify157.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

486×	`cancel-sign-sub-inv_binary32`
444×	`associate-r_binary32`
398×	`associate-l_binary32`
254×	`*-commutative_binary32`
230×	`times-frac_binary32`

Counts

131 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	4476
1	891	3953
2	3542	3944
3	4790	3914
4	5204	3914

prune272.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	95	14	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	15	111

Error

0.1b

Counts

111 → 15

Alt Table

Status	Error	Program
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	2.0b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	18.8b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	3.1b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	1.2b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3))))) (sqrt.f32 (+.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (-.f32 (.f32 1 1) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (sqrt.f32 PI.f32)) (sqrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (.f32 (cbrt.f32 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))) (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (cbrt.f32 (-.f32 ux (.f32 ux maxCos)))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy PI.f32))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3)) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 ux maxCos))))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (+.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (-.f32 (.f32 1 1) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))))

Compiler

Compiled 4375 to 2343 computations (46.4% saved)

localize94.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite466.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-sqr-sqrt_binary32`
22×	`associate-*r/_binary32`
20×	`-un-lft-identity_binary32` `associate-r*_binary32`
18×	`flip3--_binary32` `sqrt-div_binary32` `flip--_binary32`
16×	`add-cube-cbrt_binary32` `cancel-sign-sub-inv_binary32`

Counts

4 → 139

Calls

4 calls:

31.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
21.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))))
20.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (*.f32 ux maxCos) 3)))
7.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 8143 to 2988 computations (63.3% saved)

series641.0ms (2.7%)

Error

0.1b

Counts

4 → 45

Calls

4 calls:

256.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
156.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))))
81.0ms	(.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))) (-.f32 (pow.f32 ux 3) (pow.f32 (*.f32 ux maxCos) 3)))
18.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 7195 to 4699 computations (34.7% saved)

simplify163.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-r_binary32`
617×	`associate-l_binary32`
188×	`distribute-rgt-in_binary32`
187×	`distribute-lft-in_binary32`
184×	`*-commutative_binary32`

Counts

184 → 160

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	524	9366
1	1311	8553
2	5141	8553

prune396.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Error

0.0b

Counts

175 → 13

Alt Table

Status	Error	Program
	7.4b	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)) (-.f32 (pow.f32 ux 6) (pow.f32 (.f32 ux maxCos) 6))))) (sqrt.f32 (+.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (*.f32 ux maxCos))))))
	0.7b	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (-.f32 (pow.f32 ux 4) (.f32 (.f32 maxCos (.f32 ux (.f32 ux maxCos))) (.f32 (+.f32 (.f32 ux maxCos) ux) (+.f32 (.f32 ux maxCos) ux)))))) (sqrt.f32 (-.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.7b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	3.1b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux))))))) (/.f32 (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux))))))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))))) (/.f32 (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (*.f32 ux maxCos) ux))))))))
	1.9b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy PI.f32))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

Compiler

Compiled 8451 to 3745 computations (55.7% saved)

localize95.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite423.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-sqr-sqrt_binary32`
22×	`associate-*r/_binary32`
19×	`associate-l_binary32`
18×	`sqrt-div_binary32`
16×	`*-un-lft-identity_binary32`

Counts

4 → 120

Calls

4 calls:

36.0ms	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
21.0ms	(.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))))
19.0ms	(.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (*.f32 ux maxCos)))
4.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 7200 to 2844 computations (60.5% saved)

series641.0ms (2.7%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

256.0ms	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
156.0ms	(.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))))
81.0ms	(.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (*.f32 ux maxCos)))
17.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 7195 to 4691 computations (34.8% saved)

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-r_binary32`
556×	`associate-l_binary32`
214×	`distribute-rgt-in_binary32`
206×	`distribute-lft-in_binary32`
164×	`*-commutative_binary32`

Counts

165 → 140

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	485	8757
1	1303	7735
2	4979	7735

prune386.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	140	13	153

Error

0.0b

Counts

153 → 13

Alt Table

Status	Error	Program
	4.0b	(.f32 (sqrt.f32 (/.f32 (.f32 (-.f32 (+.f32 2 (.f32 ux maxCos)) ux) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3))) (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 ux (.f32 ux maxCos))))))) (-.f32 (.f32 (.f32 uy PI.f32) 2) (.f32 4/3 (pow.f32 (.f32 uy PI.f32) 3))))
	7.4b	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)) (-.f32 (pow.f32 ux 6) (pow.f32 (.f32 ux maxCos) 6))))) (sqrt.f32 (+.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (*.f32 ux maxCos))))))
	0.7b	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (-.f32 (pow.f32 ux 4) (.f32 (.f32 maxCos (.f32 ux (.f32 ux maxCos))) (.f32 (+.f32 (.f32 ux maxCos) ux) (+.f32 (.f32 ux maxCos) ux)))))) (sqrt.f32 (-.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.7b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
▶	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	3.1b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
✓	0.6b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))))) (/.f32 (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (*.f32 ux maxCos) ux))))))))
	1.9b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 uy PI.f32))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32)))) (cbrt.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

Compiler

Compiled 7983 to 3675 computations (54% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.3b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
0.3b	(*.f32 uy PI.f32)
0.4b	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos))))

rewrite229.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary32`
16×	`associate-r_binary32`
15×	`*-un-lft-identity_binary32`
14×	`sqrt-div_binary32`
13×	`pow1_binary32` `add-exp-log_binary32` `add-log-exp_binary32` `add-cbrt-cube_binary32`

Counts

4 → 89

Calls

4 calls:

19.0ms	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
9.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
8.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos))))
4.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 2922 to 1419 computations (51.4% saved)

series344.0ms (1.4%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

134.0ms	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
89.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos))))
36.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
12.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 4231 to 2802 computations (33.8% saved)

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

593×	`cancel-sign-sub-inv_binary32`
474×	`associate-r_binary32`
409×	`associate-l_binary32`
311×	`distribute-rgt-neg-in_binary32`
283×	`*-commutative_binary32`

Counts

134 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	4697
1	905	4235
2	3257	4226
3	4924	4226
4	4957	4226

prune198.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	3	8	11
Picked	0	1	1
Done	1	0	1
Total	96	12	108

Error

0.0b

Counts

108 → 12

Alt Table

Status	Error	Program
	7.4b	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)) (-.f32 (pow.f32 ux 6) (pow.f32 (.f32 ux maxCos) 6))))) (sqrt.f32 (+.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (*.f32 ux maxCos))))))
	0.8b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3)))) (.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (+.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (+.f32 (*.f32 ux maxCos) (-.f32 1 ux)))))))
	0.7b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (sqrt.f32 (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (sqrt.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 uy) (cbrt.f32 uy)) (.f32 PI.f32 (cbrt.f32 uy))))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 ux (.f32 ux maxCos)))) (sqrt.f32 (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	3.1b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))))
	0.7b	(/.f32 (.f32 (sqrt.f32 (.f32 ux (-.f32 ux (.f32 maxCos (.f32 ux maxCos))))) (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 uy PI.f32) 2)) (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (.f32 ux maxCos) ux)))))))) (/.f32 (sqrt.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos)))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 ux ux) (.f32 ux (.f32 maxCos (+.f32 (*.f32 ux maxCos) ux))))))))
	1.9b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (exp.f32 (log.f32 (.f32 (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 ux maxCos) 3)) (+.f32 (-.f32 2 ux) (.f32 ux maxCos))))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

Compiler

Compiled 3257 to 1695 computations (48% saved)

regimes14.9s (62.4%)

Accuracy

Total 0.5b remaining (87.2%)

Threshold costs 0.5b (87.2%)

Compiler

Compiled 219414 to 134120 computations (38.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary32`
7×	`+-commutative_binary32`
4×	`sub-neg_binary32`
2×	`neg-mul-1_binary32` `neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	62
1	40	62
2	48	62
3	52	62
4	54	62
5	54	62

end3.0ms (0%)

Compiler: Compiled 43 to 27 computations (37.2% saved)

sample2.5s (10.7%)

Algorithm

1×

intervals

Results

892.0ms	8000×	body	128	valid
257.0ms	8000×	pre	128	true

Compiler

Compiled 614 to 373 computations (39.3% saved)

Details

analyze741.0ms (3.1%)

sample65.0ms (0.3%)

simplify69.0ms (0.3%)

prune14.0ms (0.1%)

localize61.0ms (0.3%)

rewrite258.0ms (1.1%)

series336.0ms (1.4%)

simplify157.0ms (0.7%)

prune272.0ms (1.1%)

localize94.0ms (0.4%)

rewrite466.0ms (2%)

series641.0ms (2.7%)

simplify163.0ms (0.7%)

prune396.0ms (1.7%)

localize95.0ms (0.4%)

rewrite423.0ms (1.8%)

series641.0ms (2.7%)

simplify153.0ms (0.6%)

prune386.0ms (1.6%)

localize57.0ms (0.2%)

rewrite229.0ms (1%)

series344.0ms (1.4%)

simplify158.0ms (0.7%)

prune198.0ms (0.8%)

regimes14.9s (62.4%)

simplify5.0ms (0%)

end3.0ms (0%)

sample2.5s (10.7%)

Profiling