Details

analyze673.0ms (2.7%)

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 51 to 37 computations (27.5% saved)

sample148.0ms (0.6%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

743×	`sub-neg_binary32`
674×	`fma-neg_binary32`
386×	`associate--l-_binary32`
316×	`distribute-rgt-in_binary32`
286×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	35
2	117	35
3	431	33
4	1755	33
5	4135	33
6	4966	33

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

13.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.3b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
▶	13.2b	(.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

13.3b

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

▶

13.2b

(*.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 156 to 110 computations (29.5% saved)

localize80.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	0.4b	(.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))))))
✓	13.1b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series263.0ms (1%)

Counts

4 → 92

Calls

4 calls:

229.0ms	(.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))))))
21.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
10.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary32`
18×	`pow1_binary32`
16×	`*-un-lft-identity_binary32`
14×	`associate-r_binary32`
14×	`add-cube-cbrt_binary32`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
6.0ms	(.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))))))
5.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))

simplify240.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-l_binary32`
569×	`associate-r_binary32`
419×	`fma-def_binary32`
156×	`times-frac_binary32`
153×	`associate-/l*_binary32`

Counts

201 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	462	10137
1	1454	8391
2	5353	8391

prune428.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	238	14	252
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	240	14	254

Error

0.3b

Counts

254 → 14

Alt Table

Status	Error	Program
	12.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (-.f32 (+.f32 (fma.f32 ux ux 1) (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))))))
	1.3b	(fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	13.2b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))) (sqrt.f32 (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))
	2.2b	(-.f32 (+.f32 (.f32 4/15 (.f32 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux)))))))) (.f32 2 (.f32 (.f32 uy (PI.f32)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux))))))))) (.f32 4/3 (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 uy 3)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (*.f32 maxCos ux)))))))))
	13.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (+.f32 1 (fma.f32 maxCos ux (-.f32 1 ux))) (-.f32 1 (fma.f32 maxCos ux (-.f32 1 ux))))))
	13.2b	(/.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 1 1) (.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))) (sqrt.f32 (+.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	13.5b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (sqrt.f32 (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))) (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (sqrt.f32 (sqrt.f32 (-.f32 1 (*.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))))
	2.2b	(fma.f32 4/15 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (-.f32 (.f32 2 (.f32 (PI.f32) uy)) (.f32 4/3 (*.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))
	5.6b	(-.f32 (fma.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 6))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5)))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (+.f32 (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))) (.f32 3/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (pow.f32 (.f32 maxCos ux) 3))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (pow.f32 (.f32 maxCos ux) 3))) (.f32 3/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 5)))))) (.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (*.f32 ux (-.f32 2 ux)) 3)))))))))
	3.0b	(-.f32 (.f32 2 (.f32 (.f32 uy (PI.f32)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux)))))))) (.f32 4/3 (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux)))))))))
	1.0b	(-.f32 (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (+.f32 (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3)) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 1/2 (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3)))))))))
	13.3b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (pow.f32 (fma.f32 maxCos ux (-.f32 1 ux)) 3))))) (sqrt.f32 (+.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))
▶	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	7.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))

Compiler

Compiled 14844 to 9509 computations (35.9% saved)

localize67.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))
✓	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
	0.2b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))

series321.0ms (1.3%)

Counts

3 → 64

Calls

3 calls:

222.0ms

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

95.0ms

(sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))

4.0ms

(sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary32`
7×	`sqrt-prod_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-cube-cbrt_binary32`
6×	`associate-r_binary32`

Counts

3 → 52

Calls

3 calls:

7.0ms

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

4.0ms

(sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))

1.0ms

(sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))

simplify156.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary32`
530×	`associate-r_binary32`
453×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

116 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	508	10133
1	1697	8952
2	5419	8952

prune474.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	203	11	214
Fresh	13	0	13
Picked	1	0	1
Done	0	0	0
Total	217	11	228

Error

0.0b

Counts

228 → 11

Alt Table

Status	Error	Program
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
	0.7b	(.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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
▶	0.5b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	2.5b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cbrt.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	5.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	1.1b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	1.0b	(-.f32 (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fma.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (.f32 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3)) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 1/2 (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 (.f32 (.f32 maxCos (.f32 maxCos (.f32 ux ux))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (*.f32 ux (-.f32 2 ux)) 3)))))))))

Compiler

Compiled 16177 to 9602 computations (40.6% saved)

localize90.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
✓	0.4b	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
✓	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))))
✓	0.5b	(.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))

series2.0s (7.8%)

Counts

4 → 88

Calls

4 calls:

1.4s	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
503.0ms	(.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
27.0ms	(.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
7.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))))

rewrite240.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

190×	`pow1_binary32`
174×	`sqrt-div_binary32`
114×	`frac-times_binary32`
87×	`flip--_binary32`
87×	`flip3--_binary32`

Counts

4 → 284

Calls

4 calls:

44.0ms	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
23.0ms	(.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
11.0ms	(.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
7.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))))

simplify589.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

681×	`*-commutative_binary32`
424×	`+-commutative_binary32`
418×	`fma-def_binary32`
385×	`associate-r_binary32`
382×	`associate-+r+_binary32`

Counts

372 → 451

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1477	46358
1	4827	41492
2	5196	41492

prune2.3s (9.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	447	4	451
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	452	10	462

Error

0.0b

Counts

462 → 10

Alt Table

Status	Error	Program
▶	0.5b	(cbrt.f32 (.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	2.5b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	5.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	2.7b	(cbrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (+.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))))))
	0.7b	(.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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.9b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (exp.f32 (log.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	1.3b	(cbrt.f32 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 3) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))))) (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))))))) (.f32 (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))))
	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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cbrt.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	1.1b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))

Compiler

Compiled 76994 to 43967 computations (42.9% saved)

localize115.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
✓	0.4b	(.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))
✓	0.5b	(pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2)
	0.5b	(.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))

series1.6s (6.3%)

Counts

2 → 44

Calls

2 calls:

1.6s

(*.f32 (*.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 uy (PI.f32)))) 2))) (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))) (*.f32 (*.f32 (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))

8.0ms

(pow.f32 (sin.f32 (*.f32 2 (*.f32 uy (PI.f32)))) 2)

rewrite72.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-div_binary32`
34×	`associate-*r/_binary32`
28×	`frac-times_binary32`
27×	`flip--_binary32`
27×	`flip3--_binary32`

Counts

2 → 77

Calls

2 calls:

26.0ms

(*.f32 (*.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 uy (PI.f32)))) 2))) (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))) (*.f32 (*.f32 (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))

3.0ms

(pow.f32 (sin.f32 (*.f32 2 (*.f32 uy (PI.f32)))) 2)

simplify346.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

694×	`*-commutative_binary32`
411×	`associate-r_binary32`
261×	`+-commutative_binary32`
254×	`fma-def_binary32`
231×	`associate-+r+_binary32`

Counts

121 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1251	20426
1	3617	17158
2	4987	17156
3	4903	17156

prune1.6s (6.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	384	2	386
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	386	10	396

Error

0.0b

Counts

396 → 10

Alt Table

Status	Error	Program
✓	0.5b	(cbrt.f32 (.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	2.5b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	0.7b	(.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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.9b	(cbrt.f32 (.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (exp.f32 (log.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))))
	2.7b	(cbrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 (log1p.f32 (expm1.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 2))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (+.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))))
	1.3b	(cbrt.f32 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) 3) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))))) (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))) (fma.f32 ux ux (.f32 (.f32 ux maxCos) (fma.f32 maxCos ux 2))))))) (.f32 (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))))
	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 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cbrt.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	5.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	1.1b	(.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))

Compiler

Compiled 67378 to 39578 computations (41.3% saved)

regimes11.1s (43.7%)

Accuracy

Total 0.4b remaining (81.1%)

Threshold costs 0.4b (81.1%)

Counts

495 → 1

Compiler

Compiled 353401 to 223198 computations (36.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
3×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	66
1	47	66
2	51	66
3	53	66
4	54	66
5	50	66

end1.0ms (0%)

Compiler: Compiled 45 to 31 computations (31.1% saved)

sample2.3s (9.3%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
304.0ms	8000×	pre	128	true

Compiler

Compiled 742 to 436 computations (41.2% saved)

Details

analyze673.0ms (2.7%)

sample148.0ms (0.6%)

simplify54.0ms (0.2%)

prune5.0ms (0%)

localize80.0ms (0.3%)

series263.0ms (1%)

rewrite34.0ms (0.1%)

simplify240.0ms (0.9%)

prune428.0ms (1.7%)

localize67.0ms (0.3%)

series321.0ms (1.3%)

rewrite17.0ms (0.1%)

simplify156.0ms (0.6%)

prune474.0ms (1.9%)

localize90.0ms (0.4%)

series2.0s (7.8%)

rewrite240.0ms (0.9%)

simplify589.0ms (2.3%)

prune2.3s (9.2%)

localize115.0ms (0.5%)

series1.6s (6.3%)

rewrite72.0ms (0.3%)

simplify346.0ms (1.4%)

prune1.6s (6.4%)

regimes11.1s (43.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.3s (9.3%)

Profiling