Details

analyze610.0ms (4%)

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)

sample2.8s (18.3%)

Results

2.7s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify50.0ms (0.3%)

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

13.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.4b	(.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)))
	13.4b	(.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))))))

Status

Error

Program

▶

13.4b

(*.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)))

13.4b

(*.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))))))

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize61.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.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)))
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	14.0b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series275.0ms (1.8%)

Counts

4 → 80

Calls

4 calls:

222.0ms	(.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)))
47.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
3.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite78.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

4 → 76

Calls

2 calls:

76.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	353	70
2	4246	70
3	5106	70
0	0	0
1	0	0

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary32`
355×	`fma-def_binary32`
341×	`sub-neg_binary32`
288×	`associate-r_binary32`
275×	`associate-l_binary32`

Counts

156 → 148

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	292	6087
1	1011	5248
2	4149	5248
3	4989	5248

prune249.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	136	12	148
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Error

0.3b

Counts

150 → 12

Alt Table

Status	Error	Program
	7.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	1.2b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	13.5b	(.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32)))) 3) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	13.8b	(pow.f32 (pow.f32 (.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))) 3) 1/3)
	1.7b	(-.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7))))))
	13.5b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	20.8b	(-.f32 (exp.f32 (log1p.f32 (.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))))) 1)
	2.4b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
▶	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	13.7b	(pow.f32 (sqrt.f32 (.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)))) 2)
	13.4b	(pow.f32 (cbrt.f32 (.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)))) 3)
	1.8b	(-.f32 (+.f32 (.f32 4/15 (.f32 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 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 (.f32 8/315 (.f32 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)) (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))))))))))

Compiler

Compiled 9562 to 6329 computations (33.8% saved)

localize86.0ms (0.6%)

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

series339.0ms (2.2%)

Counts

2 → 52

Calls

2 calls:

237.0ms

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

101.0ms

(sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux)))))

rewrite75.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

38× egg-rr

Counts

2 → 38

Calls

2 calls:

74.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	78
1	440	78
2	4797	78
3	6071	78
0	0	0
1	0	0

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary32`
429×	`associate-r_binary32`
307×	`associate-l_binary32`
230×	`times-frac_binary32`
198×	`associate--r+_binary32`

Counts

90 → 128

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	429	7773
1	1496	6864
2	5221	6864

prune443.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	160	10	170
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	166	16	182

Error

0.1b

Counts

182 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (.f32 (log.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1))))) 1/2)))
	1.2b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))
	0.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 3))) (sqrt.f32 (+.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (+.f32 (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2) (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))))
	13.7b	(pow.f32 (sqrt.f32 (.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)))) 2)
	20.8b	(-.f32 (exp.f32 (log1p.f32 (.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))))) 1)
	2.4b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))
▶	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)
	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (expm1.f32 (log1p.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	13.8b	(pow.f32 (pow.f32 (.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))) 3) 1/3)
	1.8b	(-.f32 (+.f32 (.f32 4/15 (.f32 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 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 (.f32 8/315 (.f32 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)) (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))))))))))
	0.5b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.2b	(pow.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 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 2)

Compiler

Compiled 13994 to 8841 computations (36.8% saved)

localize91.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)
✓	0.3b	(.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.7b	(pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series1.6s (10.4%)

Counts

3 → 68

Calls

3 calls:

1.4s

(*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))

134.0ms

(pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)

12.0ms

(pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3)

rewrite73.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

45× egg-rr

Counts

3 → 45

Calls

2 calls:

71.0ms

((pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)) (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	96
1	475	96
2	4749	96
3	5277	96
0	0	0
1	0	0

simplify247.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

463×	`*-commutative_binary32`
403×	`times-frac_binary32`
290×	`+-commutative_binary32`
274×	`fma-def_binary32`
236×	`associate-+r+_binary32`

Counts

113 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1045	19397
1	3671	18917
2	5214	18917

prune733.0ms (4.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	166	16	182

Error

0.1b

Counts

182 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (.f32 (log.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1))))) 1/2)))
	1.2b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 3))) (sqrt.f32 (+.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (+.f32 (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2) (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))))
▶	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))))
	13.7b	(pow.f32 (sqrt.f32 (.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)))) 2)
	20.8b	(-.f32 (exp.f32 (log1p.f32 (.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))))) 1)
	2.4b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	0.7b	(cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) 3) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.5b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)
	13.8b	(pow.f32 (pow.f32 (.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))) 3) 1/3)
	1.2b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.0b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2) (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	22.1b	(cbrt.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) 1) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))

Compiler

Compiled 29098 to 20716 computations (28.8% saved)

localize115.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
✓	0.3b	(.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
	0.7b	(pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series1.9s (12.5%)

Counts

2 → 52

Calls

2 calls:

1.4s

(*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (*.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))))

478.0ms

(*.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))

rewrite67.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

31× egg-rr

Counts

2 → 31

Calls

2 calls:

65.0ms

((*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (*.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))) (*.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	153
1	514	82
2	4535	82
3	5240	82
0	0	0
1	0	0

simplify301.0ms (2%)

Algorithm

1×	egg-herbie

Rules

550×	`*-commutative_binary32`
413×	`+-commutative_binary32`
411×	`fma-def_binary32`
376×	`associate-+r+_binary32`
291×	`associate-r_binary32`

Counts

83 → 121

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1183	22393
1	4233	21721
2	5054	21721

prune836.0ms (5.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	160	16	176

Error

0.1b

Counts

176 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (.f32 (log.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1))))) 1/2)))
	1.2b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 8 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 3)) (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 3))) (sqrt.f32 (+.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 2) (+.f32 (pow.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))) 2) (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))))))))
✓	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) (cbrt.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))))
	13.7b	(pow.f32 (sqrt.f32 (.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)))) 2)
	20.8b	(-.f32 (exp.f32 (log1p.f32 (.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))))) 1)
	2.4b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	0.7b	(cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) 3) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.5b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3))
	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/4) 2)))
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)
	13.8b	(pow.f32 (pow.f32 (.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))) 3) 1/3)
	1.2b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	22.1b	(cbrt.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) 1) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))

Compiler

Compiled 33785 to 24357 computations (27.9% saved)

regimes3.5s (23.4%)

Accuracy

Total 0.4b remaining (80.6%)

Threshold costs 0.4b (80.6%)

Counts

227 → 1

Compiler

Compiled 97570 to 67915 computations (30.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
2×	`+-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	26	86
1	37	86
2	41	86
3	43	86
4	44	86
5	43	86

end387.0ms (2.6%)

Compiler: Compiled 853 to 545 computations (36.1% saved)

Details

analyze610.0ms (4%)

sample2.8s (18.3%)

simplify50.0ms (0.3%)

prune5.0ms (0%)

localize61.0ms (0.4%)

series275.0ms (1.8%)

rewrite78.0ms (0.5%)

simplify114.0ms (0.8%)

prune249.0ms (1.6%)

localize86.0ms (0.6%)

series339.0ms (2.2%)

rewrite75.0ms (0.5%)

simplify110.0ms (0.7%)

prune443.0ms (2.9%)

localize91.0ms (0.6%)

series1.6s (10.4%)

rewrite73.0ms (0.5%)

simplify247.0ms (1.6%)

prune733.0ms (4.8%)

localize115.0ms (0.8%)

series1.9s (12.5%)

rewrite67.0ms (0.4%)

simplify301.0ms (2%)

prune836.0ms (5.5%)

regimes3.5s (23.4%)

simplify3.0ms (0%)

end387.0ms (2.6%)

Profiling