Details

analyze597.0ms (2.9%)

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)

sample2.9s (14.2%)

Results

2.7s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify58.0ms (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 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
▶	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)))

Status

Error

Program

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))))))

▶

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)))

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize54.0ms (0.3%)

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)

series372.0ms (1.8%)

Counts

4 → 80

Calls

4 calls:

351.0ms	(.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)))
14.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
4.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite447.0ms (2.2%)

Algorithm

4×	egg-rewrite

Rules

60×	`egg`
33×	`egg`
29×	`egg`
22×	`egg`

Counts

4 → 144

Calls

4 calls:

142.0ms	(.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)))
124.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
110.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
68.0ms	(.f32 (.f32 uy 2) (PI.f32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	194	19
2	2486	19
3	4767	19
4	4864	19
5	5008	19
0	6	8
1	121	8
2	1353	8
3	5031	8
0	17	33
1	353	33
2	4246	33
3	5106	33
0	7	10
1	140	10
2	1571	10
3	4858	10
4	4780	10
5	4946	10

simplify193.0ms (0.9%)

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

224 → 214

Iterations

Useful iterations: 1 (0.0ms)

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

prune309.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	202	12	214
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	12	216

Error

0.3b

Counts

216 → 12

Alt Table

Status	Error	Program
	13.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (.f32 (cbrt.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)))) (cbrt.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))))) (cbrt.f32 (*.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)))) 1)))
	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))))
	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))
	7.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	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))))))
	13.7b	(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	(.f32 (sin.f32 (.f32 (*.f32 (+.f32 uy uy) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))) (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)
	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 (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))))))
	13.4b	(.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (*.f32 (cbrt.f32 (PI.f32)) (+.f32 uy uy)))) (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)

Compiler

Compiled 11629 to 7497 computations (35.5% saved)

localize73.0ms (0.4%)

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))

series353.0ms (1.7%)

Counts

2 → 52

Calls

2 calls:

241.0ms

(*.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))))))

112.0ms

(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)))))

rewrite239.0ms (1.2%)

Algorithm

2×	egg-rewrite

Rules

27×	`egg`
21×	`egg`

Counts

2 → 48

Calls

2 calls:

160.0ms

(*.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))))))

78.0ms

(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)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	440	45
2	4797	45
3	6071	45
0	15	33
1	321	32
2	4035	32
3	5208	32

simplify158.0ms (0.8%)

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

100 → 136

Iterations

Useful iterations: 1 (0.0ms)

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

prune636.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	216	9	225
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	223	14	237

Error

0.1b

Counts

237 → 14

Alt Table

Status	Error	Program
	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 2)) (pow.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1))))))))
	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)
	0.9b	(.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))))))
	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)
	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)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 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)
	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)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 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 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) 3))) (sqrt.f32 (+.f32 (.f32 4 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 2)) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1))))))))))
	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))))
	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)
	1.9b	(.f32 (sin.f32 (.f32 (pow.f32 (.f32 (pow.f32 (.f32 (+.f32 uy uy) (PI.f32)) 2) uy) 1/3) (cbrt.f32 (.f32 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))))))
▶	0.5b	(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)))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (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))))))
	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))

Compiler

Compiled 15769 to 9627 computations (38.9% saved)

localize96.0ms (0.5%)

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 (7.6%)

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))

127.0ms

(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)

17.0ms

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

rewrite287.0ms (1.4%)

Algorithm

3×	egg-rewrite

Rules

25×	`egg`
22×	`egg`
19×	`egg`

Counts

3 → 66

Calls

3 calls:

123.0ms

(*.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))

86.0ms

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

75.0ms

(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)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	184	13
2	1935	13
3	5164	13
0	23	49
1	475	49
2	4749	49
3	5277	49
0	15	34
1	314	34
2	3557	34
3	5280	34

simplify325.0ms (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

134 → 171

Iterations

Useful iterations: 1 (0.0ms)

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

prune912.0ms (4.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	222	8	230
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	231	13	244

Error

0.0b

Counts

244 → 13

Alt Table

Status	Error	Program
▶	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)))
	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)))
	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)
	0.8b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 uy) 2) (.f32 (cbrt.f32 uy) (.f32 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)))
	0.9b	(.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)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1))))))) 3))
	1.0b	(cbrt.f32 (.f32 (pow.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2) 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)))
	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (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)) 3)))
	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 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) 3))) (sqrt.f32 (+.f32 (.f32 4 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 2)) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 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)
	4.3b	(cbrt.f32 (.f32 (-.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (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)))
	13.3b	(cbrt.f32 (.f32 (pow.f32 (pow.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) 3) 1/3) (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)))
	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 (pow.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (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)))

Compiler

Compiled 31480 to 21869 computations (30.5% saved)

localize92.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.5b	(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)
	0.7b	(pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series1.9s (9.4%)

Counts

2 → 56

Calls

2 calls:

1.7s

(*.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))

256.0ms

(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)

rewrite161.0ms (0.8%)

Algorithm

2×	egg-rewrite

Rules

28×	`egg`
21×	`egg`

Counts

2 → 49

Calls

2 calls:

81.0ms

(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)

78.0ms

(*.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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	339	34
2	3754	34
3	5458	34
0	24	49
1	500	49
2	4788	49
3	4861	49

simplify407.0ms (2%)

Algorithm

1×	egg-herbie

Rules

482×	`times-frac_binary32`
459×	`*-commutative_binary32`
287×	`+-commutative_binary32`
269×	`fma-def_binary32`
236×	`associate-+r+_binary32`

Counts

105 → 144

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1041	19477
1	3663	18997
2	5067	18997

prune867.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	236	13	249

Error

0.0b

Counts

249 → 13

Alt Table

Status	Error	Program
✓	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)))
	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)))
	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)
	0.8b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 uy) 2) (.f32 (cbrt.f32 uy) (.f32 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)))
	0.9b	(.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)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1))))))) 3))
	1.0b	(cbrt.f32 (.f32 (pow.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2) 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)))
	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (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)) 3)))
	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 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) 3))) (sqrt.f32 (+.f32 (.f32 4 (pow.f32 (fma.f32 maxCos (.f32 ux ux) ux) 2)) (.f32 (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 1)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 ux (fma.f32 maxCos maxCos 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)
	4.3b	(cbrt.f32 (.f32 (-.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (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)))
	13.3b	(cbrt.f32 (.f32 (pow.f32 (pow.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) 3) 1/3) (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)))
	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 (pow.f32 (sin.f32 (.f32 (.f32 (+.f32 uy uy) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (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)))

Compiler

Compiled 31926 to 22297 computations (30.2% saved)

regimes7.1s (34.7%)

Accuracy

Total 0.4b remaining (83.5%)

Threshold costs 0.4b (83.5%)

Counts

372 → 1

Compiler

Compiled 179422 to 123005 computations (31.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	55
1	35	55
2	39	55
3	41	55
4	42	55
5	41	55

end344.0ms (1.7%)

Compiler: Compiled 663 to 448 computations (32.4% saved)

Details

analyze597.0ms (2.9%)

sample2.9s (14.2%)

simplify58.0ms (0.3%)

prune5.0ms (0%)

localize54.0ms (0.3%)

series372.0ms (1.8%)

rewrite447.0ms (2.2%)

simplify193.0ms (0.9%)

prune309.0ms (1.5%)

localize73.0ms (0.4%)

series353.0ms (1.7%)

rewrite239.0ms (1.2%)

simplify158.0ms (0.8%)

prune636.0ms (3.1%)

localize96.0ms (0.5%)

series1.6s (7.6%)

rewrite287.0ms (1.4%)

simplify325.0ms (1.6%)

prune912.0ms (4.5%)

localize92.0ms (0.5%)

series1.9s (9.4%)

rewrite161.0ms (0.8%)

simplify407.0ms (2%)

prune867.0ms (4.2%)

regimes7.1s (34.7%)

simplify4.0ms (0%)

end344.0ms (1.7%)

Profiling