Details

analyze606.0ms (2.8%)

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)

sample2.6s (12.1%)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify48.0ms (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

12.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.9b	(.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)))
	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

▶

12.9b

(*.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)))

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 156 to 110 computations (29.5% saved)

localize59.0ms (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))
✓	13.6b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series251.0ms (1.2%)

Counts

4 → 80

Calls

4 calls:

227.0ms	(.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)))
13.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
6.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`
11×	`pow1_binary32`
9×	`associate-r_binary32`

Counts

4 → 63

Calls

4 calls:

5.0ms	(.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)))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
1.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
0.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

simplify165.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

494×	`associate-l_binary32`
437×	`associate-r_binary32`
366×	`fma-def_binary32`
185×	`associate-+r+_binary32`
156×	`times-frac_binary32`

Counts

143 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	381	7705
1	1177	6694
2	5029	6694

prune273.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	161	11	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Error

0.3b

Counts

174 → 11

Alt Table

Status	Error	Program
	12.9b	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (*.f32 (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))) (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))
	1.5b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sin.f32 (.f32 2 (.f32 uy (PI.f32))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	13.0b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.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))))
	1.6b	(-.f32 (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))))) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux))))
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))) 1)))
▶	0.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	12.9b	(.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	1.6b	(-.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos 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))))))
	1.6b	(-.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))))))))))
	13.0b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 uy (PI.f32)))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	12.9b	(.f32 (sin.f32 (expm1.f32 (log1p.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 10513 to 6897 computations (34.4% saved)

localize63.0ms (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)) (.f32 ux (+.f32 ux (.f32 2 maxCos)))))
	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 ux (+.f32 ux (*.f32 2 maxCos))))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series442.0ms (2%)

Counts

2 → 36

Calls

2 calls:

276.0ms

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

166.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

7.0ms

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

3.0ms

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

simplify118.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

456×	`fma-neg_binary32`
420×	`associate-r_binary32`
367×	`fma-def_binary32`
359×	`associate-l_binary32`
272×	`times-frac_binary32`

Counts

79 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	333	5618
1	1029	4903
2	4104	4903
3	4988	4903

prune430.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	171	9	180
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	179	12	191

Error

0.1b

Counts

191 → 12

Alt Table

Status	Error	Program
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))) 1)))
▶	0.9b	(/.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 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.1b	(.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	1.5b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (*.f32 ux (fma.f32 2 maxCos ux)))))))
	1.1b	(.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)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.6b	(-.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))))))))))
	13.0b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 uy (PI.f32)))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	1.2b	(.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)) (.f32 ux (fma.f32 2 maxCos ux)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))

Compiler

Compiled 10432 to 6702 computations (35.8% saved)

localize116.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series3.7s (17.3%)

Counts

4 → 84

Calls

4 calls:

3.5s	(/.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 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
269.0ms	(.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 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux)))))
18.0ms	(.f32 ux (.f32 (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux))
5.0ms	(*.f32 (PI.f32) uy)

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
20×	`add-sqr-sqrt_binary32`
17×	`pow1_binary32`
14×	`*-un-lft-identity_binary32`

Counts

4 → 103

Calls

4 calls:

12.0ms	(/.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 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
8.0ms	(.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 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux)))))
7.0ms	(.f32 ux (.f32 (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux))
4.0ms	(*.f32 (PI.f32) uy)

simplify429.0ms (2%)

Algorithm

1×	egg-herbie

Rules

616×	`*-commutative_binary32`
413×	`+-commutative_binary32`
405×	`associate-r_binary32`
401×	`fma-def_binary32`
365×	`associate-+r+_binary32`

Counts

187 → 246

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1428	32610
1	4828	32020
2	5122	32020

prune1.2s (5.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	242	4	246
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	245	13	258

Error

0.0b

Counts

258 → 13

Alt Table

Status	Error	Program
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))) 1)))
	2.8b	(/.f32 (exp.f32 (log.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.1b	(.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	1.1b	(.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)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	13.0b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 uy (PI.f32)))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
▶	0.9b	(/.f32 1 (/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))) (.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))))
	1.0b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux)))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.2b	(.f32 (.f32 (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))))) (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux))))))) (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.6b	(-.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))))))))))
	1.2b	(.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)) (.f32 ux (fma.f32 2 maxCos ux)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))

Compiler

Compiled 48178 to 31249 computations (35.1% saved)

localize105.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 ux (.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))
✓	0.3b	(.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))) (.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))))
	0.4b	(*.f32 (PI.f32) uy)

series2.9s (13.5%)

Counts

3 → 84

Calls

3 calls:

2.7s

(/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (fma.f32 2 maxCos ux)))) (*.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 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))))

216.0ms

(*.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 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))

13.0ms

(*.f32 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
15×	`add-sqr-sqrt_binary32`
14×	`pow1_binary32`
12×	`distribute-lft-in_binary32`

Counts

3 → 89

Calls

3 calls:

13.0ms

(/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux) (*.f32 ux (fma.f32 2 maxCos ux)))) (*.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 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))))

9.0ms

(*.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 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))

6.0ms

(*.f32 ux (*.f32 ux (*.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))

simplify482.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

548×	`times-frac_binary32`
502×	`*-commutative_binary32`
310×	`+-commutative_binary32`
302×	`fma-def_binary32`
271×	`associate-+r+_binary32`

Counts

173 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1215	28329
1	3858	27677
2	4995	27677
3	4946	27677

prune1.0s (4.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	241	13	254

Error

0.0b

Counts

254 → 13

Alt Table

Status	Error	Program
	12.9b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (+.f32 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1))) 1)))
	2.8b	(/.f32 (exp.f32 (log.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.1b	(.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 2 (.f32 uy (PI.f32)))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	1.1b	(.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)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos)))))))
	13.0b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 uy (PI.f32)))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
✓	0.9b	(/.f32 1 (/.f32 (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))) (.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))))
	1.0b	(/.f32 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 ux (.f32 (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux)) ux)))))) (sqrt.f32 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos))))))
	1.0b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.2b	(.f32 (.f32 (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))))) (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux))))))) (cbrt.f32 (/.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 ux (.f32 ux (.f32 (fma.f32 2 maxCos ux) (fma.f32 2 maxCos ux))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.6b	(-.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))))))))))
	1.2b	(.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)) (.f32 ux (fma.f32 2 maxCos ux)))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))

Compiler

Compiled 41266 to 26567 computations (35.6% saved)

regimes6.0s (27.7%)

Accuracy

Total 0.5b remaining (83.9%)

Threshold costs 0.5b (83.9%)

Counts

306 → 1

Compiler

Compiled 179685 to 112597 computations (37.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary32`
13×	`+-commutative_binary32`
10×	`sub-neg_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	57
1	37	57
2	46	57
3	58	57
4	81	57
5	97	57
6	107	57
7	113	57
8	115	57
9	114	57

end422.0ms (1.9%)

Compiler: Compiled 920 to 575 computations (37.5% saved)

Details

analyze606.0ms (2.8%)

sample2.6s (12.1%)

simplify48.0ms (0.2%)

prune5.0ms (0%)

localize59.0ms (0.3%)

series251.0ms (1.2%)

rewrite13.0ms (0.1%)

simplify165.0ms (0.8%)

prune273.0ms (1.3%)

localize63.0ms (0.3%)

series442.0ms (2%)

rewrite13.0ms (0.1%)

simplify118.0ms (0.5%)

prune430.0ms (2%)

localize116.0ms (0.5%)

series3.7s (17.3%)

rewrite43.0ms (0.2%)

simplify429.0ms (2%)

prune1.2s (5.7%)

localize105.0ms (0.5%)

series2.9s (13.5%)

rewrite40.0ms (0.2%)

simplify482.0ms (2.2%)

prune1.0s (4.7%)

regimes6.0s (27.7%)

simplify5.0ms (0%)

end422.0ms (1.9%)

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