Details

analyze658.0ms (6.3%)

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)

sample2.2s (20.9%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify47.0ms (0.5%)

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

prune7.0ms (0.1%)

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

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.1b	(.f32 (cos.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))))))
	14.2b	(.f32 (cos.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

▶

14.1b

(*.f32 (cos.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))))))

14.2b

(*.f32 (cos.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)

localize49.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	13.7b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series276.0ms (2.7%)

Counts

4 → 92

Calls

4 calls:

229.0ms	(.f32 (cos.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))))))
24.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
19.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite87.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

321×	`log1p-udef_binary32`
185×	`add-sqr-sqrt_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`
173×	`add-log-exp_binary32`

Counts

4 → 94

Calls

4 calls:

84.0ms	(.f32 (cos.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))))))
84.0ms	(.f32 (.f32 uy 2) (PI.f32))
84.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
84.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	67
1	370	61
2	4672	61
3	5114	61
0	0	0
1	0	0

simplify171.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary32`
377×	`sub-neg_binary32`
318×	`fma-def_binary32`
268×	`associate-r_binary32`
250×	`associate-l_binary32`

Counts

186 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	6589
1	1005	5816
2	4151	5810
3	4975	5810
4	5062	5810

prune393.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	166	10	176
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	167	11	178

Error

0.2b

Counts

178 → 11

Alt Table

Status	Error	Program
	7.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	14.2b	(.f32 (cos.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)))
	14.2b	(.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 6)) (+.f32 1 (+.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 4))))))
	2.0b	(fma.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (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 (.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 (.f32 uy uy) (pow.f32 (PI.f32) 2))) -2))
▶	0.7b	(.f32 (cos.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))))))
	1.5b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (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 (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 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	14.1b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2)))))
	5.2b	(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))))))
	14.8b	(pow.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) 2)
	5.9b	(-.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 6))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (+.f32 (.f32 3/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 3))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 4))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 3))))) (+.f32 (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 3/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 5))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)) 5))))) (+.f32 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux)) (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2))))) (.f32 1/2 (.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))) (sqrt.f32 (/.f32 1 (pow.f32 (-.f32 (*.f32 2 ux) (pow.f32 ux 2)) 3))))))))))))
	1.0b	(-.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (+.f32 (sqrt.f32 (.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))))))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))) (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))))) (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (+.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (.f32 maxCos (.f32 ux (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))))))

Compiler

Compiled 10898 to 7344 computations (32.6% saved)

localize58.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.1b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (.f32 2 maxCos)))))
✓	0.1b	(.f32 (cos.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))

series419.0ms (4%)

Counts

3 → 48

Calls

3 calls:

312.0ms

(*.f32 (cos.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))))))

102.0ms

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

4.0ms

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

rewrite79.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

350×	`log1p-udef_binary32`
196×	`add-sqr-sqrt_binary32`
186×	`log1p-expm1-u_binary32`
186×	`expm1-log1p-u_binary32`
182×	`add-log-exp_binary32`

Counts

3 → 56

Calls

3 calls:

78.0ms

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

78.0ms

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

78.0ms

(*.f32 (cos.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))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	389	68
2	4978	68
3	5495	68
0	0	0
1	0	0

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

371×	`fma-neg_binary32`
347×	`sub-neg_binary32`
340×	`fma-def_binary32`
311×	`associate-r_binary32`
243×	`distribute-rgt-neg-in_binary32`

Counts

104 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	4068
1	883	3518
2	3350	3516
3	5151	3516

prune406.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Error

0.1b

Counts

150 → 12

Alt Table

Status	Error	Program
	1.2b	(.f32 (log.f32 (exp.f32 (cos.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))))))
	0.8b	(.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	0.7b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))
	6.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.2b	(pow.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) 3)
▶	0.7b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 uy 2) 3)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
	1.5b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (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 (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 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	14.2b	(.f32 (cos.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)))
	0.9b	(.f32 (cos.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 (fma.f32 2 maxCos ux)) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux))))))
	5.2b	(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))))))
	14.8b	(pow.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) 2)
	1.0b	(-.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (+.f32 (sqrt.f32 (.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))))))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))) (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))))) (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (+.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (.f32 maxCos (.f32 ux (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))))))

Compiler

Compiled 8118 to 5499 computations (32.3% saved)

localize79.0ms (0.8%)

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)))))
✓	0.1b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 uy 2) 3)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
✓	0.2b	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 uy 2) 3))
✓	1.0b	(pow.f32 (PI.f32) 3)

series230.0ms (2.2%)

Counts

3 → 36

Calls

3 calls:

217.0ms

(*.f32 (cos.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 uy 2) 3)))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (*.f32 ux (+.f32 ux (*.f32 2 maxCos))))))

12.0ms

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

0.0ms

(pow.f32 (PI.f32) 3)

rewrite65.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`prod-diff_binary32`
227×	`add-sqr-sqrt_binary32`
218×	`log1p-expm1-u_binary32`
218×	`expm1-log1p-u_binary32`
213×	`add-cbrt-cube_binary32`

Counts

3 → 46

Calls

3 calls:

63.0ms

(*.f32 (cos.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 uy 2) 3)))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (*.f32 ux (+.f32 ux (*.f32 2 maxCos))))))

63.0ms

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

63.0ms

(pow.f32 (PI.f32) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	473	51
2	4712	51
3	5009	51
0	0	0
1	0	0

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

584×	`cancel-sign-sub-inv_binary32`
550×	`fma-neg_binary32`
394×	`times-frac_binary32`
249×	`associate-r_binary32`
187×	`associate-l_binary32`

Counts

82 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2844
1	583	2463
2	2276	2201
3	4552	2201
4	5254	2201

prune458.0ms (4.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	131	12	143

Error

0.1b

Counts

143 → 12

Alt Table

Status	Error	Program
	1.2b	(.f32 (log.f32 (exp.f32 (cos.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))))))
	0.8b	(.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
▶	0.7b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))
	6.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.2b	(pow.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) 3)
	1.8b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 uy 2) 3)))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))) 3/2) 1/3))
	1.5b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (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 (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 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	14.2b	(.f32 (cos.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)))
	0.9b	(.f32 (cos.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 (fma.f32 2 maxCos ux)) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux))))))
	5.2b	(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))))))
	14.8b	(pow.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) 2)
	1.0b	(-.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (+.f32 (sqrt.f32 (.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))))))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))) (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))))) (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (+.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (.f32 maxCos (.f32 ux (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))))))

Compiler

Compiled 8060 to 5617 computations (30.3% saved)

localize70.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))
✓	0.2b	(log1p.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series229.0ms (2.2%)

Counts

3 → 48

Calls

3 calls:

219.0ms

(*.f32 (cos.f32 (expm1.f32 (log1p.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))))))

6.0ms

(log1p.f32 (*.f32 (*.f32 uy 2) (PI.f32)))

3.0ms

(expm1.f32 (log1p.f32 (*.f32 (*.f32 uy 2) (PI.f32))))

rewrite75.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`log1p-udef_binary32`
204×	`add-sqr-sqrt_binary32`
195×	`expm1-log1p-u_binary32`
194×	`log1p-expm1-u_binary32`
189×	`add-log-exp_binary32`

Counts

3 → 61

Calls

3 calls:

74.0ms

(*.f32 (cos.f32 (expm1.f32 (log1p.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))))))

74.0ms

(log1p.f32 (*.f32 (*.f32 uy 2) (PI.f32)))

74.0ms

(expm1.f32 (log1p.f32 (*.f32 (*.f32 uy 2) (PI.f32))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	55
1	408	53
2	4849	53
3	5392	53
0	0	0
1	0	0

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary32`
556×	`fma-neg_binary32`
263×	`sub-neg_binary32`
246×	`fma-def_binary32`
228×	`associate-r_binary32`

Counts

109 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3143
1	725	2762
2	2728	2758
3	4833	2758
4	5017	2758

prune262.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	133	12	145

Error

0.1b

Counts

145 → 12

Alt Table

Status	Error	Program
	1.2b	(.f32 (log.f32 (exp.f32 (cos.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))))))
	0.8b	(.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 ux (*.f32 2 maxCos))))))
✓	0.7b	(.f32 (cos.f32 (expm1.f32 (log1p.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))))))
	6.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (log.f32 (exp.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))))
	1.2b	(pow.f32 (cbrt.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux)))))) 3)
	1.8b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 uy 2) 3)))) (pow.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (fma.f32 2 maxCos ux))) 3/2) 1/3))
	1.5b	(-.f32 (.f32 (+.f32 (.f32 2/3 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 uy 4))) 1) (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 (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 (.f32 2 (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 4/45 (*.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6))))))
	14.2b	(.f32 (cos.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)))
	0.9b	(.f32 (cos.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 (fma.f32 2 maxCos ux)) 2))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (.f32 ux (fma.f32 2 maxCos ux))))))
	5.2b	(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))))))
	14.8b	(pow.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) 2)
	1.0b	(-.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (+.f32 (sqrt.f32 (.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))))))) (+.f32 (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))) (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))))) (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (+.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))))) (.f32 maxCos (.f32 ux (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))))))

Compiler

Compiled 6615 to 4332 computations (34.5% saved)

regimes3.4s (33%)

Accuracy

Total 0.2b remaining (64%)

Threshold costs 0.2b (64%)

Counts

207 → 1

Compiler

Compiled 95864 to 70387 computations (26.6% saved)

simplify6.0ms (0.1%)

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

end401.0ms (3.9%)

Compiler: Compiled 606 to 425 computations (29.9% saved)

Details

analyze658.0ms (6.3%)

sample2.2s (20.9%)

simplify47.0ms (0.5%)

prune7.0ms (0.1%)

localize49.0ms (0.5%)

series276.0ms (2.7%)

rewrite87.0ms (0.8%)

simplify171.0ms (1.6%)

prune393.0ms (3.8%)

localize58.0ms (0.6%)

series419.0ms (4%)

rewrite79.0ms (0.8%)

simplify87.0ms (0.8%)

prune406.0ms (3.9%)

localize79.0ms (0.8%)

series230.0ms (2.2%)

rewrite65.0ms (0.6%)

simplify85.0ms (0.8%)

prune458.0ms (4.4%)

localize70.0ms (0.7%)

series229.0ms (2.2%)

rewrite75.0ms (0.7%)

simplify98.0ms (0.9%)

prune262.0ms (2.5%)

regimes3.4s (33%)

simplify6.0ms (0.1%)

end401.0ms (3.9%)

Profiling