Details

analyze655.0ms (4.6%)

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)

sample183.0ms (1.3%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify46.0ms (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

13.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.3b	(.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))))))
	13.3b	(.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

▶

13.3b

(*.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))))))

13.3b

(*.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 (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))))))
✓	0.2b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	13.1b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series264.0ms (1.8%)

Counts

4 → 92

Calls

4 calls:

228.0ms	(.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))))))
23.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
10.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
7.0ms	(.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))))))
4.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))

simplify238.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-l_binary32`
546×	`associate-r_binary32`
390×	`fma-def_binary32`
156×	`times-frac_binary32`
153×	`associate-/l*_binary32`

Counts

201 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	450	10119
1	1413	8467
2	5203	8467

prune374.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	240	11	251
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	242	11	253

Error

0.2b

Counts

253 → 11

Alt Table

Status	Error	Program
	13.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (log.f32 (exp.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))))
	5.7b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))
	13.3b	(log.f32 (exp.f32 (.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))))
	7.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	14.0b	(exp.f32 (+.f32 (log.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (log.f32 (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))))
	1.7b	(-.f32 (+.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 2/3 (.f32 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (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 4/45 (.f32 (.f32 (pow.f32 uy 6) (pow.f32 (PI.f32) 6)) (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 (pow.f32 (PI.f32) 2) (pow.f32 uy 2)) (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))))))))))
	0.9b	(-.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 (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 (.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 (.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 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)))))))))
	0.5b	(.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))))))
	2.0b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 ux (-.f32 2 ux))))
▶	0.3b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	13.3b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))

Compiler

Compiled 13896 to 8900 computations (36% saved)

localize70.0ms (0.5%)

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

series328.0ms (2.3%)

Counts

3 → 64

Calls

3 calls:

227.0ms

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

97.0ms

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

3.0ms

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

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

6.0ms

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

5.0ms

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

1.0ms

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

simplify151.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-def_binary32`
508×	`associate-r_binary32`
438×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

116 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	496	10094
1	1653	8990
2	5257	8990

prune467.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	204	9	213
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	214	10	224

Error

0.0b

Counts

224 → 10

Alt Table

Status	Error	Program
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	5.9b	(.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)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (.f32 2 (*.f32 uy (PI.f32)))))))
▶	0.3b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	7.4b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
	0.5b	(.f32 (cos.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 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) 3))) (sqrt.f32 (fma.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux)))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))

Compiler

Compiled 15663 to 9311 computations (40.6% saved)

localize82.0ms (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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))
✓	0.1b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
✓	0.3b	(.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8))
✓	1.0b	(pow.f32 (PI.f32) 3)

series291.0ms (2%)

Counts

3 → 44

Calls

3 calls:

277.0ms

(*.f32 (cos.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))

13.0ms

(*.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) 8))

0.0ms

(pow.f32 (PI.f32) 3)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary32`
22×	`prod-exp_binary32`
16×	`add-sqr-sqrt_binary32`
15×	`associate-l_binary32`
12×	`*-un-lft-identity_binary32`

Counts

3 → 88

Calls

3 calls:

7.0ms

(*.f32 (cos.f32 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) 8)))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 ux ux (*.f32 (*.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))

6.0ms

(*.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) 8))

3.0ms

(pow.f32 (PI.f32) 3)

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-r_binary32`
456×	`associate-l_binary32`
369×	`fma-def_binary32`
156×	`associate-+l+_binary32`
132×	`*-commutative_binary32`

Counts

132 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	412	7525
1	1223	6724
2	4966	6724

prune507.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Error

0.0b

Counts

241 → 9

Alt Table

Status	Error	Program
	0.7b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (*.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))))
▶	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
	0.5b	(.f32 (cos.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 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) 3))) (sqrt.f32 (fma.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux)))))))
	0.9b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (.f32 (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))

Compiler

Compiled 17369 to 10738 computations (38.2% saved)

localize78.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series856.0ms (6%)

Counts

2 → 44

Calls

2 calls:

564.0ms

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

291.0ms

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

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary32`
21×	`cbrt-prod_binary32`
14×	`*-un-lft-identity_binary32`
14×	`add-cube-cbrt_binary32`
12×	`associate-r_binary32`

Counts

2 → 73

Calls

2 calls:

8.0ms

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

8.0ms

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

simplify131.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-r_binary32`
601×	`associate-l_binary32`
535×	`fma-def_binary32`
158×	`*-commutative_binary32`
103×	`associate-*r/_binary32`

Counts

117 → 169

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	8282
1	1306	7047
2	5122	7047

prune803.0ms (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	329	9	338

Error

0.0b

Counts

338 → 9

Alt Table

Status	Error	Program
	0.7b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.6b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))))
	0.5b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (sqrt.f32 (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2))))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))) (cos.f32 (cbrt.f32 (.f32 8 (*.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))))
✓	0.4b	(.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2)))))))
	0.5b	(.f32 (cos.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 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) 3))) (sqrt.f32 (fma.f32 (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))) (fma.f32 2 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))) (.f32 4 (.f32 (fma.f32 maxCos (.f32 ux ux) ux) (fma.f32 maxCos (.f32 ux ux) ux)))))))
	0.9b	(.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) 8)))) (.f32 (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)))))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))
	1.1b	(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 maxCos (*.f32 ux (fma.f32 maxCos ux 2)))))))))

Compiler

Compiled 25104 to 15536 computations (38.1% saved)

regimes6.4s (44.5%)

Accuracy

Total 0.2b remaining (70.6%)

Threshold costs 0.2b (70.6%)

Counts

286 → 1

Compiler

Compiled 176942 to 117854 computations (33.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	35	59
2	40	59
3	42	59
4	43	59
5	43	59

end1.0ms (0%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

sample2.2s (15.1%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
293.0ms	8000×	pre	128	true

Compiler

Compiled 670 to 409 computations (39% saved)

Details

analyze655.0ms (4.6%)

sample183.0ms (1.3%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize49.0ms (0.3%)

series264.0ms (1.8%)

rewrite33.0ms (0.2%)

simplify238.0ms (1.7%)

prune374.0ms (2.6%)

localize70.0ms (0.5%)

series328.0ms (2.3%)

rewrite16.0ms (0.1%)

simplify151.0ms (1.1%)

prune467.0ms (3.2%)

localize82.0ms (0.6%)

series291.0ms (2%)

rewrite22.0ms (0.2%)

simplify123.0ms (0.9%)

prune507.0ms (3.5%)

localize78.0ms (0.5%)

series856.0ms (6%)

rewrite24.0ms (0.2%)

simplify131.0ms (0.9%)

prune803.0ms (5.6%)

regimes6.4s (44.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.2s (15.1%)

Profiling