Details

analyze1.4s (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)

sample120.0ms (0.4%)

Algorithm

1×

intervals

Results

67.0ms	256×	body	128	valid
16.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify62.0ms (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

prune9.0ms (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

12.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.6b	(.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)))
▶	12.6b	(.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

12.6b

(*.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)))

▶

12.6b

(*.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)

localize101.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.3b	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
✓	0.4b	(.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))))))
✓	12.2b	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))

series555.0ms (1.8%)

Counts

4 → 92

Calls

4 calls:

498.0ms	(.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))))))
41.0ms	(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))
12.0ms	(.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite35.0ms (0.1%)

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)))
6.0ms	(.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))))))
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))

simplify148.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-l_binary32`
569×	`associate-r_binary32`
419×	`fma-def_binary32`
156×	`times-frac_binary32`
153×	`associate-/l*_binary32`

Counts

201 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	462	10137
1	1454	8391
2	5353	8391

prune523.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	237	15	252
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	239	15	254

Error

0.3b

Counts

254 → 15

Alt Table

Status	Error	Program
	12.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (/.f32 (-.f32 (pow.f32 1 3) (pow.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) 3)) (+.f32 (.f32 1 1) (+.f32 (.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))) (.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))))
	3.0b	(fma.f32 4/15 (.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))))) (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))) (.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))))) (-.f32 (.f32 2 (.f32 (PI.f32) uy)) (.f32 4/3 (*.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))
	12.7b	(.f32 (sin.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))))))))
	3.9b	(.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))))) (-.f32 (.f32 2 (.f32 (PI.f32) uy)) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))
	12.6b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (cbrt.f32 (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux)))))) (cbrt.f32 (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux)))))))) (cbrt.f32 (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))
	12.6b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux)))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))))
	5.4b	(-.f32 (fma.f32 1/2 (.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 6))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5)))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (+.f32 (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))) (.f32 3/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 4)))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (pow.f32 (.f32 maxCos ux) 3))))) (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 5))) (+.f32 (.f32 1/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (pow.f32 (.f32 maxCos ux) 3))) (.f32 3/2 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 5)))))) (.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (*.f32 ux (-.f32 2 ux)) 3)))))))))
▶	0.5b	(.f32 (sin.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))))))
	12.7b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	0.9b	(-.f32 (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (+.f32 (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.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))))))) (fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 1/2 (+.f32 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4)))) (.f32 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (+.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3)))))))))
	1.3b	(fma.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	8.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	0.7b	(.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))))))
	12.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (expm1.f32 (log1p.f32 (.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (fma.f32 maxCos ux (-.f32 1 ux))))))))
	2.1b	(-.f32 (+.f32 (.f32 4/15 (.f32 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux)))))))) (.f32 2 (.f32 (.f32 uy (PI.f32)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux))))))))) (+.f32 (.f32 8/315 (.f32 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux)))))))) (.f32 4/3 (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 uy 3)) (sqrt.f32 (-.f32 (+.f32 (.f32 2 (.f32 maxCos (pow.f32 ux 2))) (.f32 2 ux)) (+.f32 (pow.f32 ux 2) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 2 (.f32 maxCos ux))))))))))

Compiler

Compiled 14976 to 9591 computations (36% saved)

localize72.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))
✓	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (sin.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))))))

series259.0ms (0.8%)

Counts

3 → 68

Calls

3 calls:

241.0ms

(*.f32 (sin.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))))))

14.0ms

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

4.0ms

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

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

8.0ms

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

7.0ms

(*.f32 (sin.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))))))

1.0ms

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

simplify157.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

556×	`associate-l_binary32`
547×	`fma-neg_binary32`
463×	`associate-r_binary32`
391×	`fma-def_binary32`
156×	`times-frac_binary32`

Counts

127 → 156

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	386	7192
1	1216	6425
2	4874	6425
3	5326	6425

prune486.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	180	8	188
Fresh	13	1	14
Picked	1	0	1
Done	0	0	0
Total	194	9	203

Error

0.1b

Counts

203 → 9

Alt Table

Status	Error	Program
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	2.0b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (sin.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 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (.f32 (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))) (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 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))
	12.7b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	0.6b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))))) (sqrt.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)))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))

Compiler

Compiled 12084 to 6816 computations (43.6% saved)

localize84.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series254.0ms (0.8%)

Counts

4 → 56

Calls

4 calls:

240.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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	(log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))
3.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))
2.0ms	(*.f32 (PI.f32) uy)

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary32`
9×	`associate-r_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`
8×	`add-cbrt-cube_binary32`

Counts

4 → 68

Calls

4 calls:

6.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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	(*.f32 (PI.f32) uy)
0.0ms	(log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))
0.0ms	(expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))

simplify117.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

458×	`associate-l_binary32`
439×	`associate-r_binary32`
382×	`fma-def_binary32`
158×	`associate-+l+_binary32`
156×	`times-frac_binary32`

Counts

124 → 166

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	7313
1	1294	6319
2	5075	6319

prune306.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	164	11	175

Error

0.0b

Counts

175 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) uy)))))) (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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (.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 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	12.7b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	2.0b	(.f32 (sqrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (.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 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))))) (sqrt.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 (.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 (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 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.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 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (sin.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 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2)))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))

Compiler

Compiled 11748 to 6750 computations (42.5% saved)

localize126.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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 (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 (+.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 (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 (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))))))))
	0.3b	(*.f32 (PI.f32) uy)
✓	0.6b	(.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)))))

series7.4s (24.4%)

Counts

3 → 92

Calls

3 calls:

7.1s

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

361.0ms

(*.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 (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))))))))

26.0ms

(*.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)))))

rewrite41.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary32`
14×	`*-un-lft-identity_binary32`
14×	`add-cube-cbrt_binary32`
12×	`add-cbrt-cube_binary32`
12×	`add-exp-log_binary32`

Counts

3 → 89

Calls

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

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 (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))))))))

3.0ms

(*.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)))))

simplify508.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary32`
560×	`associate-+r+_binary32`
462×	`associate-r_binary32`
162×	`associate-*r/_binary32`
64×	`sqr-pow_binary32`

Counts

181 → 229

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1844	52638
1	5166	52638

prune2.4s (7.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	247	4	251
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	248	14	262

Error

0.0b

Counts

262 → 14

Alt Table

Status	Error	Program
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (sin.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)))))))
	3.7b	(/.f32 (exp.f32 (+.f32 (log.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))) (log.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 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))
	0.8b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) uy)))))) (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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))))) (.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 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	12.7b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (.f32 (PI.f32) uy))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	2.0b	(.f32 (sqrt.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (.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 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))))) (sqrt.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 (.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 (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 (+.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (*.f32 maxCos ux) 2))))))
	3.9b	(/.f32 (-.f32 (.f32 2 (.f32 (.f32 uy (PI.f32)) (sqrt.f32 (-.f32 (fma.f32 4 (.f32 ux ux) (fma.f32 4 (.f32 maxCos (pow.f32 ux 3)) (.f32 2 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))))) (fma.f32 4 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (+.f32 (pow.f32 ux 4) (fma.f32 4 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (.f32 (pow.f32 maxCos 4) (pow.f32 ux 4))))))))) (.f32 4/3 (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (sqrt.f32 (-.f32 (fma.f32 4 (.f32 ux ux) (fma.f32 4 (.f32 maxCos (pow.f32 ux 3)) (.f32 2 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))))) (fma.f32 4 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (+.f32 (pow.f32 ux 4) (fma.f32 4 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (.f32 (pow.f32 maxCos 4) (pow.f32 ux 4)))))))))) (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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (.f32 (PI.f32) uy)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 maxCos (.f32 ux (fma.f32 maxCos ux 2)) (.f32 ux ux)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))))))
	22.0b	(/.f32 (log.f32 (exp.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 (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 (+.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 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (/.f32 (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)))))) (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)))))))))
✓	0.6b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 (PI.f32) uy))))) (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))))))
	0.8b	(.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)) (fma.f32 ux ux (.f32 (.f32 maxCos ux) (+.f32 (.f32 maxCos ux) 2))))))

Compiler

Compiled 72966 to 47446 computations (35% saved)

regimes11.9s (39.1%)

Accuracy

Total 0.5b remaining (86.9%)

Threshold costs 0.5b (86.9%)

Counts

374 → 1

Compiler

Compiled 218804 to 141348 computations (35.4% saved)

simplify6.0ms (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	20	46
1	27	46
2	32	46
3	34	46
4	35	46
5	35	46

end1.0ms (0%)

Compiler: Compiled 33 to 21 computations (36.4% saved)

sample3.4s (11%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
434.0ms	8000×	pre	128	true

Compiler

Compiled 964 to 573 computations (40.6% saved)

Details

analyze1.4s (4.6%)

sample120.0ms (0.4%)

simplify62.0ms (0.2%)

prune9.0ms (0%)

localize101.0ms (0.3%)

series555.0ms (1.8%)

rewrite35.0ms (0.1%)

simplify148.0ms (0.5%)

prune523.0ms (1.7%)

localize72.0ms (0.2%)

series259.0ms (0.8%)

rewrite21.0ms (0.1%)

simplify157.0ms (0.5%)

prune486.0ms (1.6%)

localize84.0ms (0.3%)

series254.0ms (0.8%)

rewrite15.0ms (0%)

simplify117.0ms (0.4%)

prune306.0ms (1%)

localize126.0ms (0.4%)

series7.4s (24.4%)

rewrite41.0ms (0.1%)

simplify508.0ms (1.7%)

prune2.4s (7.8%)

regimes11.9s (39.1%)

simplify6.0ms (0%)

end1.0ms (0%)

sample3.4s (11%)

Profiling