Details

analyze1.4s (4.1%)

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 41 to 30 computations (26.8% saved)

sample189.0ms (0.5%)

Algorithm

1×

intervals

Results

64.0ms	256×	body	128	valid
14.0ms	256×	pre	128	true

Compiler

Compiled 72 to 53 computations (26.4% saved)

simplify61.0ms (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

prune10.0ms (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

13.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
▶	13.7b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Status

Error

Program

13.8b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

▶

13.7b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize129.0ms (0.4%)

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)))
✓	0.3b	(.f32 (.f32 uy 2) PI.f32)
✓	14.3b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

rewrite26.0ms (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:

10.0ms	(.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)))
7.0ms	(.f32 (.f32 uy 2) PI.f32)
3.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
1.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series594.0ms (1.7%)

Counts

4 → 80

Calls

4 calls:

499.0ms	(.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)))
66.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
23.0ms	(.f32 (.f32 uy 2) PI.f32)
5.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))

simplify359.0ms (1%)

Algorithm

1×	egg-herbie

Rules

511×	`fma-neg_binary32`
483×	`associate-l_binary32`
416×	`associate-r_binary32`
348×	`fma-def_binary32`
173×	`associate-+r+_binary32`

Counts

143 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	357	7712
1	1156	6681
2	4985	6681
3	5414	6681

prune530.0ms (1.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	235	18	253
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	237	18	255

Error

0.3b

Counts

255 → 18

Alt Table

Status	Error	Program
	13.7b	(.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.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)))
	13.8b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (log.f32 (exp.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	13.7b	(.f32 (log1p.f32 (expm1.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)))
	1.2b	(-.f32 (fma.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (.f32 (.f32 maxCos maxCos) (pow.f32 ux 3)) (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3)))) (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (+.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 (.f32 ux (-.f32 2 ux)))) (+.f32 (.f32 1/2 (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (.f32 uy PI.f32))))))) (.f32 maxCos (.f32 ux (sin.f32 (.f32 2 (.f32 uy PI.f32))))))) (.f32 1/2 (.f32 (sqrt.f32 (/.f32 1 (pow.f32 (.f32 ux (-.f32 2 ux)) 3))) (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (.f32 maxCos maxCos) (pow.f32 ux 4))) (.f32 (.f32 ux ux) (.f32 maxCos (.f32 maxCos (sin.f32 (.f32 2 (*.f32 uy PI.f32)))))))))))
	13.9b	(.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)))
	2.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 ux (-.f32 2 ux))))
	13.7b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1))))) (cbrt.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
	1.5b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (.f32 maxCos (.f32 ux ux)) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (-.f32 (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 maxCos ux) (sqrt.f32 (/.f32 1 (*.f32 ux (-.f32 2 ux))))))))
	20.6b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))))
▶	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.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))))))
	2.4b	(-.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 uy 5) (pow.f32 PI.f32 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))))))
	7.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))
	3.3b	(fma.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 uy 5) (pow.f32 PI.f32 5)))) (.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))))) (.f32 (pow.f32 uy 3) (pow.f32 PI.f32 3))) -4/3))
	13.7b	(.f32 (sin.f32 (.f32 (.f32 (.f32 uy 2) (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	6.5b	(.f32 2 (.f32 (.f32 uy PI.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)))))))
	13.7b	(.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)))
	13.7b	(.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (*.f32 PI.f32 PI.f32) PI.f32)))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	14.7b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 maxCos ux (-.f32 1 ux)) (-.f32 ux (fma.f32 maxCos ux 1)) 1)))))

Compiler

Compiled 10868 to 7105 computations (34.6% saved)

localize149.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))))
	0.2b	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
✓	0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	0.3b	(.f32 (.f32 uy 2) PI.f32)

rewrite38.0ms (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:

19.0ms

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

14.0ms

(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)))))

series554.0ms (1.6%)

Counts

2 → 52

Calls

2 calls:

414.0ms

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

139.0ms

(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)))))

simplify259.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary32`
517×	`associate-r_binary32`
446×	`associate-l_binary32`
240×	`times-frac_binary32`
207×	`associate-/l*_binary32`

Counts

95 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	472	9784
1	1643	8674
2	5404	8674

prune713.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	250	12	262
Fresh	15	2	17
Picked	1	0	1
Done	0	0	0
Total	266	14	280

Error

0.0b

Counts

280 → 14

Alt Table

Status	Error	Program
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.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)))))))
	13.7b	(.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (*.f32 PI.f32 PI.f32) PI.f32)))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
▶	0.6b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.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))))))
	2.1b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	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)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	2.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 ux (-.f32 2 ux))))
	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.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))))) (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)))))) (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))))))))
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	0.6b	(.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 PI.f32 PI.f32) PI.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))))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))) (cbrt.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)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	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 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	3.2b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))

Compiler

Compiled 16328 to 9949 computations (39.1% saved)

localize88.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite16.0ms (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:

9.0ms	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.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))))))
3.0ms	(*.f32 uy PI.f32)
0.0ms	(expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))
0.0ms	(log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32)))))

series1.1s (3.3%)

Counts

4 → 56

Calls

4 calls:

606.0ms	(log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32)))))
521.0ms	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.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))))))
8.0ms	(*.f32 uy PI.f32)
5.0ms	(expm1.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))

simplify309.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-neg_binary32`
466×	`associate-r_binary32`
402×	`fma-def_binary32`
381×	`associate-l_binary32`
148×	`times-frac_binary32`

Counts

124 → 216

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	387	7305
1	1204	6389
2	4905	6389
3	5412	6389

prune543.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	218	12	230

Error

0.0b

Counts

230 → 12

Alt Table

Status	Error	Program
	0.9b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 uy) (cbrt.f32 uy)) (.f32 (cbrt.f32 uy) PI.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))))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))) (sqrt.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)))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 uy PI.f32)) (sqrt.f32 (.f32 uy PI.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))))))
	2.1b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	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)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
▶	0.6b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.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))))) (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)))))) (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))))))))
	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)))) maxCos) (-.f32 (.f32 (.f32 ux ux) (sin.f32 (.f32 2 (.f32 uy PI.f32)))) (.f32 ux (sin.f32 (.f32 2 (*.f32 uy PI.f32)))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	1.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (exp.f32 (log.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))) (cbrt.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)))))))
	3.2b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))

Compiler

Compiled 11949 to 7186 computations (39.9% saved)

localize229.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32)))
✓	0.4b	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.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))))) (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)))))) (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)))))))
✓	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (*.f32 uy 2) PI.f32)))
✓	0.5b	(.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))))) (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))))))

rewrite244.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`pow1_binary32`
120×	`sqrt-div_binary32`
86×	`frac-times_binary32`
60×	`flip--_binary32`
60×	`flip3--_binary32`

Counts

4 → 239

Calls

4 calls:

111.0ms	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.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))))) (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)))))) (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)))))))
34.0ms	(.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))))) (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))))))
15.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32)))
9.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (*.f32 uy 2) PI.f32)))

series2.4s (6.8%)

Counts

4 → 80

Calls

4 calls:

2.2s	(.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.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))))) (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)))))) (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)))))))
96.0ms	(.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))))) (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))))))
30.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32)))
18.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (*.f32 uy 2) PI.f32)))

simplify998.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

482×	`*-commutative_binary32`
245×	`associate-r_binary32`
232×	`+-commutative_binary32`
226×	`fma-def_binary32`
205×	`associate-+r+_binary32`

Counts

319 → 603

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1041	33687
1	3286	28348
2	4958	28348

prune2.6s (7.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	598	5	603
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	603	12	615

Error

0.0b

Counts

615 → 12

Alt Table

Status	Error	Program
	0.6b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) 3) (.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))))) (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)))))) (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))))))))
	18.7b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (cos.f32 (-.f32 (.f32 (.f32 uy 2) PI.f32) (.f32 (.f32 uy 2) PI.f32))) (cos.f32 (+.f32 (.f32 (.f32 uy 2) PI.f32) (.f32 (.f32 uy 2) PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (.f32 (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3))) (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3)))) (sqrt.f32 (-.f32 (pow.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) 3) (pow.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) 3))))) (.f32 2 (.f32 (.f32 (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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))))))) (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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)))))))) (sqrt.f32 (+.f32 (.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux))) (+.f32 (.f32 (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux))) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (.f32 maxCos ux)))) (.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)))))))))))
	0.7b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (fabs.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (sqrt.f32 (cbrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))))))
	0.9b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 uy) (cbrt.f32 uy)) (.f32 (cbrt.f32 uy) PI.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))))))
	4.6b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))) 3)) (fma.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 PI.f32 3)) (.f32 (*.f32 (pow.f32 uy 5) (pow.f32 PI.f32 5)) -16))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))) (cbrt.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)))))))
	0.7b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (.f32 (.f32 (cbrt.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)))))) (cbrt.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))))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (cbrt.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux)))))))) (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))))))))
	7.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (.f32 (-.f32 2 (.f32 2 maxCos)) ux) (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))))))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 2 (.f32 (sqrt.f32 (.f32 uy PI.f32)) (sqrt.f32 (.f32 uy PI.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))))))
	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)) (+.f32 (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)) (.f32 2 (*.f32 maxCos ux))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32)))))) (cbrt.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	3.2b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (.f32 ux (+.f32 (.f32 2 maxCos) (.f32 (fma.f32 maxCos maxCos 1) ux))))) (sin.f32 (.f32 2 (.f32 uy PI.f32))))))

Compiler

Compiled 57715 to 33142 computations (42.6% saved)

regimes16.7s (47.7%)

Accuracy

Total 0.4b remaining (85.2%)

Threshold costs 0.4b (85.2%)

Compiler

Compiled 349631 to 199768 computations (42.9% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary32`
16×	`+-commutative_binary32`
14×	`sub-neg_binary32`
13×	`distribute-rgt-neg-in_binary32`
12×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	84
1	52	84
2	68	84
3	99	84
4	135	84
5	150	84
6	157	84
7	158	84
8	156	84

end2.0ms (0%)

Compiler: Compiled 59 to 36 computations (39% saved)

sample4.7s (13.4%)

Algorithm

1×

intervals

Results

2.1s	8000×	body	128	valid
467.0ms	8000×	pre	128	true

Compiler

Compiled 1181 to 686 computations (41.9% saved)

Details

analyze1.4s (4.1%)

sample189.0ms (0.5%)

simplify61.0ms (0.2%)

prune10.0ms (0%)

localize129.0ms (0.4%)

rewrite26.0ms (0.1%)

series594.0ms (1.7%)

simplify359.0ms (1%)

prune530.0ms (1.5%)

localize149.0ms (0.4%)

rewrite38.0ms (0.1%)

series554.0ms (1.6%)

simplify259.0ms (0.7%)

prune713.0ms (2%)

localize88.0ms (0.3%)

rewrite16.0ms (0%)

series1.1s (3.3%)

simplify309.0ms (0.9%)

prune543.0ms (1.6%)

localize229.0ms (0.7%)

rewrite244.0ms (0.7%)

series2.4s (6.8%)

simplify998.0ms (2.9%)

prune2.6s (7.5%)

regimes16.7s (47.7%)

simplify15.0ms (0%)

end2.0ms (0%)

sample4.7s (13.4%)

Profiling