Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 118 to 85 computations (28% saved)

sample4.1s (33.9%)

Results

4.1s

8256×

body

128

valid

Compiler

Compiled 236 to 170 computations (28% saved)

preprocess63.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

404×	`distribute-rgt-neg-in_binary32`
374×	`distribute-lft-neg-in_binary32`
320×	`distribute-rgt-in_binary32`
274×	`distribute-lft-in_binary32`
271×	`associate-r_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	191	1584
1	601	1552
2	2217	1120
3	4855	1120
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 71 to 50 computations (29.6% saved)

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

362×	`distribute-rgt-in_binary32`
340×	`fma-def_binary32`
335×	`distribute-lft-in_binary32`
255×	`distribute-neg-in_binary32`
228×	`distribute-rgt-neg-out_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	67	97
2	214	70
3	839	66
4	2903	66
5	4998	66

Stop Event

1×	node limit

Counts

1 → 2

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))

Status

Error

Program

▶

0.3b

(fma.f32 ux (*.f32 (-.f32 1 ux) (*.f32 maxCos zi)) (*.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (*.f32 (*.f32 ux (*.f32 maxCos (*.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (*.f32 uy (*.f32 2 (PI.f32)))) xi (*.f32 (sin.f32 (*.f32 uy (*.f32 2 (PI.f32)))) yi))))

0.3b

(+.f32 (+.f32 (*.f32 (*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) xi) (*.f32 (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))

Compiler

Compiled 354 to 245 computations (30.8% saved)

localize102.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
✓	0.2b	(cos.f32 (.f32 uy (.f32 2 (PI.f32))))
✓	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
✓	0.4b	(.f32 uy (.f32 2 (PI.f32)))

series28.0ms (0.2%)

Counts

4 → 68

Calls

21 calls:

3.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)	yi	-inf
3.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)	uy	inf
3.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)	yi	0
2.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)	yi	inf
2.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)	uy	0

rewrite59.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`prod-diff_binary32`
173×	`add-sqr-sqrt_binary32`
169×	`*-un-lft-identity_binary32`
169×	`pow1_binary32`
158×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	341	41
2	4116	41
0	17	41

Stop Event

1×	saturated
1×	node limit

Counts

4 → 69

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-neg_binary32`
583×	`associate-r_binary32`
576×	`associate-l_binary32`
450×	`unswap-sqr_binary32`
220×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	878
1	252	870
2	756	861
3	3680	860

Stop Event

1×	node limit

Counts

137 → 98

prune377.0ms (3.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	14	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	15	117

Error

0.1b

Counts

117 → 15

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 uy (.f32 2 (PI.f32)))) 2)) yi))))
	1.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 uy uy)) -2 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) 1)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi)) 3))))
	0.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (pow.f32 (.f32 uy (.f32 2 (PI.f32))) 3) 1/3)) yi))))
	0.3b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (log1p.f32 (expm1.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32))))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (log.f32 (exp.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	1.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 uy 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 uy uy) -2))))) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	5.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) 3) (pow.f32 yi 3))))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 uy (.f32 2 (PI.f32)))) 3)) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
▶	0.3b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (pow.f32 (sqrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))

Compiler

Compiled 7191 to 4312 computations (40% saved)

localize106.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
	0.2b	(cos.f32 (.f32 uy (.f32 2 (PI.f32))))
	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
	0.4b	(.f32 uy (.f32 2 (PI.f32)))

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

2.0ms	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))	uy	0
0.0ms	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))	uy	inf
0.0ms	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))	uy	-inf

rewrite32.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

649×	`pow1_binary32`
595×	`add-log-exp_binary32`
595×	`log1p-expm1-u_binary32`
595×	`expm1-log1p-u_binary32`
70×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	140	10
2	1616	10
0	7	10

Stop Event

1×	saturated
1×	node limit

Counts

1 → 17

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary32`
544×	`cancel-sign-sub-inv_binary32`
402×	`unswap-sqr_binary32`
368×	`fma-neg_binary32`
316×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	202
1	94	198
2	305	196
3	1329	196
4	4255	196

Stop Event

1×	node limit

Counts

29 → 27

prune474.0ms (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Error

0.1b

Counts

129 → 14

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 uy (.f32 2 (PI.f32)))) 2)) yi))))
	1.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 uy uy)) -2 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) 1)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	4.8b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))) yi))))
▶	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (log.f32 (exp.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	1.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 uy 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 uy uy) -2))))) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	5.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) 3) (pow.f32 yi 3))))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi)) 3))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32))))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 3) yi))))
	1.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (pow.f32 (sqrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.3b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32)))))) yi))))

Compiler

Compiled 7144 to 3954 computations (44.7% saved)

localize101.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series252.0ms (2.1%)

Counts

4 → 108

Calls

27 calls:

33.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)	uy	inf
28.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)	yi	-inf
25.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)	yi	0
25.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)	yi	inf
24.0ms	(.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)	uy	-inf

rewrite38.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

205×	`associate-r_binary32`
203×	`add-sqr-sqrt_binary32`
198×	`*-un-lft-identity_binary32`
198×	`pow1_binary32`
186×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	401	64
0	19	82

Stop Event

1×	saturated
1×	node limit

Counts

4 → 63

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary32`
468×	`associate-r_binary32`
426×	`fma-neg_binary32`
346×	`associate-l_binary32`
258×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	5170
1	1044	4710
2	3893	4706

Stop Event

1×	node limit

Counts

171 → 137

prune1.2s (10%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	288	14	302

Error

0.1b

Counts

302 → 14

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 uy (.f32 2 (PI.f32)))) 2)) yi))))
	1.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 uy uy)) -2 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) 1)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	4.8b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))) yi))))
✓	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (log.f32 (exp.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	1.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 uy 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 uy uy) -2))))) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	5.5b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (cbrt.f32 (.f32 (pow.f32 (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (pow.f32 (.f32 ux (.f32 (-.f32 1 ux) maxCos)) 2)))) 3) (pow.f32 yi 3)))) (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi)) 3))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32))))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 3) yi))))
	1.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (pow.f32 (sqrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
▶	0.3b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32)))))) yi))))

Compiler

Compiled 23064 to 15490 computations (32.8% saved)

localize119.0ms (1%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.2%)

Counts

3 → 48

Calls

12 calls:

3.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (*.f32 2 (PI.f32)))))) yi)	uy	0
3.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (*.f32 2 (PI.f32)))))) yi)	yi	-inf
3.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (*.f32 2 (PI.f32)))))) yi)	yi	0
3.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 uy (*.f32 2 (PI.f32)))))) yi)	yi	inf
2.0ms	(log1p.f32 (.f32 uy (.f32 2 (PI.f32))))	uy	0

rewrite46.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

849×	`expm1-log1p-u_binary32`
848×	`log1p-expm1-u_binary32`
98×	`add-sqr-sqrt_binary32`
97×	`pow1_binary32`
96×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	200	31
2	2305	31
0	11	39

Stop Event

1×	saturated
1×	node limit

Counts

3 → 70

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-l_binary32`
517×	`associate-r_binary32`
291×	`fma-def_binary32`
232×	`cancel-sign-sub-inv_binary32`
204×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	899
1	324	885
2	1045	869
3	4875	869

Stop Event

1×	node limit

Counts

118 → 103

prune448.0ms (3.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	136	15	151

Error

0.1b

Counts

151 → 15

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 uy (.f32 2 (PI.f32)))) 2)) yi))))
	1.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 uy uy)) -2 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) 1)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	0.3b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 2 (PI.f32))) (.f32 (sqrt.f32 (.f32 2 (PI.f32))) uy))) yi))))
	5.5b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 3) (pow.f32 yi 3))))))
	4.8b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))) yi))))
✓	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.7b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (log.f32 (exp.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (pow.f32 (cbrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2)) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	1.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (+.f32 1 (fma.f32 2/3 (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 uy 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 uy uy) -2))))) xi (.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 uy (.f32 2 (PI.f32))))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 3) yi))))
	1.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (pow.f32 (sqrt.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) 2) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.3b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 2 (PI.f32))) 2) (.f32 (cbrt.f32 (.f32 2 (PI.f32))) uy))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (*.f32 2 (PI.f32))))) yi))))

Compiler

Compiled 7819 to 4234 computations (45.8% saved)

regimes3.8s (31.3%)

Accuracy

Total 0.2b remaining (62.3%)

Threshold costs 0.2b (62.3%)

Counts

210 → 1

Compiler

Compiled 129718 to 91747 computations (29.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary32`
6×	`+-commutative_binary32`
5×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	77
1	54	77
2	65	77
3	71	77
4	75	77
5	76	77

Stop Event

1×

saturated

end462.0ms (3.8%)

Stop Event

1×

fuel

Compiler

Compiled 991 to 697 computations (29.7% saved)

Details

analyze8.0ms (0.1%)

sample4.1s (33.9%)

preprocess63.0ms (0.5%)

simplify32.0ms (0.3%)

prune7.0ms (0.1%)

localize102.0ms (0.8%)

series28.0ms (0.2%)

rewrite59.0ms (0.5%)

simplify41.0ms (0.3%)

prune377.0ms (3.1%)

localize106.0ms (0.9%)

series3.0ms (0%)

rewrite32.0ms (0.3%)

simplify29.0ms (0.2%)

prune474.0ms (3.9%)

localize101.0ms (0.8%)

series252.0ms (2.1%)

rewrite38.0ms (0.3%)

simplify94.0ms (0.8%)

prune1.2s (10%)

localize119.0ms (1%)

series23.0ms (0.2%)

rewrite46.0ms (0.4%)

simplify46.0ms (0.4%)

prune448.0ms (3.7%)

regimes3.8s (31.3%)

simplify4.0ms (0%)

end462.0ms (3.8%)

Profiling