Details

analyze24.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 118 to 85 computations (28% saved)

sample4.2s (45.8%)

Results

4.1s

8256×

body

128

valid

Compiler

Compiled 307 to 220 computations (28.3% saved)

simplify38.0ms (0.4%)

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

0.4b

Counts

3 → 2

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 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(+.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

▶

0.4b

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

0.4b

(+.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)

localize103.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
✓	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
✓	0.3b	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
✓	0.3b	(.f32 uy (.f32 2 (PI.f32)))

series32.0ms (0.3%)

Counts

4 → 68

Calls

4 calls:

15.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
10.0ms	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
3.0ms	(.f32 uy (.f32 2 (PI.f32)))
3.0ms	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`prod-diff_binary32`
161×	`add-sqr-sqrt_binary32`
149×	`log1p-expm1-u_binary32`
149×	`expm1-log1p-u_binary32`
148×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	323	41
2	3899	41

Stop Event

1×	node limit

Counts

4 → 69

Calls

4 calls:

54.0ms	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
54.0ms	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
54.0ms	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
54.0ms	(.f32 uy (.f32 2 (PI.f32)))

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-neg_binary32`
628×	`distribute-rgt-neg-in_binary32`
506×	`associate-l_binary32`
416×	`associate-r_binary32`
229×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	902
1	223	894
2	690	880
3	3132	878

Stop Event

1×	node limit

Counts

137 → 97

prune396.0ms (4.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	99	15	114
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	100	16	116

Error

0.1b

Counts

116 → 16

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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	4.6b	(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 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	0.4b	(+.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))
	4.6b	(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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) 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 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 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 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (fma.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (fma.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3) (.f32 (pow.f32 uy 7) (.f32 (pow.f32 (PI.f32) 7) -8/315))))))))
▶	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 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) 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 (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 (cos.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	12.3b	(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 (pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3) 1/3))))
	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 (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))) 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 (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)) 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 uy (.f32 2 (PI.f32)))) yi))))
	4.6b	(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 (exp.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) 1) 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 (PI.f32) (.f32 uy 2))) 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 (sqrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 2)) yi))))

Compiler

Compiled 7254 to 4353 computations (40% saved)

localize119.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
✓	0.3b	(sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))))
	0.3b	(.f32 uy (.f32 2 (PI.f32)))
✓	1.0b	(pow.f32 (*.f32 2 (PI.f32)) 3)

series16.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
4.0ms	(sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))))
0.0ms	(pow.f32 (*.f32 2 (PI.f32)) 3)

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

873×	`log1p-expm1-u_binary32`
873×	`expm1-log1p-u_binary32`
256×	`prod-diff_binary32`
102×	`add-sqr-sqrt_binary32`
97×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	227	29
2	2509	29

Stop Event

1×	node limit

Counts

3 → 61

Calls

3 calls:

48.0ms	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
48.0ms	(sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))))
48.0ms	(pow.f32 (*.f32 2 (PI.f32)) 3)

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	386
1	113	382
2	374	380
3	1583	380
4	4559	380

Stop Event

1×	node limit

Counts

85 → 75

prune414.0ms (4.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	93	15	108

Error

0.1b

Counts

108 → 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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	4.6b	(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 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	0.4b	(+.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))
	4.6b	(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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) 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 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 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 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) 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 (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 (cos.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	12.3b	(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 (pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3) 1/3))))
	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 (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))) 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 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (exp.f32 (.f32 3 (log.f32 (*.f32 2 (PI.f32)))))))) 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 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 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) uy))) 2) 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 (PI.f32) (.f32 uy 2))) 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 (cbrt.f32 (.f32 (pow.f32 uy 3) (expm1.f32 (log1p.f32 (.f32 8 (pow.f32 (PI.f32) 3))))))) yi))))

Compiler

Compiled 6267 to 3910 computations (37.6% saved)

localize98.0ms (1.1%)

Local error

Found 4 expressions with local error:

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

series9.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f32 maxCos (*.f32 ux maxCos))

rewrite29.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

428×	`log1p-expm1-u_binary32`
428×	`expm1-log1p-u_binary32`
357×	`unpow-prod-down_binary32`
266×	`log-prod_binary32`
174×	`pow-prod-down_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	99	7
2	1192	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

28.0ms

(*.f32 maxCos (*.f32 ux maxCos))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary32`
448×	`associate-l_binary32`
434×	`unswap-sqr_binary32`
281×	`cube-prod_binary32`
277×	`fabs-mul_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	12	168
2	23	168
3	44	168
4	105	168
5	314	168
6	1257	168
7	2131	168
8	2295	168
9	2479	168
10	2687	168
11	2979	168
12	3372	168
13	3852	168
14	4415	168

Stop Event

1×	node limit

Counts

41 → 19

prune472.0ms (5.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	107	13	120

Error

0.1b

Counts

120 → 13

Alt Table

Status	Error	Program
	0.4b	(+.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))
	4.6b	(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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) 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 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 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 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) yi))))
	4.6b	(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))))
▶	0.4b	(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 (log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	12.3b	(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 (pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3) 1/3))))
	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 (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))) 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 (PI.f32) (.f32 uy 2)))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.7b	(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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) -4/3))))))))
	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 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) uy))) 2) 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 (PI.f32) (.f32 uy 2))) 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 (cbrt.f32 (.f32 (pow.f32 uy 3) (expm1.f32 (log1p.f32 (.f32 8 (pow.f32 (PI.f32) 3))))))) yi))))

Compiler

Compiled 6418 to 3543 computations (44.8% saved)

localize117.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))
	0.3b	(.f32 uy (.f32 2 (PI.f32)))
✓	0.3b	(.f32 (PI.f32) (.f32 uy 2))
✓	11.5b	(log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))

series492.0ms (5.3%)

Counts

3 → 36

Calls

3 calls:

484.0ms	(log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))
5.0ms	(.f32 (PI.f32) (.f32 uy 2))
3.0ms	(expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))

rewrite46.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`log1p-expm1-u_binary32`
780×	`expm1-log1p-u_binary32`
145×	`prod-diff_binary32`
85×	`add-sqr-sqrt_binary32`
82×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	187	26
2	2130	26

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

44.0ms	(expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))
44.0ms	(.f32 (PI.f32) (.f32 uy 2))
44.0ms	(log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary32`
304×	`*-commutative_binary32`
300×	`unswap-sqr_binary32`
224×	`distribute-rgt-out_binary32`
216×	`associate-/l/_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	387
1	101	384
2	279	378
3	1138	369
4	3416	361
5	4006	361

Stop Event

1×	node limit

Counts

118 → 74

prune360.0ms (3.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Error

0.1b

Counts

104 → 13

Alt Table

Status	Error	Program
	0.4b	(+.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))
	4.6b	(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 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) 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 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 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 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) yi))))
	4.6b	(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))))
✓	0.4b	(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 (log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	12.3b	(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 (pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3) 1/3))))
	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 (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))) 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 (PI.f32) (.f32 uy 2)))) 1)) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.7b	(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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) -4/3))))))))
	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 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) uy))) 2) 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 (PI.f32) (.f32 uy 2))) 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 (cbrt.f32 (.f32 (pow.f32 uy 3) (expm1.f32 (log1p.f32 (.f32 8 (pow.f32 (PI.f32) 3))))))) yi))))

Compiler

Compiled 5330 to 3219 computations (39.6% saved)

regimes1.5s (16.8%)

Accuracy

Total 0.2b remaining (54.5%)

Threshold costs 0.2b (54.5%)

Counts

96 → 1

Compiler

Compiled 52643 to 37146 computations (29.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	74
1	50	74
2	53	74
3	55	74
4	56	74

Stop Event

1×

saturated

end379.0ms (4.1%)

Compiler: Compiled 828 to 590 computations (28.7% saved)

Details

analyze24.0ms (0.3%)

sample4.2s (45.8%)

simplify38.0ms (0.4%)

prune7.0ms (0.1%)

localize103.0ms (1.1%)

series32.0ms (0.3%)

rewrite55.0ms (0.6%)

simplify41.0ms (0.4%)

prune396.0ms (4.3%)

localize119.0ms (1.3%)

series16.0ms (0.2%)

rewrite49.0ms (0.5%)

simplify47.0ms (0.5%)

prune414.0ms (4.5%)

localize98.0ms (1.1%)

series9.0ms (0.1%)

rewrite29.0ms (0.3%)

simplify60.0ms (0.6%)

prune472.0ms (5.1%)

localize117.0ms (1.3%)

series492.0ms (5.3%)

rewrite46.0ms (0.5%)

simplify42.0ms (0.5%)

prune360.0ms (3.9%)

regimes1.5s (16.8%)

simplify3.0ms (0%)

end379.0ms (4.1%)

Profiling