Details

analyze67.0ms (0.5%)

Algorithm

1×

Search

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

Compiler

Compiled 118 to 85 computations (28% saved)

sample8.7s (63.8%)

Results

8.5s

8256×

body

128

valid

Compiler

Compiled 307 to 220 computations (28.3% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

929×	`unsub-neg_binary32`
384×	`associate--l-_binary32`
362×	`distribute-rgt-in_binary32`
356×	`distribute-neg-in_binary32`
347×	`distribute-rgt-neg-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	67	97
2	204	70
3	683	66
4	1864	66
5	2617	66
6	4625	66
7	5073	66

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
	0.4b	(+.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))
▶	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

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))

▶

0.4b

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

Compiler

Compiled 354 to 242 computations (31.6% saved)

localize93.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

15.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
14.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
3.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite81.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

336×	`log1p-udef_binary32`
188×	`add-sqr-sqrt_binary32`
176×	`log1p-expm1-u_binary32`
176×	`expm1-log1p-u_binary32`
173×	`add-log-exp_binary32`

Counts

4 → 71

Calls

4 calls:

77.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
77.0ms	(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))
77.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
77.0ms	(.f32 (.f32 uy 2) (PI.f32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	47
1	374	47
2	4556	47
3	5065	47
0	0	0
1	0	0

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

849×	`distribute-rgt-neg-in_binary32`
676×	`associate-l_binary32`
675×	`associate-r_binary32`
560×	`unswap-sqr_binary32`
262×	`fma-def_binary32`

Counts

143 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1164
1	262	1126
2	818	1004
3	3578	996
4	5507	996

prune381.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Error

0.1b

Counts

123 → 13

Alt Table

Status	Error	Program
	1.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))) (.f32 yi (+.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)) (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315)))))))))
▶	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 3))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	16.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 2))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) yi))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 7206 to 4417 computations (38.7% saved)

localize105.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
✓	0.3b	(.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	1.0b	(pow.f32 (PI.f32) 3)

series13.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

13.0ms	(.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3))
0.0ms	(pow.f32 (PI.f32) 3)

rewrite43.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

718×	`log1p-expm1-u_binary32`
718×	`expm1-log1p-u_binary32`
144×	`expm1-udef_binary32`
144×	`log1p-udef_binary32`
135×	`log-pow_binary32`

Counts

2 → 37

Calls

2 calls:

42.0ms	(.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3))
42.0ms	(pow.f32 (PI.f32) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	189	16
2	1915	16
3	4913	16
0	0	0
1	0	0

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

974×	`unswap-sqr_binary32`
865×	`sqr-pow_binary32`
584×	`*-commutative_binary32`
536×	`associate-l_binary32`
357×	`associate-r_binary32`

Counts

49 → 39

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	168
1	26	168
2	79	168
3	288	168
4	1044	132
5	1321	132
6	2745	132
7	2745	132
8	2927	132
9	3094	132
10	3280	132
11	3368	132
12	3609	132
13	3583	132
14	3945	132
15	4434	132
16	4959	132

prune396.0ms (2.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Error

0.1b

Counts

105 → 13

Alt Table

Status	Error	Program
	1.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))) (.f32 yi (+.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)) (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315)))))))))
✓	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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))
▶	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 3))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	16.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 2))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) yi))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 6081 to 3902 computations (35.8% saved)

localize110.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
	0.3b	(.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
	1.0b	(pow.f32 (PI.f32) 3)

prune388.0ms (2.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	92	13	105

Error

0.1b

Counts

105 → 13

Alt Table

Status	Error	Program
	1.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))) (.f32 yi (+.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)) (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315)))))))))
✓	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32))))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 3))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) yi))))
▶	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 maxCos (.f32 maxCos (neg.f32 (pow.f32 (-.f32 1 ux) 2))))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) 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))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	16.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 2))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 6093 to 3916 computations (35.7% saved)

localize111.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(pow.f32 (-.f32 1 ux) 2)
	1.0b	(pow.f32 (PI.f32) 3)

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(pow.f32 (-.f32 1 ux) 2)

rewrite79.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

509×	`log1p-expm1-u_binary32`
509×	`expm1-log1p-u_binary32`
448×	`prod-diff_binary32`
304×	`unpow-prod-down_binary32`
221×	`log-prod_binary32`

Counts

1 → 59

Calls

1 calls:

78.0ms

(pow.f32 (-.f32 1 ux) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	7
2	1287	7
3	4995	7
4	5482	7
0	0	0
1	0	0

simplify186.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

584×	`distribute-rgt-neg-in_binary32`
557×	`sqr-pow_binary32`
547×	`*-commutative_binary32`
547×	`distribute-lft-neg-in_binary32`
541×	`associate-r_binary32`

Counts

71 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	114
1	29	90
2	49	82
3	108	76
4	247	76
5	602	76
6	1660	76
7	2682	76
8	3357	76
9	3747	76
10	2841	76
11	3167	76
12	3455	76
13	4111	76
14	4556	76
15	4843	76
16	4615	76

prune530.0ms (3.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	123	13	136

Error

0.1b

Counts

136 → 13

Alt Table

Status	Error	Program
	1.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))) (.f32 yi (+.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)) (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315)))))))))
✓	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) yi))))
✓	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 maxCos (.f32 maxCos (neg.f32 (pow.f32 (-.f32 1 ux) 2))))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 maxCos (.f32 maxCos (neg.f32 (pow.f32 (-.f32 1 ux) 2))))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 uy 2) 3) (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (-.f32 (exp.f32 (log1p.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) 1) xi (.f32 (sin.f32 (.f32 (.f32 uy 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))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 3))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 uy) 2) (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	16.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) 2))))
	0.6b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (log.f32 (+.f32 1 (expm1.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (pow.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 7183 to 4941 computations (31.2% saved)

regimes1.7s (12.2%)

Accuracy

Total 0.2b remaining (62.8%)

Threshold costs 0.2b (62.8%)

Counts

100 → 1

Compiler

Compiled 56580 to 40079 computations (29.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	74
1	48	74
2	55	74
3	59	74
4	61	74
5	60	74

end381.0ms (2.8%)

Compiler: Compiled 840 to 590 computations (29.8% saved)

Details

analyze67.0ms (0.5%)

sample8.7s (63.8%)

simplify66.0ms (0.5%)

prune7.0ms (0.1%)

localize93.0ms (0.7%)

series36.0ms (0.3%)

rewrite81.0ms (0.6%)

simplify63.0ms (0.5%)

prune381.0ms (2.8%)

localize105.0ms (0.8%)

series13.0ms (0.1%)

rewrite43.0ms (0.3%)

simplify123.0ms (0.9%)

prune396.0ms (2.9%)

localize110.0ms (0.8%)

prune388.0ms (2.9%)

localize111.0ms (0.8%)

series2.0ms (0%)

rewrite79.0ms (0.6%)

simplify186.0ms (1.4%)

prune530.0ms (3.9%)

regimes1.7s (12.2%)

simplify3.0ms (0%)

end381.0ms (2.8%)

Profiling