Details

analyze10.0ms (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)

sample210.0ms (1.5%)

Algorithm

1×

intervals

Results

77.0ms	256×	body	128	valid
19.0ms	256×	pre	128	true

Compiler

Compiled 195 to 141 computations (27.7% saved)

simplify64.0ms (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
▶	0.3b	(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 (.f32 (sin.f32 (.f32 (.f32 uy 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 (-.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))))

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 242 computations (31.6% saved)

localize137.0ms (1%)

Local error

Found 4 expressions with local error:

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

series35.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

15.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
13.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
3.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
13×	`*-un-lft-identity_binary32`

Counts

4 → 92

Calls

4 calls:

10.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
4.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
1.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-l_binary32`
517×	`fma-neg_binary32`
481×	`associate-r_binary32`
301×	`cancel-sign-sub-inv_binary32`
270×	`exp-prod_binary32`

Counts

164 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	3041
1	658	2723
2	2786	2610
3	4428	2602
4	4967	2602

prune954.0ms (7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	194	10	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	195	11	206

Error

0.1b

Counts

206 → 11

Alt Table

Status	Error	Program
	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 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) yi)))))
	0.3b	(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 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	1.2b	(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 (+.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)))))))))
	1.1b	(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 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))))) yi))))
	0.3b	(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 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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))
	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 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.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 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))) (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	15.3b	(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 (exp.f32 (log.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	0.7b	(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 (exp.f32 (+.f32 (log.f32 (*.f32 uy 2)) (log.f32 (PI.f32))))) yi))))

Compiler

Compiled 11701 to 6808 computations (41.8% saved)

localize89.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 9

Calls

1 calls:

2.0ms

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

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

621×	`distribute-rgt-neg-in_binary32`
538×	`distribute-lft-neg-in_binary32`
489×	`fma-def_binary32`
357×	`*-commutative_binary32`
356×	`cancel-sign-sub-inv_binary32`

Counts

21 → 25

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	41	322
1	97	297
2	240	293
3	951	291
4	2423	285
5	3716	282
6	4742	273
7	4939	273
8	4905	273

prune501.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	140	11	151
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	150	12	162

Error

0.1b

Counts

162 → 12

Alt Table

Status	Error	Program
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 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)))))))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (exp.f32 (log.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	1.1b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))) yi))))
	15.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	0.7b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 uy 2)) (log.f32 (PI.f32))))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 yi (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))
	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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 7772 to 4461 computations (42.6% saved)

localize138.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 uy uy) uy)
✓	0.3b	(.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series16.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
3.0ms	(.f32 (.f32 uy uy) uy)
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite114.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

656×	`pow1_binary32`
307×	`pow-prod-down_binary32`
223×	`pow-plus_binary32`
223×	`pow-prod-up_binary32`
184×	`add-cbrt-cube_binary32`

Counts

3 → 241

Calls

3 calls:

40.0ms	(.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
8.0ms	(.f32 (.f32 uy uy) uy)
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary32`
497×	`+-commutative_binary32`
477×	`*-commutative_binary32`
473×	`sqr-pow_binary32`
375×	`associate-+l+_binary32`

Counts

265 → 139

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	3862
1	254	2919
2	1104	2833
3	2741	2679
4	4360	2590
5	5364	2590

prune748.0ms (5.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	169	12	181

Error

0.1b

Counts

181 → 12

Alt Table

Status	Error	Program
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 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)))))))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (exp.f32 (log.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	1.1b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))) yi))))
	15.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
✓	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	0.7b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 uy 2)) (log.f32 (PI.f32))))) yi))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 yi (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))
	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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 10516 to 5601 computations (46.7% saved)

localize90.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series317.0ms (2.3%)

Counts

2 → 84

Calls

2 calls:

295.0ms

(*.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)

22.0ms

(*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
9×	`cbrt-unprod_binary32`
9×	`prod-exp_binary32`

Counts

2 → 47

Calls

2 calls:

9.0ms

(*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi)

8.0ms

(*.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)

simplify136.0ms (1%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-r_binary32`
672×	`associate-l_binary32`
428×	`fma-neg_binary32`
358×	`*-commutative_binary32`
256×	`fma-def_binary32`

Counts

131 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	6397
1	1186	5664
2	4725	5660
3	5052	5660

prune948.0ms (6.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	213	13	226

Error

0.1b

Counts

226 → 13

Alt Table

Status	Error	Program
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 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)))))))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (exp.f32 (log.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 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 1 ux) maxCos) (*.f32 ux zi)))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (.f32 yi (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	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 maxCos ux) (*.f32 maxCos (pow.f32 ux 2))) zi))
	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	1.1b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32))))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))) yi))))
	15.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
✓	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32)))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))) (cbrt.f32 (.f32 yi (sin.f32 (.f32 2 (.f32 uy (PI.f32))))))))))
	0.7b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 uy 2)) (log.f32 (PI.f32))))) yi))))
	1.9b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sqrt.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 (neg.f32 (.f32 maxCos maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))

Compiler

Compiled 18468 to 12182 computations (34% saved)

regimes4.7s (34.6%)

Accuracy

Total 0.3b remaining (66.7%)

Threshold costs 0.3b (66.7%)

Counts

214 → 1

Compiler

Compiled 122985 to 85615 computations (30.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	56
1	49	56
2	60	56
3	68	56
4	71	56
5	70	56

end1.0ms (0%)

Compiler: Compiled 42 to 29 computations (31% saved)

sample4.1s (29.6%)

Algorithm

1×

intervals

Results

2.3s	8000×	body	128	valid
512.0ms	8000×	pre	128	true

Compiler

Compiled 907 to 637 computations (29.8% saved)

Details

analyze10.0ms (0.1%)

sample210.0ms (1.5%)

simplify64.0ms (0.5%)

prune7.0ms (0.1%)

localize137.0ms (1%)

series35.0ms (0.3%)

rewrite23.0ms (0.2%)

simplify105.0ms (0.8%)

prune954.0ms (7%)

localize89.0ms (0.7%)

series3.0ms (0%)

rewrite2.0ms (0%)

simplify95.0ms (0.7%)

prune501.0ms (3.7%)

localize138.0ms (1%)

series16.0ms (0.1%)

rewrite114.0ms (0.8%)

simplify144.0ms (1.1%)

prune748.0ms (5.5%)

localize90.0ms (0.7%)

series317.0ms (2.3%)

rewrite21.0ms (0.2%)

simplify136.0ms (1%)

prune948.0ms (6.9%)

regimes4.7s (34.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.1s (29.6%)

Profiling