Details

analyze1.6s (19.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.8%	99.2%	0
0%	0.8%	99.2%	1
0%	0.8%	99.2%	2
0%	0.8%	99.2%	3
0%	0.8%	99.2%	4
0%	0.8%	99.2%	5
0.2%	0.4%	99.4%	6
0.2%	0.4%	99.4%	7
0.2%	0.4%	99.4%	8
0.2%	0.4%	99.4%	9
0.3%	0.2%	99.5%	10
0.3%	0.2%	99.5%	11
0.3%	0.2%	99.5%	12
0.3%	0.2%	99.5%	13
0.3%	0.1%	99.6%	14

Compiler

Compiled 48 to 35 computations (27.1% saved)

sample93.0ms (1.1%)

Algorithm

1×

intervals

Results

50.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true
2.0ms	35×	pre	128	false

Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify208.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2213×	`fma-def_binary32`
1110×	`div-sub_binary32`
1069×	`fma-neg_binary32`
619×	`times-frac_binary32`
350×	`sub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	38	31
2	78	31
3	137	26
4	203	26
5	232	26
6	274	26
7	372	26
8	432	26
9	523	26
10	666	26
11	1121	26
12	2051	26
13	2034	26
14	2092	26
15	2417	26
16	2722	26
17	2897	26
18	2169	26
19	2439	26
20	2299	26
21	2299	26
22	2299	26
23	2299	26
24	2299	26
25	2299	26
26	2114	26

prune4.0ms (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

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.0b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	8.2b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))

Status

Error

Program

▶

1.0b

(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

8.2b

(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))

Compiler

Compiled 146 to 95 computations (34.9% saved)

localize60.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (-.f32 1 u) normAngle)
✓	0.2b	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
✓	0.4b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
✓	1.6b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary32`
32×	`add-sqr-sqrt_binary32`
26×	`add-exp-log_binary32`
20×	`add-cbrt-cube_binary32`
19×	`add-cube-cbrt_binary32`

Counts

4 → 166

Calls

4 calls:

17.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
17.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
15.0ms	(*.f32 (-.f32 1 u) normAngle)
14.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series216.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

122.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
41.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
39.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
14.0ms	(*.f32 (-.f32 1 u) normAngle)

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-r_binary32`
490×	`associate-l_binary32`
430×	`fma-def_binary32`
271×	`associate-+r+_binary32`
188×	`associate-+l+_binary32`

Counts

262 → 423

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	4585
1	1225	4256
2	4979	4256

prune402.0ms (4.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	412	11	423
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	413	12	425

Error

0.0b

Counts

425 → 12

Alt Table

Status	Error	Program
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))) 2) n1_i))
▶	0.9b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 u n1_i))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))) 3) n1_i))
	1.0b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
	5.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) 1) n1_i))
	8.2b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	0.9b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.0b	(+.f32 (.f32 (.f32 (cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)) 2)) (cbrt.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	9.3b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 normAngle (.f32 normAngle (pow.f32 (-.f32 1 u) 2)))) (cbrt.f32 (.f32 normAngle (-.f32 1 u))))) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.1b	(+.f32 (.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (-.f32 1 u) normAngle)) 2)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.2b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (sqrt.f32 (sin.f32 (.f32 u normAngle)))) (*.f32 (sqrt.f32 (/.f32 1 (sin.f32 normAngle))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle))))) n1_i))

Compiler

Compiled 9723 to 5581 computations (42.6% saved)

localize44.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 u n1_i))
	0.2b	(*.f32 (-.f32 1 u) normAngle)
	0.2b	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
	0.4b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary32`
5×	`add-cube-cbrt_binary32`
4×	`*-un-lft-identity_binary32`
4×	`flip3-+_binary32`
4×	`pow1_binary32`

Counts

1 → 41

Calls

1 calls:

21.0ms

(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))

series135.0ms (1.6%)

Counts

1 → 48

Calls

1 calls:

135.0ms

(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

572×	`cancel-sign-sub-inv_binary32`
335×	`associate-r_binary32`
323×	`fma-def_binary32`
268×	`distribute-rgt-neg-in_binary32`
263×	`associate-l_binary32`

Counts

89 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2800
1	697	2609
2	2856	2590
3	4965	2590

prune353.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	482	4	486
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	490	8	498

Error

Counts

498 → 8

Alt Table

Status	Error	Program
	0.9b	(fma.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i (*.f32 u n1_i))
	1.0b	(+.f32 (.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
▶	0.7b	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))) 3) n1_i))
	1.0b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
	5.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) 1) n1_i))
	8.2b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	2.8b	(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))

Compiler

Compiled 8753 to 5106 computations (41.7% saved)

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 n0_i u)
✓	0.1b	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cube-cbrt_binary32`
15×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
8×	`add-exp-log_binary32`
8×	`add-cbrt-cube_binary32`

Counts

2 → 85

Calls

2 calls:

15.0ms	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))
13.0ms	(*.f32 n0_i u)

series46.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))
17.0ms	(*.f32 n0_i u)

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

459×	`fma-def_binary32`
358×	`unswap-sqr_binary32`
302×	`distribute-rgt-in_binary32`
261×	`distribute-lft-in_binary32`
248×	`exp-prod_binary32`

Counts

133 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1334
1	261	1257
2	914	1237
3	3112	1229
4	4617	1229
5	4796	1229

prune86.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	220	8	228

Error

Counts

228 → 8

Alt Table

Status	Error	Program
▶	0.7b	(fma.f32 n1_i u (-.f32 n0_i (*.f32 n0_i u)))
	2.8b	(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
✓	0.7b	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))) 3) n1_i))
	1.0b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
	1.0b	(+.f32 (.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	0.7b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
	8.2b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))

Compiler

Compiled 2229 to 586 computations (73.7% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f32 n0_i u)
✓	0.0b	(-.f32 n0_i (*.f32 n0_i u))
✓	0.1b	(fma.f32 n1_i u (-.f32 n0_i (*.f32 n0_i u)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cube-cbrt_binary32`
10×	`add-sqr-sqrt_binary32`
8×	`add-log-exp_binary32`
8×	`pow1_binary32`
7×	`fma-udef_binary32`

Counts

2 → 80

Calls

2 calls:

14.0ms	(-.f32 n0_i (*.f32 n0_i u))
9.0ms	(fma.f32 n1_i u (-.f32 n0_i (*.f32 n0_i u)))

series46.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

31.0ms	(fma.f32 n1_i u (-.f32 n0_i (*.f32 n0_i u)))
15.0ms	(-.f32 n0_i (*.f32 n0_i u))

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-neg_binary32`
698×	`associate-l_binary32`
559×	`associate-r_binary32`
481×	`fma-def_binary32`
252×	`cancel-sign-sub-inv_binary32`

Counts

140 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1453
1	271	1357
2	891	1328
3	4049	1328
4	4867	1328

prune102.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	305	8	313

Error

Counts

313 → 8

Alt Table

Status	Error	Program
✓	0.7b	(fma.f32 n1_i u (-.f32 n0_i (*.f32 n0_i u)))
	2.8b	(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
✓	0.7b	(-.f32 (fma.f32 n1_i u n0_i) (*.f32 n0_i u))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))) 3) n1_i))
	1.0b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
	1.0b	(+.f32 (.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	0.7b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
	8.2b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))

Compiler

Compiled 2350 to 650 computations (72.3% saved)

regimes1.1s (12.7%)

Accuracy

Total 0.6b remaining (97.1%)

Threshold costs 0.6b (97.1%)

Compiler

Compiled 19243 to 13367 computations (30.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	23	11
3	29	11
4	33	11
5	34	11
6	34	11

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample3.2s (38.3%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
482.0ms	8000×	pre	128	true
53.0ms	965×	pre	128	false

Compiler

Compiled 219 to 148 computations (32.4% saved)

Details

analyze1.6s (19.9%)

sample93.0ms (1.1%)

simplify208.0ms (2.5%)

prune4.0ms (0.1%)

localize60.0ms (0.7%)

rewrite71.0ms (0.9%)

series216.0ms (2.6%)

simplify119.0ms (1.4%)

prune402.0ms (4.9%)

localize44.0ms (0.5%)

rewrite24.0ms (0.3%)

series135.0ms (1.6%)

simplify93.0ms (1.1%)

prune353.0ms (4.3%)

localize19.0ms (0.2%)

rewrite33.0ms (0.4%)

series46.0ms (0.6%)

simplify103.0ms (1.2%)

prune86.0ms (1%)

localize19.0ms (0.2%)

rewrite27.0ms (0.3%)

series46.0ms (0.6%)

simplify90.0ms (1.1%)

prune102.0ms (1.2%)

regimes1.1s (12.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (38.3%)

Profiling