Details

analyze1.7s (19.1%)

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 62 to 45 computations (27.4% saved)

sample3.5s (40%)

Results

3.0s	8256×	body	128	valid
400.0ms	1029×	body	128	invalid

Compiler

Compiled 153 to 110 computations (28.1% saved)

simplify198.0ms (2.2%)

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%)

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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.8b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
▶	1.4b	(+.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))

Status

Error

Program

8.8b

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

▶

1.4b

(+.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))

Compiler

Compiled 146 to 95 computations (34.9% saved)

localize59.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f32 (-.f32 1 u) normAngle)
✓	0.2b	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
✓	0.5b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
✓	2.1b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series110.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

59.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
26.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
20.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
4.0ms	(*.f32 (-.f32 1 u) normAngle)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary32`
39×	`add-exp-log_binary32`
32×	`associate-r_binary32`
28×	`*-un-lft-identity_binary32`
25×	`add-cbrt-cube_binary32`

Counts

4 → 127

Calls

4 calls:

8.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
7.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
7.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
5.0ms	(*.f32 (-.f32 1 u) normAngle)

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-r_binary32`
451×	`associate-l_binary32`
394×	`fma-def_binary32`
309×	`*-commutative_binary32`
269×	`associate-+r+_binary32`

Counts

223 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	4670
1	1199	4259
2	4415	4255
3	5052	4255

prune306.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	230	7	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	231	8	239

Error

0.1b

Counts

239 → 8

Alt Table

Status	Error	Program
	1.5b	(+.f32 (.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sqrt.f32 (sin.f32 normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.4b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 (sqrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
	1.6b	(+.f32 (.f32 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (cbrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)))) (/.f32 (cbrt.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle)))) (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.7b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
	8.8b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	1.4b	(+.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.4b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
▶	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 u n1_i))

Compiler

Compiled 9314 to 4871 computations (47.7% 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))
	0.1b	(*.f32 (-.f32 1 u) normAngle)
	0.2b	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
	0.5b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

series64.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

64.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary32`
1×	`+-commutative_binary32`
1×	`flip-+_binary32`
1×	`*-un-lft-identity_binary32`
1×	`flip3-+_binary32`

Counts

1 → 14

Calls

1 calls:

8.0ms

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

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

484×	`cancel-sign-sub-inv_binary32`
324×	`fma-neg_binary32`
315×	`associate-r_binary32`
267×	`fma-def_binary32`
246×	`distribute-rgt-out_binary32`

Counts

62 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2000
1	650	1890
2	2605	1818
3	4581	1818
4	4995	1818
5	4981	1818

prune281.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	212	6	218

Error

0.0b

Counts

218 → 6

Alt Table

Status	Error	Program
	8.8b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	1.4b	(+.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	1.4b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 (sqrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
▶	0.6b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
	1.9b	(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))

Compiler

Compiled 7061 to 3768 computations (46.6% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

7.0ms	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
6.0ms	(*.f32 u (-.f32 n1_i n0_i))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary32`
36×	`prod-diff_binary32`
35×	`*-un-lft-identity_binary32`
33×	`add-cube-cbrt_binary32`
26×	`distribute-lft-in_binary32`

Counts

2 → 92

Calls

2 calls:

19.0ms	(*.f32 u (-.f32 n1_i n0_i))
5.0ms	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

969×	`fma-neg_binary32`
665×	`fma-def_binary32`
409×	`distribute-rgt-in_binary32`
379×	`distribute-lft-in_binary32`
287×	`*-commutative_binary32`

Counts

164 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1649
1	288	1433
2	1030	1375
3	3371	1321
4	4230	1321
5	5050	1321

prune133.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	8.8b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	1.4b	(+.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	1.4b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 (sqrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
▶	0.6b	(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))
✓	0.6b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))

Compiler

Compiled 2630 to 721 computations (72.6% saved)

localize21.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))

series9.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary32`
3×	`fma-def_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`

Counts

1 → 18

Calls

1 calls:

2.0ms

(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-neg_binary32`
556×	`neg-sub0_binary32`
519×	`neg-mul-1_binary32`
378×	`distribute-rgt-neg-out_binary32`
309×	`distribute-lft-neg-out_binary32`

Counts

54 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	608
1	147	546
2	497	455
3	2313	455
4	3832	455
5	5085	455

prune33.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	41	6	47

Error

0.0b

Counts

47 → 6

Alt Table

Status	Error	Program
	8.8b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	1.4b	(+.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	1.4b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 (sqrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
✓	0.6b	(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))
✓	0.6b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))

Compiler

Compiled 679 to 201 computations (70.4% saved)

regimes1.8s (20%)

Accuracy

Total 0.4b remaining (95.4%)

Threshold costs 0.4b (95.4%)

Counts

271 → 1

Compiler

Compiled 35893 to 22547 computations (37.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	24	52
1	35	52
2	39	52
3	41	52
4	42	52
5	41	52

end94.0ms (1.1%)

Compiler: Compiled 233 to 138 computations (40.8% saved)

Details

analyze1.7s (19.1%)

sample3.5s (40%)

simplify198.0ms (2.2%)

prune4.0ms (0%)

localize59.0ms (0.7%)

series110.0ms (1.2%)

rewrite34.0ms (0.4%)

simplify117.0ms (1.3%)

prune306.0ms (3.5%)

localize44.0ms (0.5%)

series64.0ms (0.7%)

rewrite9.0ms (0.1%)

simplify102.0ms (1.1%)

prune281.0ms (3.2%)

localize18.0ms (0.2%)

series14.0ms (0.2%)

rewrite31.0ms (0.4%)

simplify95.0ms (1.1%)

prune133.0ms (1.5%)

localize21.0ms (0.2%)

series9.0ms (0.1%)

rewrite3.0ms (0%)

simplify60.0ms (0.7%)

prune33.0ms (0.4%)

regimes1.8s (20%)

simplify4.0ms (0%)

end94.0ms (1.1%)

Profiling