Details

analyze1.6s (20.1%)

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)

sample240.0ms (3.1%)

Algorithm

1×

intervals

Results

94.0ms	256×	body	128	valid
15.0ms	256×	pre	128	true
2.0ms	34×	pre	128	false

Compiler

Compiled 95 to 69 computations (27.4% saved)

simplify197.0ms (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

prune5.0ms (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))
	9.3b	(/.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))

9.3b

(/.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)

localize130.0ms (1.7%)

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)
✓	0.6b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
✓	1.7b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series118.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

60.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
27.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
26.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
5.0ms	(*.f32 (-.f32 1 u) normAngle)

rewrite38.0ms (0.5%)

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)))
6.0ms	(*.f32 (-.f32 1 u) normAngle)

simplify144.0ms (1.8%)

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

prune377.0ms (4.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	225	12	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	226	13	239

Error

0.1b

Counts

239 → 13

Alt Table

Status	Error	Program
	20.1b	(+.f32 (.f32 (.f32 (sin.f32 (neg.f32 (.f32 u normAngle))) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (log1p.f32 (expm1.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))
	2.5b	(+.f32 (.f32 (.f32 (sin.f32 (exp.f32 (log.f32 (-.f32 normAngle (.f32 u normAngle))))) (/.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 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle))))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	9.3b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
	1.1b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
	1.1b	(+.f32 (.f32 (log.f32 (exp.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 (exp.f32 (log.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))
	1.1b	(+.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))
	0.9b	(+.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) 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 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (sqrt.f32 (sin.f32 normAngle))) (/.f32 (sqrt.f32 (sin.f32 (*.f32 u normAngle))) (sqrt.f32 (sin.f32 normAngle)))) n1_i))

Compiler

Compiled 9586 to 5071 computations (47.1% saved)

localize49.0ms (0.6%)

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)
	0.6b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

series72.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

71.0ms

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

rewrite11.0ms (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:

10.0ms

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

simplify102.0ms (1.3%)

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

prune283.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Error

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
▶	0.7b	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
	0.7b	(+.f32 (.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	0.9b	(+.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.7b	(-.f32 (+.f32 (.f32 n1_i u) n0_i) (.f32 n0_i u))
	2.7b	(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
	9.3b	(/.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 6959 to 3730 computations (46.4% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series39.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
7.0ms	(*.f32 u (-.f32 n1_i n0_i))

rewrite19.0ms (0.2%)

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×	`associate-+r+_binary32`

Counts

2 → 92

Calls

2 calls:

6.0ms	(*.f32 u (-.f32 n1_i n0_i))
5.0ms	(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))

simplify92.0ms (1.2%)

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 → 141

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

prune143.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	141	6	147

Error

0.0b

Counts

147 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f32 (.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	0.9b	(+.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 n0_i (+.f32 (.f32 (fma.f32 (.f32 (cbrt.f32 n1_i) (cbrt.f32 n1_i)) (cbrt.f32 n1_i) (neg.f32 (.f32 n0_i 1))) u) (.f32 (fma.f32 (neg.f32 n0_i) 1 (*.f32 n0_i 1)) u)))
	0.6b	(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))
▶	0.6b	(fma.f32 (-.f32 n1_i n0_i) u n0_i)
	9.3b	(/.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 2668 to 735 computations (72.5% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f32 (-.f32 n1_i n0_i) u n0_i)

rewrite1.0ms (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 → 10

Calls

1 calls:

0.0ms

(fma.f32 (-.f32 n1_i n0_i) u n0_i)

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

762×	`neg-sub0_binary32`
713×	`neg-mul-1_binary32`
619×	`distribute-neg-out_binary32`
618×	`distribute-rgt-neg-out_binary32`
414×	`unsub-neg_binary32`

Counts

46 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	472
1	68	374
2	141	374
3	350	374
4	1783	374
5	3599	374
6	5394	374

prune23.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	31	6	37

Error

0.0b

Counts

37 → 6

Alt Table

Status	Error	Program
	0.7b	(+.f32 (.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)))) n0_i) (*.f32 u n1_i))
	0.9b	(+.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 n0_i (+.f32 (.f32 (fma.f32 (.f32 (cbrt.f32 n1_i) (cbrt.f32 n1_i)) (cbrt.f32 n1_i) (neg.f32 (.f32 n0_i 1))) u) (.f32 (fma.f32 (neg.f32 n0_i) 1 (*.f32 n0_i 1)) u)))
	0.6b	(+.f32 (fma.f32 n1_i u n0_i) (*.f32 (neg.f32 n0_i) u))
✓	0.6b	(fma.f32 (-.f32 n1_i n0_i) u n0_i)
	9.3b	(/.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 396 to 147 computations (62.9% saved)

regimes1.2s (15.7%)

Accuracy

Total 0.4b remaining (95%)

Threshold costs 0.4b (95%)

Counts

177 → 1

Compiler

Compiled 20108 to 13062 computations (35% saved)

simplify4.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 38 to 25 computations (34.2% saved)

sample2.8s (36.3%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
464.0ms	8000×	pre	128	true
56.0ms	935×	pre	128	false

Compiler

Compiled 226 to 153 computations (32.3% saved)

Details

analyze1.6s (20.1%)

sample240.0ms (3.1%)

simplify197.0ms (2.5%)

prune5.0ms (0.1%)

localize130.0ms (1.7%)

series118.0ms (1.5%)

rewrite38.0ms (0.5%)

simplify144.0ms (1.8%)

prune377.0ms (4.8%)

localize49.0ms (0.6%)

series72.0ms (0.9%)

rewrite11.0ms (0.1%)

simplify102.0ms (1.3%)

prune283.0ms (3.6%)

localize16.0ms (0.2%)

series39.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify92.0ms (1.2%)

prune143.0ms (1.8%)

localize13.0ms (0.2%)

series13.0ms (0.2%)

rewrite1.0ms (0%)

simplify55.0ms (0.7%)

prune23.0ms (0.3%)

regimes1.2s (15.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.8s (36.3%)

Profiling