Details

analyze3.2s (2.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	3%	97%	0
0%	3%	97%	1
0%	3%	97%	2
0%	3%	97%	3
0%	3%	97%	4
0%	3%	97%	5
0%	1.5%	98.5%	6
0%	1.5%	98.5%	7
0%	1.5%	98.5%	8
0%	1.5%	98.5%	9
0%	1.5%	98.5%	10
0%	1.5%	98.5%	11
0%	1.5%	98.5%	12
0%	1.5%	98.5%	13
0%	1.5%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample3.0s (2%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.9s	8256×	body	128	valid
51.0ms	169×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify48.0ms (0%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary32`
718×	`fma-def_binary32`
560×	`exp-diff_binary32`
512×	`exp-sum_binary32`
448×	`sub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	31
3	532	29
4	2119	29
5	4431	29
6	4975	29

prune5.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Status

Error

Program

▶

0.1b

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

0.1b

(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize71.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	7.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	7.7b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series136.0ms (0.1%)

Counts

4 → 84

Calls

4 calls:

68.0ms	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
33.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
20.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
15.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary32`
54×	`times-frac_binary32`
49×	`prod-diff_binary32`
43×	`add-sqr-sqrt_binary32`
41×	`add-cube-cbrt_binary32`

Counts

4 → 160

Calls

4 calls:

26.0ms	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
9.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

simplify144.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

578×	`times-frac_binary32`
420×	`associate-r_binary32`
389×	`associate-/l*_binary32`
341×	`associate-l_binary32`
279×	`associate-/r*_binary32`

Counts

244 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	491	8860
1	1363	7761
2	5247	7761

prune323.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	232	3	235

Error

0.0b

Counts

235 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	3.8b	(/.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (exp.f32 (-.f32 (-.f32 (/.f32 1 v) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
	0.1b	(/.f32 (exp.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)) (exp.f32 (log.f32 (*.f32 2 v))))

Compiler

Compiled 11646 to 5975 computations (48.7% saved)

localize85.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	0.4b	(cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
	7.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	7.7b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series3.0s (2%)

Counts

1 → 60

Calls

1 calls:

3.0s	(cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cbrt-prod_binary32`
3×	`cbrt-div_binary32`
3×	`exp-diff_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`

Counts

1 → 17

Calls

1 calls:

25.0ms

(cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))

simplify130.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

472×	`times-frac_binary32`
322×	`associate-r_binary32`
266×	`associate-/l*_binary32`
248×	`associate-/r*_binary32`
246×	`associate-+r+_binary32`

Counts

77 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	5983
1	1042	5756
2	4849	5388
3	5004	5388

prune2.1s (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	685	2	687
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	686	4	690

Error

0.0b

Counts

690 → 4

Alt Table

Status	Error	Program
	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v)))))) (pow.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v))))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))))
	3.8b	(/.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (exp.f32 (-.f32 (-.f32 (/.f32 1 v) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))))
	0.1b	(/.f32 (exp.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)) (exp.f32 (log.f32 (*.f32 2 v))))
▶	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v)))))) (exp.f32 (log.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))))) (cbrt.f32 (exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (.f32 2 v)))))))

Compiler

Compiled 73171 to 37986 computations (48.1% saved)

localize138.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
✓	5.1b	(log.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
	7.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	7.7b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Details

analyze3.2s (2.1%)

sample3.0s (2%)

simplify48.0ms (0%)

prune5.0ms (0%)

localize71.0ms (0%)

series136.0ms (0.1%)

rewrite58.0ms (0%)

simplify144.0ms (0.1%)

prune323.0ms (0.2%)

localize85.0ms (0.1%)

series3.0s (2%)

rewrite26.0ms (0%)

simplify130.0ms (0.1%)

prune2.1s (1.4%)

localize138.0ms (0.1%)

series2.3min (91.7%)

Profiling