Details

analyze2.4s (1.6%)

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
0.6%	0.9%	98.5%	11
0.6%	0.9%	98.5%	12
0.6%	0.9%	98.5%	13
0.6%	0.9%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.8s (1.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.6s	8256×	body	128	valid
48.0ms	157×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify50.0ms (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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	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)))))
▶	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)))))

Status

Error

Program

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)))))

▶

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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize66.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.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))
✓	7.9b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	8.6b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series328.0ms (0.2%)

Counts

4 → 84

Calls

4 calls:

274.0ms	(+.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))))
28.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite93.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary32`
57×	`times-frac_binary32`
49×	`prod-diff_binary32`
45×	`add-sqr-sqrt_binary32`
43×	`add-cube-cbrt_binary32`

Counts

4 → 174

Calls

4 calls:

27.0ms	(+.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))))
8.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
6.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
6.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify184.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

963×	`times-frac_binary32`
573×	`fma-neg_binary32`
137×	`associate-l_binary32`
117×	`associate-/l*_binary32`
112×	`associate-*l/_binary32`

Counts

258 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	6557
1	729	5637
2	2621	5212
3	4950	5212
4	5167	5212

prune237.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	229	2	231

Error

0.1b

Counts

231 → 2

Alt Table

Status	Error	Program
▶	0.1b	(exp.f32 (log.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 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 (log.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 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 8691 to 3851 computations (55.7% saved)

localize55.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
✓	0.1b	(exp.f32 (log.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
✓	0.1b	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
✓	4.5b	(log.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))

Details

analyze2.4s (1.6%)

sample2.8s (1.8%)

simplify50.0ms (0%)

prune4.0ms (0%)

localize66.0ms (0%)

series328.0ms (0.2%)

rewrite93.0ms (0.1%)

simplify184.0ms (0.1%)

prune237.0ms (0.2%)

localize55.0ms (0%)

series2.4min (95.9%)

Profiling