Details

analyze1.9s (33.2%)

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)

sample130.0ms (2.3%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

31.0ms	256×	body	128	valid
15.0ms	258×	pre	128	true
0.0ms	2×	body	128	nan

Compiler

Compiled 104 to 78 computations (25% saved)

simplify49.0ms (0.9%)

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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.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 100 to 68 computations (32% saved)

localize49.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series109.0ms (1.9%)

Counts

4 → 156

Calls

4 calls:

47.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
38.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
14.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
9.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary32`
24×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
14×	`exp-sum_binary32`

Counts

4 → 83

Calls

4 calls:

4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
2.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify150.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

373×	`distribute-rgt-in_binary32`
252×	`times-frac_binary32`
214×	`fma-neg_binary32`
180×	`associate-r_binary32`
152×	`associate-+r+_binary32`

Counts

239 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	6210
1	704	5860
2	3071	5155
3	4888	5155
4	4936	5155

prune174.0ms (3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	1	161

Error

0.0b

Counts

161 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.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 6612 to 3775 computations (42.9% saved)

localize50.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
✓	0.0b	(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series51.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

51.0ms

(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`unpow-prod-up_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`add-cube-cbrt_binary32`
9×	`prod-diff_binary32`

Counts

1 → 37

Calls

1 calls:

4.0ms

(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary32`
252×	`times-frac_binary32`
220×	`associate-/l/_binary32`
167×	`associate-r_binary32`
166×	`associate-/l*_binary32`

Counts

97 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	4140
1	685	4037
2	2826	3929
3	4927	3929

prune173.0ms (3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	166	1	167

Error

0.0b

Counts

167 → 1

Alt Table

Status	Error	Program
✓	0.0b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.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 6955 to 3833 computations (44.9% saved)

regimes385.0ms (6.7%)

Accuracy

Total 0.0b remaining (0.4%)

Threshold costs 0.0b (0.4%)

Counts

45 → 1

Compiler

Compiled 9778 to 7210 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
3×	`*-commutative_binary32`
2×	`sub-neg_binary32`
1×	`+-rgt-identity_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	27
1	28	27
2	32	27
3	34	27
4	35	27
5	34	27

end19.0ms (0.3%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 115 to 85 computations (26.1% saved)

sample2.4s (41.4%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
467.0ms	8128×	pre	128	true
16.0ms	128×	body	128	nan

Compiler

Compiled 123 to 91 computations (26% saved)

Details

analyze1.9s (33.2%)

sample130.0ms (2.3%)

simplify49.0ms (0.9%)

prune4.0ms (0.1%)

localize49.0ms (0.8%)

series109.0ms (1.9%)

rewrite15.0ms (0.3%)

simplify150.0ms (2.6%)

prune174.0ms (3%)

localize50.0ms (0.9%)

series51.0ms (0.9%)

rewrite8.0ms (0.1%)

simplify92.0ms (1.6%)

prune173.0ms (3%)

regimes385.0ms (6.7%)

simplify3.0ms (0%)

end19.0ms (0.3%)

sample2.4s (41.4%)

Profiling