Details

analyze2.0s (1.3%)

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)

sample2.6s (1.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.5s	8256×	body	128	valid
35.0ms	118×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify52.0ms (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	(*.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)

localize68.0ms (0%)

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))
✓	0.1b	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
✓	6.5b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	6.6b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series99.0ms (0.1%)

Counts

4 → 84

Calls

4 calls:

40.0ms	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
32.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

184×	`*-un-lft-identity_binary32`
176×	`prod-diff_binary32`
168×	`add-sqr-sqrt_binary32`
164×	`times-frac_binary32`
149×	`associate-+l+_binary32`

Counts

4 → 307

Calls

4 calls:

32.0ms	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
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)

simplify189.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

965×	`times-frac_binary32`
601×	`fma-neg_binary32`
167×	`sub-neg_binary32`
160×	`associate-l_binary32`
124×	`associate-r_binary32`

Counts

391 → 452

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	9660
1	735	7306
2	2413	6848
3	4999	6848

prune526.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	452	0	452
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	452	2	454

Error

0.1b

Counts

454 → 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 21607 to 9372 computations (56.6% saved)

localize50.0ms (0%)

Local error

Found 4 expressions with local error:

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

series243.0ms (0.2%)

Counts

4 → 180

Calls

4 calls:

135.0ms	(*.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)))))
53.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
44.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary32`
39×	`*-un-lft-identity_binary32`
35×	`add-cube-cbrt_binary32`
28×	`exp-sum_binary32`
27×	`prod-diff_binary32`

Counts

4 → 123

Calls

4 calls:

12.0ms	(*.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)))))
4.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
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))))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify218.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

392×	`times-frac_binary32`
288×	`associate-/l*_binary32`
278×	`associate-r_binary32`
275×	`associate-+r+_binary32`
243×	`fma-def_binary32`

Counts

303 → 237

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	11185
1	1203	10395
2	5156	10395

prune403.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	234	5	239

Error

0.0b

Counts

239 → 5

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)))))
▶	0.1b	(*.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)))))
	12.6b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	2.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 11238 to 6470 computations (42.4% saved)

localize54.0ms (0%)

Local error

Found 4 expressions with local error:

New	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)))))
	0.1b	(-.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)
✓	0.1b	(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))))

series207.0ms (0.1%)

Counts

2 → 120

Calls

2 calls:

149.0ms

(*.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)))))

58.0ms

(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))))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary32`
29×	`*-un-lft-identity_binary32`
28×	`unpow-prod-up_binary32`
27×	`add-cube-cbrt_binary32`
21×	`associate-r_binary32`

Counts

2 → 100

Calls

2 calls:

13.0ms

(*.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)))))

7.0ms

(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))))

simplify148.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

392×	`times-frac_binary32`
313×	`associate-r_binary32`
308×	`associate-/l*_binary32`
264×	`associate-+r+_binary32`
230×	`fma-def_binary32`

Counts

220 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	439	10195
1	1211	9762
2	4989	9762

prune603.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	268	7	275

Error

0.0b

Counts

275 → 7

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)))))
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 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))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (.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)))))) (cbrt.f32 (.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))))))) (cbrt.f32 (*.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)))))))
▶	0.1b	(exp.f32 (log.f32 (*.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)))))))
	12.6b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	2.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 12913 to 7229 computations (44% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.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)
	0.1b	(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))))
✓	5.8b	(log.f32 (*.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))))))

Details

analyze2.0s (1.3%)

sample2.6s (1.8%)

simplify52.0ms (0%)

prune5.0ms (0%)

localize68.0ms (0%)

series99.0ms (0.1%)

rewrite98.0ms (0.1%)

simplify189.0ms (0.1%)

prune526.0ms (0.4%)

localize50.0ms (0%)

series243.0ms (0.2%)

rewrite33.0ms (0%)

simplify218.0ms (0.1%)

prune403.0ms (0.3%)

localize54.0ms (0%)

series207.0ms (0.1%)

rewrite32.0ms (0%)

simplify148.0ms (0.1%)

prune603.0ms (0.4%)

localize60.0ms (0%)

series2.4min (94.9%)

Profiling