Details

analyze2.1s (20.9%)

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)

sample2.7s (27.4%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.6s	8256×	body	128	valid
36.0ms	134×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify54.0ms (0.5%)

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

0.0b

Counts

3 → 2

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)))))
▶	0.0b	(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

0.0b

(*.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)))))

▶

0.0b

(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)

localize67.0ms (0.7%)

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))
✓	7.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	7.9b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

series300.0ms (3%)

Counts

4 → 84

Calls

4 calls:

233.0ms	(+.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))))
37.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
16.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite57.0ms (0.6%)

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:

25.0ms	(+.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))
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify162.0ms (1.6%)

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 → 228

Iterations

Useful iterations: 2 (0.0ms)

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

prune240.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	228	2	230

Error

0.0b

Counts

230 → 2

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)))))
✓	0.0b	(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

▶

0.0b

(*.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)))))

✓

0.0b

(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 8632 to 3823 computations (55.7% saved)

localize52.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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 (/.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)

series245.0ms (2.5%)

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)))))
51.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
48.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
10.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite35.0ms (0.4%)

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:

16.0ms	(*.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	(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)))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify169.0ms (1.7%)

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 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	10899
1	1203	10395
2	5156	10395

prune368.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	232	3	235

Error

0.0b

Counts

235 → 3

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)))))
▶	0.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 1/2 (cbrt.f32 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))))))
✓	0.0b	(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 10839 to 6250 computations (42.3% saved)

localize98.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.3b	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
✓	0.3b	(/.f32 1/2 (cbrt.f32 v))
✓	0.5b	(*.f32 (cbrt.f32 v) (cbrt.f32 v))

series168.0ms (1.7%)

Counts

3 → 36

Calls

3 calls:

67.0ms	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
56.0ms	(/.f32 1/2 (cbrt.f32 v))
45.0ms	(*.f32 (cbrt.f32 v) (cbrt.f32 v))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary32`
28×	`cbrt-prod_binary32`
28×	`*-un-lft-identity_binary32`
28×	`add-cube-cbrt_binary32`
21×	`times-frac_binary32`

Counts

3 → 120

Calls

3 calls:

6.0ms	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
5.0ms	(*.f32 (cbrt.f32 v) (cbrt.f32 v))
3.0ms	(/.f32 1/2 (cbrt.f32 v))

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary32`
592×	`fma-neg_binary32`
292×	`times-frac_binary32`
285×	`*-commutative_binary32`
215×	`log-prod_binary32`

Counts

156 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1721
1	244	1535
2	562	1475
3	1689	1461
4	2536	1313
5	4093	1313
6	4995	1313
7	4836	1313

prune251.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	181	3	184

Error

0.0b

Counts

184 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f32 (/.f32 1 (.f32 (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))))) (*.f32 (/.f32 1/2 (cbrt.f32 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))))))
	0.0b	(*.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)))))
✓	0.0b	(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 6205 to 3045 computations (50.9% saved)

localize81.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 1 (.f32 (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))))
	0.3b	(/.f32 1/2 (cbrt.f32 v))
✓	0.5b	(*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))
✓	0.5b	(.f32 (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))))

series137.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

67.0ms

(/.f32 1 (*.f32 (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))))

39.0ms

(*.f32 (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))))

31.0ms

(*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))

rewrite137.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

465×	`pow1_binary32`
326×	`sqrt-pow1_binary32`
312×	`pow-prod-up_binary32`
232×	`pow1/2_binary32`
150×	`pow-sqr_binary32`

Counts

3 → 379

Calls

3 calls:

32.0ms

(/.f32 1 (*.f32 (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))))

25.0ms

(*.f32 (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))))

10.0ms

(*.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v)))

simplify155.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-neg_binary32`
558×	`times-frac_binary32`
462×	`log-div_binary32`
350×	`unswap-sqr_binary32`
344×	`log-prod_binary32`

Counts

415 → 375

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	2411
1	266	1877
2	794	1697
3	2035	1586
4	3850	1586
5	4871	1586
6	4977	1586

prune944.0ms (9.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	522	0	522
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	522	3	525

Error

0.0b

Counts

525 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f32 (/.f32 1 (.f32 (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))) (.f32 (sqrt.f32 (cbrt.f32 v)) (sqrt.f32 (cbrt.f32 v))))) (*.f32 (/.f32 1/2 (cbrt.f32 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))))))
	0.0b	(*.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)))))
✓	0.0b	(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 21149 to 9496 computations (55.1% saved)

regimes1.2s (11.6%)

Accuracy

Total 0.1b remaining (58%)

Threshold costs 0.1b (58%)

Counts

105 → 1

Compiler

Compiled 29317 to 20969 computations (28.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary32`
2×	`*-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	20	32
1	28	32
2	32	32
3	34	32
4	35	32
5	34	32

end101.0ms (1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 256 to 184 computations (28.1% saved)

Details

analyze2.1s (20.9%)

sample2.7s (27.4%)

simplify54.0ms (0.5%)

prune5.0ms (0%)

localize67.0ms (0.7%)

series300.0ms (3%)

rewrite57.0ms (0.6%)

simplify162.0ms (1.6%)

prune240.0ms (2.4%)

localize52.0ms (0.5%)

series245.0ms (2.5%)

rewrite35.0ms (0.4%)

simplify169.0ms (1.7%)

prune368.0ms (3.7%)

localize98.0ms (1%)

series168.0ms (1.7%)

rewrite19.0ms (0.2%)

simplify117.0ms (1.2%)

prune251.0ms (2.5%)

localize81.0ms (0.8%)

series137.0ms (1.4%)

rewrite137.0ms (1.4%)

simplify155.0ms (1.6%)

prune944.0ms (9.5%)

regimes1.2s (11.6%)

simplify3.0ms (0%)

end101.0ms (1%)

Profiling