Details

analyze2.2s (3.2%)

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)

sample2.8s (4.1%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.7s	8256×	body	128	valid
36.0ms	129×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify50.0ms (0.1%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.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)))))
▶	0.2b	(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

0.2b

(*.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)))))

▶

0.2b

(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)

localize72.0ms (0.1%)

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	(log.f32 (/.f32 1 (*.f32 2 v)))
✓	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series119.0ms (0.2%)

Counts

4 → 72

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)))))
26.0ms	(log.f32 (/.f32 1 (*.f32 2 v)))
13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
11.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite51.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

4 → 76

Calls

2 calls:

47.0ms

((/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (log.f32 (/.f32 1 (*.f32 2 v))) (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))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	505	50
2	5026	50
0	0	0
1	0	0

simplify102.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

468×	`times-frac_binary32`
309×	`associate-r_binary32`
267×	`associate-/l*_binary32`
241×	`associate-+r+_binary32`
240×	`associate-/r*_binary32`

Counts

148 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4691
1	865	4599
2	4329	4301
3	5092	4301

prune177.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Error

0.1b

Counts

115 → 5

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) (-.f32 (log.f32 1/2) (log.f32 v))))
	0.2b	(pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2)
	0.3b	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.2b	(.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 5920 to 3770 computations (36.3% saved)

localize74.0ms (0.1%)

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) (-.f32 (log.f32 1/2) (log.f32 v))))
✓	0.3b	(-.f32 (log.f32 1/2) (log.f32 v))
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series99.0ms (0.1%)

Counts

2 → 68

Calls

2 calls:

60.0ms

(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) (-.f32 (log.f32 1/2) (log.f32 v))))

38.0ms

(-.f32 (log.f32 1/2) (log.f32 v))

rewrite36.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

47× egg-rr

Counts

2 → 47

Calls

2 calls:

35.0ms

((-.f32 (log.f32 1/2) (log.f32 v)) (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) (-.f32 (log.f32 1/2) (log.f32 v)))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	507	36
2	5122	36
0	0	0
1	0	0

simplify114.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary32`
292×	`associate-r_binary32`
263×	`associate-/l*_binary32`
240×	`associate-+r+_binary32`
240×	`associate-/r*_binary32`

Counts

115 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	5172
1	875	5004
2	4384	4638
3	5177	4638

prune231.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	7	125

Error

0.0b

Counts

125 → 7

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) (-.f32 (log.f32 1/2) (log.f32 v))))
▶	0.1b	(/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))) v)
	0.1b	(.f32 1/2 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (+.f32 (log.f32 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.2b	(pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2)
	0.3b	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
	0.2b	(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))))
	0.2b	(.f32 (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 6547 to 4106 computations (37.3% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	10.0b	(+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))

series63.0ms (0.1%)

Counts

3 → 66

Calls

3 calls:

22.0ms

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

21.0ms

(+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))

20.0ms

(+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

rewrite77.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

95× egg-rr

Counts

3 → 95

Calls

2 calls:

75.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	333	50
2	4515	50
3	4889	50
0	0	0
1	0	0

simplify49.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

865×	`associate-/l*_binary32`
486×	`associate-l_binary32`
455×	`associate-/r*_binary32`
415×	`fma-def_binary32`
193×	`associate-*l/_binary32`

Counts

161 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1814
1	313	1718
2	1269	1528
3	5222	1528

prune250.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	141	6	147

Error

0.0b

Counts

147 → 6

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) (-.f32 (log.f32 1/2) (log.f32 v))))
	0.1b	(.f32 1/2 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (+.f32 (log.f32 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
▶	0.1b	(/.f32 (exp.f32 (-.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (/.f32 1 v))) v)
	0.3b	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
	0.8b	(/.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))) 3) 1/3) v)
	0.2b	(/.f32 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))) v)

Compiler

Compiled 4222 to 2819 computations (33.2% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (-.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (/.f32 1 v)))
✓	0.9b	(pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3)
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	10.0b	(+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))

series60.0s (88.6%)

Counts

2 → 72

Calls

2 calls:

59.9s

(pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3)

20.0ms

(exp.f32 (-.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (/.f32 1 v)))

rewrite74.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

65× egg-rr

Counts

2 → 65

Calls

2 calls:

72.0ms

((pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (exp.f32 (-.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (/.f32 1 v))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	378	38
2	4849	38
3	5196	38
0	0	0
1	0	0

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

834×	`associate-/r*_binary32`
642×	`fma-def_binary32`
312×	`associate-/r/_binary32`
212×	`times-frac_binary32`
180×	`associate-/l*_binary32`

Counts

137 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3412
1	579	3208
2	2196	2782
3	5410	2782

prune216.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	162	6	168

Error

0.0b

Counts

168 → 6

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) (-.f32 (log.f32 1/2) (log.f32 v))))
	0.1b	(.f32 1/2 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (+.f32 (log.f32 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
✓	0.1b	(/.f32 (exp.f32 (-.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) 3) (/.f32 1 v))) v)
	0.3b	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)) 6931/10000)))
	0.8b	(/.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))) 3) 1/3) v)
	0.2b	(/.f32 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))) v)

Compiler

Compiled 5283 to 3515 computations (33.5% saved)

regimes600.0ms (0.9%)

Accuracy

Total 0.1b remaining (54%)

Threshold costs 0.1b (54%)

Counts

68 → 1

Compiler

Compiled 15348 to 11761 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`*-commutative_binary32`
1×	`distribute-neg-frac_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	19	22
2	25	22
3	27	22
4	28	22
5	26	22

end126.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 266 to 219 computations (17.7% saved)

Details

analyze2.2s (3.2%)

sample2.8s (4.1%)

simplify50.0ms (0.1%)

prune5.0ms (0%)

localize72.0ms (0.1%)

series119.0ms (0.2%)

rewrite51.0ms (0.1%)

simplify102.0ms (0.2%)

prune177.0ms (0.3%)

localize74.0ms (0.1%)

series99.0ms (0.1%)

rewrite36.0ms (0.1%)

simplify114.0ms (0.2%)

prune231.0ms (0.3%)

localize47.0ms (0.1%)

series63.0ms (0.1%)

rewrite77.0ms (0.1%)

simplify49.0ms (0.1%)

prune250.0ms (0.4%)

localize62.0ms (0.1%)

series60.0s (88.6%)

rewrite74.0ms (0.1%)

simplify75.0ms (0.1%)

prune216.0ms (0.3%)

regimes600.0ms (0.9%)

simplify2.0ms (0%)

end126.0ms (0.2%)

Profiling