Details

analyze2.0s (13.3%)

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)

sample3.0s (20.6%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.9s	8256×	body	128	valid
35.0ms	121×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify52.0ms (0.4%)

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)

localize67.0ms (0.5%)

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))
✓	7.8b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	8.6b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series260.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

207.0ms	(+.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))
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite55.0ms (0.4%)

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:

23.0ms	(+.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))
4.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify171.0ms (1.2%)

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

prune297.0ms (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	(*.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)))))
	15.6b	(exp.f32 (/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) 3) (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) (fma.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 -6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) 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)))))

15.6b

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

Compiler

Compiled 8793 to 3913 computations (55.5% saved)

localize57.0ms (0.4%)

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	(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	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series249.0ms (1.7%)

Counts

4 → 180

Calls

4 calls:

136.0ms	(*.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)))))
52.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
50.0ms	(-.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)

rewrite40.0ms (0.3%)

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:

13.0ms	(*.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)))))
7.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
4.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
1.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify170.0ms (1.2%)

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

prune421.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	234	5	239

Error

0.0b

Counts

239 → 5

Alt Table

Status	Error	Program
	2.6b	(*.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))))))
▶	0.1b	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v))) (*.f32 (cbrt.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))))))
	12.8b	(.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))))))))
	12.8b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (neg.f32 (.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)))))))) (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)))))))))

Compiler

Compiled 11473 to 6608 computations (42.4% saved)

localize56.0ms (0.4%)

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	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
✓	0.1b	(+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series266.0ms (1.8%)

Counts

2 → 120

Calls

2 calls:

209.0ms

(+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))

56.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary32`
20×	`add-sqr-sqrt_binary32`
18×	`add-cube-cbrt_binary32`
14×	`associate-+l+_binary32`
13×	`associate-+r+_binary32`

Counts

2 → 74

Calls

2 calls:

8.0ms

(+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))

7.0ms

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

simplify122.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

469×	`times-frac_binary32`
325×	`associate-r_binary32`
273×	`associate-/l*_binary32`
243×	`associate-/r*_binary32`
227×	`associate-+l+_binary32`

Counts

194 → 156

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	397	8778
1	1209	7667
2	5092	7667

prune531.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	222	6	228

Error

0.0b

Counts

228 → 6

Alt Table

Status	Error	Program
	2.6b	(*.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))))))
✓	0.1b	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	0.1b	(pow.f32 (E.f32) (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	12.8b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (neg.f32 (.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)))))))) (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)))))))))
	12.8b	(.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))))))))
▶	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))))

Compiler

Compiled 10873 to 6516 computations (40.1% saved)

localize75.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	0.1b	(+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.4b	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))

series1.9s (12.7%)

Counts

1 → 60

Calls

1 calls:

1.9s	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cbrt-prod_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`cbrt-div_binary32`
2×	`exp-diff_binary32`

Counts

1 → 16

Calls

1 calls:

7.0ms

(cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

472×	`times-frac_binary32`
322×	`associate-r_binary32`
266×	`associate-/l*_binary32`
246×	`associate-/r*_binary32`
240×	`associate-+r+_binary32`

Counts

76 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	5730
1	1030	5421
2	4755	5163
3	5031	5163

prune2.8s (19.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	700	2	702
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	702	6	708

Error

0.0b

Counts

708 → 6

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (E.f32) (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	12.8b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (neg.f32 (.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)))))))) (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)))))))))
	2.6b	(*.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))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (/.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 1/2))) (exp.f32 (log.f32 v)))))
	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))) (pow.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))) 1/3))
✓	0.1b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))))

Compiler

Compiled 72324 to 44300 computations (38.7% saved)

regimes1.7s (11.8%)

Accuracy

Total 0.0b remaining (24.7%)

Threshold costs 0.0b (24.7%)

Counts

147 → 1

Compiler

Compiled 52858 to 36275 computations (31.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	24	104
1	30	104
2	34	104
3	36	104
4	37	104
5	36	104

end268.0ms (1.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 847 to 522 computations (38.4% saved)

Details

analyze2.0s (13.3%)

sample3.0s (20.6%)

simplify52.0ms (0.4%)

prune4.0ms (0%)

localize67.0ms (0.5%)

series260.0ms (1.8%)

rewrite55.0ms (0.4%)

simplify171.0ms (1.2%)

prune297.0ms (2%)

localize57.0ms (0.4%)

series249.0ms (1.7%)

rewrite40.0ms (0.3%)

simplify170.0ms (1.2%)

prune421.0ms (2.9%)

localize56.0ms (0.4%)

series266.0ms (1.8%)

rewrite22.0ms (0.2%)

simplify122.0ms (0.8%)

prune531.0ms (3.6%)

localize75.0ms (0.5%)

series1.9s (12.7%)

rewrite8.0ms (0.1%)

simplify123.0ms (0.8%)

prune2.8s (19.1%)

regimes1.7s (11.8%)

simplify4.0ms (0%)

end268.0ms (1.8%)

Profiling