Details

analyze2.2s (15.5%)

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
0.7%	0.7%	98.5%	11
0.7%	0.7%	98.5%	12
0.7%	0.7%	98.5%	13
0.7%	0.7%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample3.8s (26.9%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

3.6s	8256×	body	128	valid
59.0ms	138×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify86.0ms (0.6%)

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

prune12.0ms (0.1%)

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)

localize98.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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	(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)
✓	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)))))

series354.0ms (2.5%)

Counts

4 → 180

Calls

4 calls:

215.0ms	(*.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)))))
71.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
55.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite57.0ms (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:

19.0ms	(*.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))))
7.0ms	(-.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)

simplify200.0ms (1.4%)

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 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	11185
1	1198	10395
2	5156	10395

prune660.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	5	225

Error

0.1b

Counts

225 → 5

Alt Table

Status	Error	Program
	0.2b	(.f32 (.f32 (/.f32 1/2 v) (*.f32 (cbrt.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))))) (cbrt.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))))))) (cbrt.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))))))
▶	0.1b	(exp.f32 (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.2b	(*.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)))))
	0.2b	(.f32 (/.f32 (.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) 1) (*.f32 (/.f32 (cbrt.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	(.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))))))

Compiler

Compiled 10837 to 6298 computations (41.9% saved)

localize125.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.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 (log.f32 1/2) (log.f32 v)) (-.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)
✓	0.3b	(-.f32 (log.f32 1/2) (log.f32 v))

series555.0ms (3.9%)

Counts

3 → 128

Calls

3 calls:

343.0ms

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

119.0ms

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

92.0ms

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

rewrite92.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary32`
46×	`pow1_binary32`
43×	`log-pow_binary32`
41×	`prod-diff_binary32`
38×	`add-sqr-sqrt_binary32`

Counts

3 → 156

Calls

3 calls:

26.0ms

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

20.0ms

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

9.0ms

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

simplify276.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary32`
377×	`associate-r_binary32`
296×	`associate-l_binary32`
286×	`fma-def_binary32`
265×	`associate-/l*_binary32`

Counts

284 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	470	10834
1	1368	9951
2	5293	9951

prune533.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	218	7	225

Error

0.0b

Counts

225 → 7

Alt Table

Status	Error	Program
	0.2b	(.f32 (.f32 (/.f32 1/2 v) (*.f32 (cbrt.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))))) (cbrt.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))))))) (cbrt.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))))))
✓	0.1b	(exp.f32 (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.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 (exp.f32 (log.f32 1/2)) (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.2b	(*.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 1/2 (/.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))))))
	0.1b	(pow.f32 (E.f32) (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.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 (exp.f32 (-.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 1/2))) (/.f32 1 v))) v)

Compiler

Compiled 11111 to 6464 computations (41.8% saved)

localize69.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series265.0ms (1.9%)

Counts

2 → 120

Calls

2 calls:

207.0ms

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

58.0ms

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

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary32`
57×	`add-sqr-sqrt_binary32`
49×	`prod-diff_binary32`
33×	`add-cube-cbrt_binary32`
30×	`exp-sum_binary32`

Counts

2 → 117

Calls

2 calls:

11.0ms

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

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

448×	`times-frac_binary32`
287×	`associate-r_binary32`
257×	`associate-+r+_binary32`
245×	`associate-/l*_binary32`
232×	`associate-/r*_binary32`

Counts

237 → 167

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	424	11600
1	1162	9761
2	5218	9761

prune534.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	230	7	237

Error

0.0b

Counts

237 → 7

Alt Table

Status	Error	Program
✓	0.1b	(exp.f32 (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.2b	(*.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 1/2 (/.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))))))
	0.1b	(pow.f32 (E.f32) (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.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 (exp.f32 (log.f32 1/2)) (*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (sqrt.f32 (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	0.2b	(/.f32 (exp.f32 (log.f32 1/2)) (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 (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)))))))
	0.1b	(/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 1/2))) (/.f32 1 v))) v)

Compiler

Compiled 13099 to 7391 computations (43.6% saved)

localize77.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series187.0ms (1.3%)

Counts

1 → 60

Calls

1 calls:

187.0ms

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

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary32`
32×	`*-un-lft-identity_binary32`
30×	`exp-sum_binary32`
27×	`add-sqr-sqrt_binary32`
20×	`prod-diff_binary32`

Counts

1 → 54

Calls

1 calls:

15.0ms

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

simplify165.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

348×	`fma-def_binary32`
243×	`associate-+r+_binary32`
226×	`*-commutative_binary32`
210×	`times-frac_binary32`
194×	`+-commutative_binary32`

Counts

114 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	7838
1	1076	6203
2	4335	5610
3	4976	5610

prune2.1s (14.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	555	6	561

Error

0.0b

Counts

561 → 6

Alt Table

Status	Error	Program
✓	0.1b	(exp.f32 (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.2b	(*.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)))))
	3.3b	(/.f32 (exp.f32 (log.f32 1/2)) (.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (.f32 (sqrt.f32 (/.f32 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))))))) (sqrt.f32 (pow.f32 1 (*.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	(pow.f32 (E.f32) (+.f32 (-.f32 (log.f32 1/2) (log.f32 v)) (-.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 (exp.f32 (log.f32 1/2)) (*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (sqrt.f32 (exp.f32 (-.f32 (log.f32 v) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	0.2b	(/.f32 (exp.f32 (log.f32 1/2)) (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 (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)))))))

Compiler

Compiled 46982 to 26071 computations (44.5% saved)

regimes1.1s (8.1%)

Accuracy

Total 0.0b remaining (57.4%)

Threshold costs 0.0b (57.4%)

Counts

93 → 1

Compiler

Compiled 30496 to 20687 computations (32.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary32`
7×	`sub-neg_binary32`
6×	`cancel-sign-sub-inv_binary32`
5×	`*-commutative_binary32`
4×	`distribute-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	43	64
2	54	64
3	66	64
4	77	64
5	80	64
6	75	64

end357.0ms (2.5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 549 to 365 computations (33.5% saved)

Details

analyze2.2s (15.5%)

sample3.8s (26.9%)

simplify86.0ms (0.6%)

prune12.0ms (0.1%)

localize98.0ms (0.7%)

series354.0ms (2.5%)

rewrite57.0ms (0.4%)

simplify200.0ms (1.4%)

prune660.0ms (4.7%)

localize125.0ms (0.9%)

series555.0ms (3.9%)

rewrite92.0ms (0.6%)

simplify276.0ms (1.9%)

prune533.0ms (3.8%)

localize69.0ms (0.5%)

series265.0ms (1.9%)

rewrite37.0ms (0.3%)

simplify174.0ms (1.2%)

prune534.0ms (3.8%)

localize77.0ms (0.5%)

series187.0ms (1.3%)

rewrite35.0ms (0.2%)

simplify165.0ms (1.2%)

prune2.1s (14.6%)

regimes1.1s (8.1%)

simplify7.0ms (0%)

end357.0ms (2.5%)

Profiling