Details

analyze2.1s (21.7%)

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)

sample2.9s (30.2%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.8s	8256×	body	128	valid
38.0ms	137×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify50.0ms (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 (0.1%)

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

0.1b

Counts

3 → 2

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) (log.f32 (/.f32 1 (*.f32 2 v)))))
▶	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)))))

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

▶

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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize51.0ms (0.5%)

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)

series237.0ms (2.5%)

Counts

4 → 180

Calls

4 calls:

125.0ms	(*.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)))))
55.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
46.0ms	(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)

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:

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)))))
5.0ms	(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 (1.8%)

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

prune466.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	230	7	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

0.1b

Counts

239 → 7

Alt Table

Status	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))))
	1.4b	(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	3.3b	(*.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))))))
	0.2b	(*.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 1/2 v) (pow.f32 (exp.f32 (.f32 (cbrt.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 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.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 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
▶	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.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 11433 to 6600 computations (42.3% saved)

localize65.0ms (0.7%)

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 (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 (sqrt.f32 1/2) (sqrt.f32 v))

series17.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

17.0ms

(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary32`
36×	`times-frac_binary32`
31×	`add-sqr-sqrt_binary32`
29×	`*-un-lft-identity_binary32`
29×	`add-cube-cbrt_binary32`

Counts

1 → 64

Calls

1 calls:

4.0ms

(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))

simplify137.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-neg_binary32`
761×	`times-frac_binary32`
622×	`div-sub_binary32`
577×	`associate-/l/_binary32`
510×	`fma-def_binary32`

Counts

64 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1071
1	122	1037
2	218	1037
3	339	1037
4	488	1037
5	626	1037
6	1177	1037
7	3142	1037
8	4430	1037
9	4328	1037
10	4940	1037
11	4751	1037

prune601.0ms (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	252	7	259

Error

0.1b

Counts

259 → 7

Alt Table

Status	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))))
	1.4b	(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	3.3b	(*.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))))))
	0.2b	(*.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 1/2 v) (pow.f32 (exp.f32 (.f32 (cbrt.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 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.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 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
✓	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.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 11834 to 6803 computations (42.5% saved)

localize57.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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	(-.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 (-.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))))

series283.0ms (3%)

Counts

2 → 120

Calls

2 calls:

225.0ms

(+.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)))

58.0ms

(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))))

rewrite23.0ms (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)))

8.0ms

(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))))

simplify127.0ms (1.3%)

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 → 157

Iterations

Useful iterations: 1 (0.0ms)

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

prune510.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	224	7	231

Error

0.0b

Counts

231 → 7

Alt Table

Status	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))))
	1.4b	(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
▶	0.1b	(/.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)))
	0.2b	(pow.f32 (exp.f32 (*.f32 (cbrt.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 (-.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 (-.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)))))
	3.3b	(*.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))))))
	0.2b	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (.f32 (cbrt.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 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.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 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.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 10692 to 6427 computations (39.9% saved)

localize69.0ms (0.7%)

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 1/2)))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	3.0b	(exp.f32 (log.f32 v))

series54.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

52.0ms	(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 1/2)))
2.0ms	(exp.f32 (log.f32 v))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary32`
11×	`exp-prod_binary32`
6×	`add-log-exp_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`

Counts

2 → 37

Calls

2 calls:

8.0ms	(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 1/2)))
1.0ms	(exp.f32 (log.f32 v))

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-/r/_binary32`
273×	`times-frac_binary32`
228×	`associate-+r+_binary32`
209×	`associate-/l/_binary32`
204×	`associate-r_binary32`

Counts

109 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	4269
1	720	4044
2	3144	3896
3	5328	3896

prune380.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	152	8	160

Error

0.0b

Counts

160 → 8

Alt Table

Status	Error	Program
	3.3b	(*.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))))))
	1.4b	(/.f32 (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (*.f32 2 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (exp.f32 (log.f32 v)))
	0.2b	(pow.f32 (exp.f32 (*.f32 (cbrt.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 (-.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 (-.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	(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 (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))) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (log.f32 v)) (cbrt.f32 (log.f32 v)))) (cbrt.f32 (log.f32 v))))
	0.2b	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (.f32 (cbrt.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 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.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 (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))) v)
✓	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.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 7332 to 4230 computations (42.3% saved)

regimes902.0ms (9.5%)

Accuracy

Total 0.1b remaining (61.6%)

Threshold costs 0.1b (61.6%)

Counts

83 → 1

Compiler

Compiled 23359 to 16351 computations (30% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`/-rgt-identity_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	41
1	28	41
2	32	41
3	34	41
4	35	41
5	34	41

end230.0ms (2.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 518 to 351 computations (32.2% saved)

Details

analyze2.1s (21.7%)

sample2.9s (30.2%)

simplify50.0ms (0.5%)

prune5.0ms (0.1%)

localize51.0ms (0.5%)

series237.0ms (2.5%)

rewrite35.0ms (0.4%)

simplify169.0ms (1.8%)

prune466.0ms (4.9%)

localize65.0ms (0.7%)

series17.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify137.0ms (1.4%)

prune601.0ms (6.3%)

localize57.0ms (0.6%)

series283.0ms (3%)

rewrite23.0ms (0.2%)

simplify127.0ms (1.3%)

prune510.0ms (5.4%)

localize69.0ms (0.7%)

series54.0ms (0.6%)

rewrite11.0ms (0.1%)

simplify98.0ms (1%)

prune380.0ms (4%)

regimes902.0ms (9.5%)

simplify3.0ms (0%)

end230.0ms (2.4%)

Profiling