Details

analyze2.0s (16.9%)

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)

sample2.5s (21.5%)

Results

2.5s	8256×	body	128	valid
28.0ms	114×	body	128	invalid

Compiler

Compiled 138 to 102 computations (26.1% saved)

preprocess55.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

880×	`fma-neg_binary32`
278×	`associate-+l-_binary32`
233×	`associate-+l+_binary32`
231×	`associate-+r-_binary32`
214×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	385
1	327	363
2	978	341
3	4387	330
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary32`
512×	`exp-sum_binary32`
492×	`fma-neg_binary32`
429×	`exp-diff_binary32`
212×	`times-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	147	31
3	584	29
4	2863	29

Stop Event

1×	node limit

Counts

1 → 2

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

Compiler

Compiled 160 to 112 computations (30% saved)

localize49.0ms (0.4%)

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

series210.0ms (1.8%)

Counts

4 → 180

Calls

54 calls:

22.0ms	(*.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)))) (/.f32 1/2 v))	v	-inf
22.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)	v	-inf
20.0ms	(*.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)))) (/.f32 1/2 v))	v	inf
9.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	-inf
8.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	inf

rewrite86.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`prod-diff_binary32`
190×	`add-sqr-sqrt_binary32`
177×	`add-cbrt-cube_binary32`
177×	`log1p-expm1-u_binary32`
177×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
1	382	81
2	4976	81

Stop Event

1×	node limit

Counts

4 → 133

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

389×	`times-frac_binary32`
263×	`associate-/l*_binary32`
261×	`associate-+r+_binary32`
246×	`cancel-sign-sub-inv_binary32`
224×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	7456
1	982	7024
2	4430	6574

Stop Event

1×	node limit

Counts

313 → 202

prune335.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	199	5	204

Error

0.1b

Counts

204 → 5

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (cbrt.f32 (*.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)))) (/.f32 1/2 v))) 3)
	2.9b	(/.f32 (*.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(*.f32 (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)))) (/.f32 1/2 v))
▶	0.1b	(*.f32 (pow.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))))) 3) (/.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))))

Compiler

Compiled 8400 to 5022 computations (40.2% saved)

localize66.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 (pow.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))))) 3) (/.f32 1/2 v))
✓	0.0b	(pow.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))))) 3)
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	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))))

series768.0ms (6.5%)

Counts

2 → 120

Calls

30 calls:

97.0ms	(pow.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))))) 3)	v	-inf
95.0ms	(pow.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))))) 3)	v	inf
54.0ms	(pow.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))))) 3)	cosTheta_O	inf
47.0ms	(pow.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))))) 3)	sinTheta_i	inf
43.0ms	(pow.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))))) 3)	sinTheta_i	-inf

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary32`
197×	`log1p-expm1-u_binary32`
197×	`expm1-log1p-u_binary32`
196×	`add-cbrt-cube_binary32`
194×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	443	52

Stop Event

1×	node limit

Counts

2 → 54

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Rules

384×	`times-frac_binary32`
309×	`cancel-sign-sub-inv_binary32`
248×	`associate-/l*_binary32`
248×	`fma-def_binary32`
238×	`associate-+r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	259	7332
1	926	7074
2	4341	7074

Stop Event

1×	node limit

Counts

174 → 103

prune389.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	181	6	187

Error

0.1b

Counts

187 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (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)))))) (/.f32 1/2 v))
	0.1b	(pow.f32 (cbrt.f32 (*.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)))) (/.f32 1/2 v))) 3)
	2.9b	(/.f32 (*.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (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) (/.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 (.f32 (pow.f32 (pow.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)))) 1/6) 3) (pow.f32 (pow.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)))) 1/6) 3)) (/.f32 1/2 v))

Compiler

Compiled 9010 to 5686 computations (36.9% saved)

localize76.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (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)))))) (/.f32 1/2 v))
✓	0.0b	(pow.f32 (cbrt.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)))))) 2)
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	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))))

series1.2s (10.2%)

Counts

2 → 120

Calls

30 calls:

120.0ms	(pow.f32 (cbrt.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)))))) 2)	cosTheta_O	inf
119.0ms	(pow.f32 (cbrt.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)))))) 2)	cosTheta_i	-inf
118.0ms	(pow.f32 (cbrt.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)))))) 2)	sinTheta_O	-inf
114.0ms	(pow.f32 (cbrt.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)))))) 2)	sinTheta_O	inf
114.0ms	(pow.f32 (cbrt.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)))))) 2)	cosTheta_O	-inf

rewrite31.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

241×	`add-sqr-sqrt_binary32`
236×	`log1p-expm1-u_binary32`
236×	`expm1-log1p-u_binary32`
230×	`add-cbrt-cube_binary32`
227×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	93
1	528	59

Stop Event

1×	node limit

Counts

2 → 29

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary32`
461×	`associate-r_binary32`
359×	`fma-def_binary32`
357×	`associate-/l*_binary32`
308×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	380	7704
1	1319	7302

Stop Event

1×	node limit

Counts

149 → 90

prune663.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	248	6	254

Error

0.0b

Counts

254 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (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)))))) (/.f32 1/2 v))
▶	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (cbrt.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (.f32 1/9 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2) 3) (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)))))) (/.f32 1/2 v))
	2.9b	(/.f32 (*.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (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) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.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)))) 1/6) 3) (pow.f32 (pow.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)))) 1/6) 3)) (/.f32 1/2 v))

Compiler

Compiled 17539 to 10933 computations (37.7% saved)

localize94.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
	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	(cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	0.5b	(pow.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)))) 2)

series273.0ms (2.3%)

Counts

2 → 48

Calls

30 calls:

45.0ms	(pow.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)))) 2)	v	-inf
44.0ms	(pow.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)))) 2)	v	inf
34.0ms	(cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	-inf
31.0ms	(cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))	v	inf
12.0ms	(pow.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)))) 2)	cosTheta_i	0

rewrite63.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
174×	`add-sqr-sqrt_binary32`
165×	`log1p-expm1-u_binary32`
165×	`expm1-log1p-u_binary32`
164×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	358	49
2	4497	49

Stop Event

1×	node limit

Counts

2 → 43

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary32`
338×	`times-frac_binary32`
279×	`associate-+r+_binary32`
262×	`associate-r_binary32`
227×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	296	6602
1	1122	6372

Stop Event

1×	node limit

Counts

91 → 90

prune939.0ms (8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	272	8	280

Error

0.0b

Counts

280 → 8

Alt Table

Status	Error	Program
✓	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (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)))))) (/.f32 1/2 v))
✓	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (cbrt.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.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)))))) 2) 3) (cbrt.f32 (pow.f32 (exp.f32 (pow.f32 (pow.f32 (cbrt.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))))) 3) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (.f32 1/9 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2) 3) (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)))))) (/.f32 1/2 v))
	2.9b	(/.f32 (*.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (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) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (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)))))) 2) 3) (cbrt.f32 (pow.f32 (exp.f32 (pow.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)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (pow.f32 (pow.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)))) 1/6) 3) (pow.f32 (pow.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)))) 1/6) 3)) (/.f32 1/2 v))

Compiler

Compiled 26337 to 16028 computations (39.1% saved)

regimes1.2s (9.9%)

Accuracy

Total 0.0b remaining (42.6%)

Threshold costs 0.0b (42.6%)

Counts

111 → 1

Compiler

Compiled 35007 to 24610 computations (29.7% saved)

simplify3.0ms (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	30	96
1	36	96
2	40	96
3	42	96
4	43	96

Stop Event

1×

saturated

end280.0ms (2.4%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 824 to 528 computations (35.9% saved)

Details

analyze2.0s (16.9%)

sample2.5s (21.5%)

preprocess55.0ms (0.5%)

simplify21.0ms (0.2%)

prune4.0ms (0%)

localize49.0ms (0.4%)

series210.0ms (1.8%)

rewrite86.0ms (0.7%)

simplify133.0ms (1.1%)

prune335.0ms (2.9%)

localize66.0ms (0.6%)

series768.0ms (6.5%)

rewrite38.0ms (0.3%)

simplify122.0ms (1%)

prune389.0ms (3.3%)

localize76.0ms (0.6%)

series1.2s (10.2%)

rewrite31.0ms (0.3%)

simplify92.0ms (0.8%)

prune663.0ms (5.6%)

localize94.0ms (0.8%)

series273.0ms (2.3%)

rewrite63.0ms (0.5%)

simplify81.0ms (0.7%)

prune939.0ms (8%)

regimes1.2s (9.9%)

simplify3.0ms (0%)

end280.0ms (2.4%)

Profiling