Details

analyze2.1s (18.1%)

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)

sample147.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

36.0ms	256×	body	128	valid
14.0ms	259×	pre	128	true
0.0ms	3×	body	128	nan

Compiler

Compiled 104 to 78 computations (25% saved)

simplify50.0ms (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

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

0.1b

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)

localize56.0ms (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)))))
✓	0.0b	(-.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)

series291.0ms (2.5%)

Counts

4 → 180

Calls

4 calls:

169.0ms	(*.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)))))
59.0ms	(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)))
12.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite39.0ms (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:

12.0ms	(*.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)))))
6.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify197.0ms (1.7%)

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

prune481.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	233	6	239

Error

0.0b

Counts

239 → 6

Alt Table

Status	Error	Program
	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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)))))))
	13.0b	(.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 (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))))))
	0.1b	(*.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 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))
	14.8b	(.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))))))))

Compiler

Compiled 11493 to 6630 computations (42.3% saved)

localize69.0ms (0.6%)

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)
✓	0.3b	(sqrt.f32 (*.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))))))

series342.0ms (3%)

Counts

1 → 48

Calls

1 calls:

342.0ms

(sqrt.f32 (*.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))))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary32`
3×	`sqrt-div_binary32`
2×	`exp-diff_binary32`
2×	`sqrt-pow1_binary32`
1×	`*-un-lft-identity_binary32`

Counts

1 → 16

Calls

1 calls:

10.0ms

(sqrt.f32 (*.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))))))

simplify115.0ms (1%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary32`
423×	`*-commutative_binary32`
371×	`associate-/l*_binary32`
274×	`times-frac_binary32`
234×	`associate-/l/_binary32`

Counts

64 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	3039
1	388	2923
2	1013	2899
3	2348	2883
4	4959	2883
5	4984	2883

prune949.0ms (8.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	340	6	346

Error

0.0b

Counts

346 → 6

Alt Table

Status	Error	Program
	14.8b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (.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)))))))))))
	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))))))
▶	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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	(*.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 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))
	3.6b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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))))))))

Compiler

Compiled 23825 to 13665 computations (42.6% saved)

localize65.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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	(sqrt.f32 (/.f32 1/2 v))
✓	0.3b	(sqrt.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)))))

series103.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

94.0ms	(sqrt.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)))))
9.0ms	(sqrt.f32 (/.f32 1/2 v))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-prod_binary32`
24×	`add-sqr-sqrt_binary32`
20×	`*-un-lft-identity_binary32`
18×	`add-cube-cbrt_binary32`
14×	`exp-sum_binary32`

Counts

2 → 62

Calls

2 calls:

5.0ms	(sqrt.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)))))
2.0ms	(sqrt.f32 (/.f32 1/2 v))

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

270×	`cancel-sign-sub-inv_binary32`
268×	`fma-neg_binary32`
224×	`fma-def_binary32`
175×	`times-frac_binary32`
161×	`neg-mul-1_binary32`

Counts

86 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	4458
1	780	3586
2	2942	3130
3	4669	3128
4	4921	3128

prune987.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	341	7	348

Error

0.0b

Counts

348 → 7

Alt Table

Status	Error	Program
	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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)))))))
✓	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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)))))))
	14.8b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (.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)))))))))))
▶	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))))))
	0.1b	(*.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 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))
	3.6b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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))))))))

Compiler

Compiled 25813 to 15250 computations (40.9% saved)

localize64.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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	(cbrt.f32 (/.f32 1/2 v))
✓	0.5b	(*.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v)))

series86.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

52.0ms	(*.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v)))
34.0ms	(cbrt.f32 (/.f32 1/2 v))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary32`
65×	`add-sqr-sqrt_binary32`
51×	`times-frac_binary32`
41×	`*-un-lft-identity_binary32`
41×	`add-cube-cbrt_binary32`

Counts

2 → 104

Calls

2 calls:

12.0ms	(*.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v)))
2.0ms	(cbrt.f32 (/.f32 1/2 v))

simplify150.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

454×	`sqr-pow_binary32`
429×	`associate-/l*_binary32`
357×	`associate-/r*_binary32`
337×	`fma-def_binary32`
301×	`associate-l_binary32`

Counts

128 → 150

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2254
1	217	2200
2	590	2115
3	1396	2095
4	3279	1940
5	3500	1940
6	3961	1940
7	4872	1940
8	4858	1940

prune861.0ms (7.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	293	2	295
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	295	7	302

Error

0.0b

Counts

302 → 7

Alt Table

Status	Error	Program
	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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)))))))
✓	0.1b	(.f32 (.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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 (sqrt.f32 (/.f32 1/2 v)) (sqrt.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)))))))
	14.8b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (.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)))))))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v))) (*.f32 (cbrt.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 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 1/2 v))) 5) (cbrt.f32 (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))))))
✓	0.1b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))
	3.6b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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))))))))

Compiler

Compiled 13506 to 8645 computations (36% saved)

regimes1.5s (13.3%)

Accuracy

Total 0.0b remaining (27.3%)

Threshold costs 0.0b (27.3%)

Counts

134 → 1

Compiler

Compiled 44589 to 30802 computations (30.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	27	57
1	34	57
2	38	57
3	40	57
4	41	57
5	40	57

end25.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 210 to 160 computations (23.8% saved)

sample2.6s (22.7%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
460.0ms	8123×	pre	128	true
14.0ms	123×	body	128	nan

Compiler

Compiled 542 to 355 computations (34.5% saved)

Details

analyze2.1s (18.1%)

sample147.0ms (1.3%)

simplify50.0ms (0.4%)

prune5.0ms (0%)

localize56.0ms (0.5%)

series291.0ms (2.5%)

rewrite39.0ms (0.3%)

simplify197.0ms (1.7%)

prune481.0ms (4.2%)

localize69.0ms (0.6%)

series342.0ms (3%)

rewrite11.0ms (0.1%)

simplify115.0ms (1%)

prune949.0ms (8.3%)

localize65.0ms (0.6%)

series103.0ms (0.9%)

rewrite13.0ms (0.1%)

simplify119.0ms (1%)

prune987.0ms (8.6%)

localize64.0ms (0.6%)

series86.0ms (0.8%)

rewrite22.0ms (0.2%)

simplify150.0ms (1.3%)

prune861.0ms (7.5%)

regimes1.5s (13.3%)

simplify4.0ms (0%)

end25.0ms (0.2%)

sample2.6s (22.7%)

Profiling