Details

analyze1.9s (15.9%)

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)

sample130.0ms (1.1%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

33.0ms	256×	body	128	valid
14.0ms	260×	pre	128	true
0.0ms	4×	body	128	nan

Compiler

Compiled 104 to 78 computations (25% saved)

simplify47.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	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)))))
▶	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)))))

Status

Error

Program

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)))))

▶

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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize50.0ms (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 (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)))))

series218.0ms (1.8%)

Counts

4 → 180

Calls

4 calls:

122.0ms	(*.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)))))
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))))
38.0ms	(-.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)

rewrite33.0ms (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)))))
4.0ms	(-.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))))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify162.0ms (1.3%)

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

prune448.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	6	225

Error

0.0b

Counts

225 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (*.f32 (/.f32 1/2 (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	(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)))))
	11.5b	(.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))))))))
	0.2b	(.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)))))))
	0.2b	(.f32 (.f32 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	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))))))

Compiler

Compiled 11125 to 6446 computations (42.1% saved)

localize68.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.2b	(/.f32 1/2 (cbrt.f32 v))
✓	0.3b	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
✓	0.6b	(*.f32 (cbrt.f32 v) (cbrt.f32 v))

series159.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

65.0ms	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
53.0ms	(/.f32 1/2 (cbrt.f32 v))
42.0ms	(*.f32 (cbrt.f32 v) (cbrt.f32 v))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary32`
28×	`cbrt-prod_binary32`
28×	`*-un-lft-identity_binary32`
28×	`add-cube-cbrt_binary32`
21×	`times-frac_binary32`

Counts

3 → 120

Calls

3 calls:

6.0ms	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
4.0ms	(*.f32 (cbrt.f32 v) (cbrt.f32 v))
3.0ms	(/.f32 1/2 (cbrt.f32 v))

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary32`
592×	`fma-neg_binary32`
292×	`times-frac_binary32`
285×	`*-commutative_binary32`
215×	`log-prod_binary32`

Counts

156 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1791
1	244	1605
2	562	1495
3	1689	1461
4	2536	1313
5	4093	1313
6	4995	1313
7	4836	1313

prune343.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	181	6	187

Error

0.0b

Counts

187 → 6

Alt Table

Status	Error	Program
	0.2b	(.f32 (expm1.f32 (log1p.f32 (pow.f32 (/.f32 1 v) 2/3))) (.f32 (/.f32 1/2 (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))))))
	0.2b	(.f32 (.f32 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	0.1b	(.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (.f32 (.f32 (*.f32 (cbrt.f32 (/.f32 1/2 (cbrt.f32 v))) (cbrt.f32 (/.f32 1/2 (cbrt.f32 v)))) (cbrt.f32 (/.f32 1/2 (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 (.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (*.f32 (/.f32 1/2 (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))))))
	22.7b	(.f32 (/.f32 1 (log.f32 (exp.f32 (cbrt.f32 (.f32 v v))))) (*.f32 (/.f32 1/2 (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))))))
	11.5b	(.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 6683 to 3341 computations (50% saved)

localize81.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))
✓	0.4b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))
✓	0.5b	(.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))
	0.6b	(*.f32 (cbrt.f32 v) (cbrt.f32 v))

series485.0ms (4%)

Counts

2 → 24

Calls

2 calls:

419.0ms

(*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

65.0ms

(*.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary32`
44×	`add-sqr-sqrt_binary32`
33×	`times-frac_binary32`
28×	`*-un-lft-identity_binary32`
28×	`pow1_binary32`

Counts

2 → 122

Calls

2 calls:

13.0ms

(*.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

8.0ms

(*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

simplify162.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

793×	`associate-/r/_binary32`
557×	`fma-def_binary32`
461×	`sqr-pow_binary32`
377×	`swap-sqr_binary32`
317×	`associate-l_binary32`

Counts

146 → 158

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	105	3687
1	171	3525
2	451	3046
3	1717	2917
4	2982	2221
5	3307	2194
6	4504	2194
7	4830	2194

prune1.2s (9.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	483	2	485
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	485	6	491

Error

0.0b

Counts

491 → 6

Alt Table

Status	Error	Program
	22.7b	(.f32 (/.f32 1 (log.f32 (exp.f32 (cbrt.f32 (.f32 v v))))) (*.f32 (/.f32 1/2 (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 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (pow.f32 (cbrt.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v)))) 4)) (.f32 (/.f32 1/2 (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))))))
	0.2b	(.f32 (expm1.f32 (log1p.f32 (pow.f32 (/.f32 1 v) 2/3))) (.f32 (/.f32 1/2 (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))))))
	0.2b	(.f32 (.f32 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	11.5b	(.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 (exp.f32 (log.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (*.f32 (/.f32 1/2 (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 25515 to 12447 computations (51.2% saved)

localize92.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (exp.f32 (log.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))
	0.5b	(.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))
	0.6b	(*.f32 (cbrt.f32 v) (cbrt.f32 v))
✓	2.2b	(exp.f32 (log.f32 (.f32 (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))))

series511.0ms (4.2%)

Counts

2 → 24

Calls

2 calls:

444.0ms

(exp.f32 (log.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))))

67.0ms

(*.f32 (exp.f32 (log.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary32`
16×	`cbrt-div_binary32`
13×	`cbrt-prod_binary32`
12×	`exp-prod_binary32`
12×	`pow1_binary32`

Counts

2 → 68

Calls

2 calls:

16.0ms

(*.f32 (exp.f32 (log.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))))))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))

6.0ms

(exp.f32 (log.f32 (*.f32 (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))) (cbrt.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v)))))))

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

742×	`unswap-sqr_binary32`
428×	`associate-l_binary32`
428×	`times-frac_binary32`
336×	`associate-r_binary32`
287×	`associate-/l*_binary32`

Counts

92 → 113

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	3350
1	171	1861
2	371	1840
3	779	1715
4	2973	1546
5	5064	1546

prune905.0ms (7.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	373	5	378

Error

0.0b

Counts

378 → 5

Alt Table

Status	Error	Program
	0.2b	(.f32 (expm1.f32 (log1p.f32 (pow.f32 (/.f32 1 v) 2/3))) (.f32 (/.f32 1/2 (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))))))
	0.2b	(.f32 (.f32 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	22.7b	(.f32 (/.f32 1 (log.f32 (exp.f32 (cbrt.f32 (.f32 v v))))) (*.f32 (/.f32 1/2 (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))))))
	11.5b	(.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 (exp.f32 (log.f32 (.f32 1 (pow.f32 (cbrt.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v)))) 4)))) (cbrt.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (*.f32 (/.f32 1/2 (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 20551 to 10331 computations (49.7% saved)

regimes2.5s (20%)

Accuracy

Total 0.0b remaining (27.3%)

Threshold costs 0.0b (27.3%)

Counts

213 → 1

Compiler

Compiled 71267 to 48009 computations (32.6% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`*-lft-identity_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	65
1	40	65
2	44	65
3	46	65
4	47	65
5	46	65

end19.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 230 to 160 computations (30.4% saved)

sample2.5s (20.1%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
480.0ms	8139×	pre	128	true
15.0ms	139×	body	128	nan

Compiler

Compiled 393 to 262 computations (33.3% saved)

Details

analyze1.9s (15.9%)

sample130.0ms (1.1%)

simplify47.0ms (0.4%)

prune4.0ms (0%)

localize50.0ms (0.4%)

series218.0ms (1.8%)

rewrite33.0ms (0.3%)

simplify162.0ms (1.3%)

prune448.0ms (3.7%)

localize68.0ms (0.6%)

series159.0ms (1.3%)

rewrite18.0ms (0.1%)

simplify117.0ms (1%)

prune343.0ms (2.8%)

localize81.0ms (0.7%)

series485.0ms (4%)

rewrite35.0ms (0.3%)

simplify162.0ms (1.3%)

prune1.2s (9.5%)

localize92.0ms (0.8%)

series511.0ms (4.2%)

rewrite29.0ms (0.2%)

simplify95.0ms (0.8%)

prune905.0ms (7.4%)

regimes2.5s (20%)

simplify18.0ms (0.1%)

end19.0ms (0.2%)

sample2.5s (20.1%)

Profiling