Details

analyze2.1s (1.4%)

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 51 to 38 computations (25.5% saved)

sample84.0ms (0.1%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
12.0ms	257×	pre	128	true
0.0ms	1×	body	128	nan

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify53.0ms (0%)

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

prune6.0ms (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
	0.2b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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)) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize50.0ms (0%)

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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
✓	0.1b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite29.0ms (0%)

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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

series352.0ms (0.2%)

Counts

4 → 180

Calls

4 calls:

154.0ms	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
117.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
52.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
28.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

simplify237.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

383×	`times-frac_binary32`
278×	`associate-/l*_binary32`
276×	`associate-+r+_binary32`
269×	`associate-r_binary32`
240×	`fma-def_binary32`

Counts

303 → 515

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	420	11189
1	1191	10393
2	5087	10393

prune502.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	508	7	515
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	510	7	517

Error

0.1b

Counts

517 → 7

Alt Table

Status	Error	Program
	12.7b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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)))))))
	12.7b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (neg.f32 (.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))))))) (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 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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 (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.2b	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	2.5b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 11191 to 6440 computations (42.5% saved)

localize67.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
✓	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-div_binary32`
2×	`exp-diff_binary32`
1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`
1×	`cbrt-prod_binary32`

Counts

1 → 14

Calls

1 calls:

7.0ms

(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

series2.6s (1.7%)

Counts

1 → 60

Calls

1 calls:

2.6s	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

simplify157.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

512×	`associate-r_binary32`
494×	`times-frac_binary32`
301×	`associate-l_binary32`
273×	`fma-def_binary32`
266×	`associate-/l*_binary32`

Counts

74 → 141

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	381	5435
1	1193	5270
2	5072	5270

prune1.1s (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	653	6	659
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	657	9	666

Error

0.1b

Counts

666 → 9

Alt Table

Status	Error	Program
	0.1b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	12.7b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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)))))))
	0.2b	(exp.f32 (+.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 (/.f32 1/2 v))))
	2.5b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	12.6b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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)))))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	2.7b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (exp.f32 (.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)))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
▶	0.1b	(.f32 (.f32 (exp.f32 (log.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.1b	(.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 1/3) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.2b	(.f32 (.f32 (.f32 (cbrt.f32 1/2) (exp.f32 (.f32 1/3 (-.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (log.f32 v))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))

Compiler

Compiled 29401 to 19008 computations (35.3% saved)

localize79.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.6b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
✓	4.9b	(log.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary32`
3×	`log-div_binary32`
3×	`cbrt-div_binary32`
2×	`add-exp-log_binary32`
2×	`*-un-lft-identity_binary32`

Counts

1 → 19

Calls

1 calls:

2.0ms

(log.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))

Details

analyze2.1s (1.4%)

sample84.0ms (0.1%)

simplify53.0ms (0%)

prune6.0ms (0%)

localize50.0ms (0%)

rewrite29.0ms (0%)

series352.0ms (0.2%)

simplify237.0ms (0.2%)

prune502.0ms (0.3%)

localize67.0ms (0%)

rewrite8.0ms (0%)

series2.6s (1.7%)

simplify157.0ms (0.1%)

prune1.1s (0.7%)

localize79.0ms (0.1%)

rewrite3.0ms (0%)

series2.4min (95.1%)

Profiling