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)

sample82.0ms (0.1%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
11.0ms	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

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
▶	0.2b	(*.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)))))
	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)))))

Status

Error

Program

▶

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)))))

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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize49.0ms (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))))

rewrite76.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-cube-cbrt_binary32`
24×	`pow1_binary32`
22×	`add-sqr-sqrt_binary32`
14×	`add-log-exp_binary32`
14×	`add-cbrt-cube_binary32`

Counts

4 → 166

Calls

4 calls:

30.0ms	(*.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)))))
14.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
11.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
10.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

series413.0ms (0.3%)

Counts

4 → 180

Calls

4 calls:

169.0ms	(*.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)))))
146.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
69.0ms	(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)

simplify257.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

384×	`times-frac_binary32`
274×	`associate-/l*_binary32`
269×	`associate-r_binary32`
269×	`fma-def_binary32`
249×	`fma-neg_binary32`

Counts

346 → 538

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	410	11050
1	1241	10640
2	4995	10640
3	5177	10640

prune533.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	530	8	538
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	532	8	540

Error

0.1b

Counts

540 → 8

Alt Table

Status	Error	Program
	2.7b	(/.f32 1/2 (/.f32 (*.f32 v (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496))))
▶	0.1b	(pow.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)))))) 3)
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (cbrt.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))))) 3))
	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	(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))))
	0.2b	(.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))))))
	15.9b	(sqrt.f32 (*.f32 (pow.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)))) 2) (pow.f32 (/.f32 1/2 v) 2)))
	1.2b	(.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (*.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 11393 to 6491 computations (43% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	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))))))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`cbrt-div_binary32`
5×	`frac-times_binary32`
5×	`exp-diff_binary32`
5×	`pow1/3_binary32`
5×	`add-cube-cbrt_binary32`

Counts

1 → 36

Calls

1 calls:

13.0ms

(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))))))

simplify118.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

96 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	389	5852
1	1217	5687
2	5136	5687

prune508.0ms (0.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	550	4	554
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	556	6	562

Error

0.1b

Counts

562 → 6

Alt Table

Status	Error	Program
	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))))
	0.2b	(pow.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))))))) 3)
▶	0.1b	(pow.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)))))))) 3)
	1.2b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (*.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) 3)
	2.7b	(/.f32 1/2 (/.f32 (*.f32 v (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496))))
	28.8b	(pow.f32 (+.f32 (.f32 1/162 (.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (cbrt.f32 1/2) (pow.f32 cosTheta_O 3))) (pow.f32 (/.f32 (exp.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 v 10)) 1/3))) (+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (pow.f32 (/.f32 (exp.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 v 4)) 1/3))) (+.f32 (.f32 1/18 (.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (cbrt.f32 1/2) (pow.f32 cosTheta_O 2))) (pow.f32 (/.f32 (exp.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 v 7)) 1/3))) (.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) v) 1/3) (cbrt.f32 1/2))))) 3)

Compiler

Compiled 13818 to 8824 computations (36.1% 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))))
✓	0.1b	(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))))))))
	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)))))))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cube-cbrt_binary32`
15×	`exp-diff_binary32`
10×	`log-div_binary32`
10×	`cbrt-div_binary32`
10×	`frac-times_binary32`

Counts

2 → 76

Calls

2 calls:

13.0ms

(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)))))))

12.0ms

(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))))))))

Details

analyze2.1s (1.4%)

sample82.0ms (0.1%)

simplify53.0ms (0%)

prune5.0ms (0%)

localize49.0ms (0%)

rewrite76.0ms (0.1%)

series413.0ms (0.3%)

simplify257.0ms (0.2%)

prune533.0ms (0.4%)

localize60.0ms (0%)

rewrite16.0ms (0%)

series2.6s (1.7%)

simplify118.0ms (0.1%)

prune508.0ms (0.3%)

localize67.0ms (0%)

rewrite32.0ms (0%)

series2.4min (95.3%)

Profiling