Details

analyze1.9s (11.4%)

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 69 to 51 computations (26.1% saved)

sample2.6s (15.6%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.5s	8256×	body	128	valid
39.0ms	129×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify49.0ms (0.3%)

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

0.2b

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) 6931/10000) (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)) 6931/10000) (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) 6931/10000) (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)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize65.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	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	(log.f32 (/.f32 1 (*.f32 2 v)))
✓	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series113.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

61.0ms	(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)))))
27.0ms	(log.f32 (/.f32 1 (*.f32 2 v)))
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary32`
26×	`add-exp-log_binary32`
22×	`distribute-lft-out_binary32`
15×	`exp-prod_binary32`
15×	`add-log-exp_binary32`

Counts

4 → 108

Calls

4 calls:

24.0ms	(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)))))
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(log.f32 (/.f32 1 (*.f32 2 v)))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

576×	`times-frac_binary32`
367×	`associate-/l*_binary32`
354×	`associate-r_binary32`
281×	`associate-/r*_binary32`
269×	`associate-l_binary32`

Counts

180 → 167

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	394	6031
1	1123	5810
2	5056	5810

prune235.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	6	169

Error

0.1b

Counts

169 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v)))
	0.2b	(.f32 (sqrt.f32 (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)))))) (sqrt.f32 (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 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))))
▶	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2))))
	0.3b	(pow.f32 (E.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	(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) (*.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))))))

Compiler

Compiled 8086 to 4905 computations (39.3% saved)

localize59.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2)))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2))))
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series268.0ms (1.6%)

Counts

2 → 120

Calls

2 calls:

207.0ms

(-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2)))

61.0ms

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

rewrite68.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`*-un-lft-identity_binary32`
85×	`distribute-lft-out_binary32`
68×	`pow1_binary32`
60×	`prod-diff_binary32`
44×	`log-pow_binary32`

Counts

2 → 141

Calls

2 calls:

23.0ms

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

21.0ms

(-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2)))

simplify167.0ms (1%)

Algorithm

1×	egg-herbie

Rules

468×	`times-frac_binary32`
283×	`associate-r_binary32`
271×	`associate-+r+_binary32`
268×	`associate-/l*_binary32`
242×	`associate-/r*_binary32`

Counts

261 → 152

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	396	11810
1	1093	10726
2	5272	10726

prune531.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	209	5	214

Error

0.1b

Counts

214 → 5

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2))))
	0.2b	(/.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v)))
	0.2b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))))
▶	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))))
	0.2b	(.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))) (exp.f32 (.f32 (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))) (cbrt.f32 (log.f32 (.f32 v 2))))))

Compiler

Compiled 10280 to 6052 computations (41.1% saved)

localize102.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	29.7b	(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))

series3.3s (19.7%)

Counts

2 → 24

Calls

2 calls:

2.9s

(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (*.f32 v 2)))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2)))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))

392.0ms

(*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary32`
33×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
16×	`log-pow_binary32`
14×	`swap-sqr_binary32`

Counts

2 → 64

Calls

2 calls:

7.0ms

(*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))

0.0ms

(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (*.f32 v 2)))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2)))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-neg_binary32`
588×	`fma-def_binary32`
546×	`log-prod_binary32`
394×	`exp-prod_binary32`
347×	`*-commutative_binary32`

Counts

88 → 80

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	78	1394
1	139	1358
2	334	1099
3	1346	901
4	2698	778
5	3746	776
6	4911	776
7	4503	776

prune953.0ms (5.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	255	3	258
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	257	6	263

Error

0.0b

Counts

263 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))))))
	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2))))
	0.2b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))))
	0.2b	(.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))) (exp.f32 (.f32 (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))) (cbrt.f32 (log.f32 (.f32 v 2))))))
	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (.f32 2 v)))) 4) (cbrt.f32 (cbrt.f32 (pow.f32 (log.f32 (*.f32 2 v)) 2))))))))
	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (.f32 (cbrt.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))) (cbrt.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))) (cbrt.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))))

Compiler

Compiled 21289 to 15579 computations (26.8% saved)

localize126.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3)
	6.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	29.7b	(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))))

series2.7s (16%)

Counts

2 → 20

Calls

2 calls:

2.2s

(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (*.f32 v 2)))) (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))

459.0ms

(pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`unpow-prod-down_binary32`
9×	`*-un-lft-identity_binary32`
6×	`pow1_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`

Counts

2 → 41

Calls

2 calls:

5.0ms

(pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3)

0.0ms

(fma.f32 (neg.f32 (cbrt.f32 (log.f32 (*.f32 v 2)))) (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (*.f32 (cbrt.f32 (log.f32 (*.f32 v 2))) (cbrt.f32 (log.f32 (*.f32 v 2))))))

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary32`
729×	`log-prod_binary32`
669×	`fma-neg_binary32`
549×	`times-frac_binary32`
420×	`exp-prod_binary32`

Counts

61 → 62

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	94	1388
1	188	1187
2	424	1143
3	1871	810
4	3302	707
5	4017	675
6	4680	675
7	4446	675

prune527.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Error

0.0b

Counts

124 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))))))
	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (.f32 (cbrt.f32 (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3)) (cbrt.f32 (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3))) (cbrt.f32 (pow.f32 (pow.f32 (+.f32 (log.f32 2) (log.f32 v)) 2) 1/3))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))))))
	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (log.f32 (*.f32 v 2))))
	0.2b	(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))))))) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v)))))))
	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (+.f32 (neg.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2))))))))
	0.1b	(.f32 (exp.f32 (fma.f32 1 (+.f32 6931/10000 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))) (neg.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))))))) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (cbrt.f32 (log.f32 (.f32 v 2)))) (.f32 (cbrt.f32 (log.f32 (.f32 v 2))) (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (.f32 2 v)))) 4) (cbrt.f32 (cbrt.f32 (pow.f32 (log.f32 (*.f32 2 v)) 2))))))))

Compiler

Compiled 9513 to 6882 computations (27.7% saved)

regimes2.2s (13.3%)

Accuracy

Total 0.0b remaining (37.5%)

Threshold costs 0.0b (37.5%)

Counts

168 → 1

Compiler

Compiled 67392 to 50028 computations (25.8% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary32`
11×	`+-commutative_binary32`
8×	`sub-neg_binary32`
7×	`neg-sub0_binary32`
7×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	118
1	55	118
2	70	118
3	84	118
4	92	118
5	97	118
6	99	118
7	98	118

end393.0ms (2.3%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 906 to 710 computations (21.6% saved)

Details

analyze1.9s (11.4%)

sample2.6s (15.6%)

simplify49.0ms (0.3%)

prune5.0ms (0%)

localize65.0ms (0.4%)

series113.0ms (0.7%)

rewrite40.0ms (0.2%)

simplify99.0ms (0.6%)

prune235.0ms (1.4%)

localize59.0ms (0.4%)

series268.0ms (1.6%)

rewrite68.0ms (0.4%)

simplify167.0ms (1%)

prune531.0ms (3.2%)

localize102.0ms (0.6%)

series3.3s (19.7%)

rewrite12.0ms (0.1%)

simplify110.0ms (0.7%)

prune953.0ms (5.7%)

localize126.0ms (0.7%)

series2.7s (16%)

rewrite9.0ms (0.1%)

simplify105.0ms (0.6%)

prune527.0ms (3.1%)

regimes2.2s (13.3%)

simplify7.0ms (0%)

end393.0ms (2.3%)

Profiling