Details

analyze2.3s (29.9%)

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 51 to 38 computations (25.5% saved)

sample94.0ms (1.2%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
13.0ms	260×	pre	128	true
0.0ms	4×	body	128	nan

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

982×	`exp-sum_binary32`
570×	`exp-diff_binary32`
458×	`sub-neg_binary32`
380×	`cancel-sign-sub-inv_binary32`
307×	`div-exp_binary32`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	33
3	513	33
4	1979	33
5	3856	33
6	4782	33
7	5305	33

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.0b	(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)))))
	0.1b	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496)))

Status

Error

Program

▶

0.0b

(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)))))

0.1b

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

Compiler

Compiled 141 to 101 computations (28.4% saved)

localize83.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496)
0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
7.9b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite234.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`*-un-lft-identity_binary32`
27×	`cancel-sign-sub-inv_binary32`
22×	`associate-+l+_binary32`
21×	`times-frac_binary32`
21×	`add-sqr-sqrt_binary32`

Counts

4 → 106

Calls

4 calls:

21.0ms	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496)
9.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
4.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 3273 to 1625 computations (50.4% saved)

series340.0ms (4.5%)

Error

0.0b

Counts

4 → 59

Calls

4 calls:

128.0ms	(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 3121444901730491/4503599627370496)
79.0ms	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
55.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
54.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 3229 to 2388 computations (26% saved)

simplify183.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary32`
293×	`distribute-rgt-in_binary32`
284×	`distribute-lft-in_binary32`
192×	`sub-neg_binary32`
123×	`exp-prod_binary32`

Counts

165 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	3429
1	611	3190
2	1895	2972
3	4842	2972
4	4962	2972

prune86.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	1	134

Error

0.0b

Counts

134 → 1

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (+.f32 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 3121444901730491/4503599627370496 (/.f32 (/.f32 -1 (sqrt.f32 v)) (sqrt.f32 v)))) (log.f32 (/.f32 1 (*.f32 2 v)))))

Status

Error

Program

▶

0.0b

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

Compiler

Compiled 1387 to 720 computations (48.1% saved)

localize87.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 -1 (sqrt.f32 v))
0.3b	(/.f32 (/.f32 -1 (sqrt.f32 v)) (sqrt.f32 v))
7.9b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.1b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite437.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

282×	`times-frac_binary32`
160×	`*-un-lft-identity_binary32`
160×	`add-sqr-sqrt_binary32`
160×	`add-cube-cbrt_binary32`
144×	`sqrt-prod_binary32`

Counts

4 → 256

Calls

4 calls:

10.0ms	(/.f32 (/.f32 -1 (sqrt.f32 v)) (sqrt.f32 v))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
4.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 -1 (sqrt.f32 v))

Compiler

Compiled 8186 to 3912 computations (52.2% saved)

series145.0ms (1.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

54.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
53.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
15.0ms	(/.f32 (/.f32 -1 (sqrt.f32 v)) (sqrt.f32 v))
15.0ms	(/.f32 -1 (sqrt.f32 v))

Compiler

Compiled 1693 to 1207 computations (28.7% saved)

simplify273.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-*l/_binary32`
525×	`associate-/r/_binary32`
432×	`associate-l_binary32`
386×	`associate-*r/_binary32`
267×	`associate-/l/_binary32`

Counts

280 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	325	6334
1	728	5753
2	1945	5485
3	4364	5443
4	4970	5443
5	4982	5443

prune150.0ms (2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	213	1	214

Error

0.0b

Counts

214 → 1

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (+.f32 (+.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 3121444901730491/4503599627370496 (/.f32 (/.f32 -1 (sqrt.f32 v)) (sqrt.f32 v)))) (log.f32 (/.f32 1 (*.f32 2 v)))))

Status

Error

Program

✓

0.0b

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

Compiler

Compiled 3115 to 1548 computations (50.3% saved)

regimes554.0ms (7.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Compiler

Compiled 6555 to 4957 computations (24.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary32`
7×	`*-commutative_binary32`
5×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	45
1	35	45
2	40	45
3	50	45
4	57	45
5	62	45
6	64	45
7	63	45

end33.0ms (0.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 170 to 120 computations (29.4% saved)

sample2.5s (33.5%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
392.0ms	8132×	pre	128	true
14.0ms	132×	body	128	nan

Compiler

Compiled 124 to 91 computations (26.6% saved)

Details

analyze2.3s (29.9%)

sample94.0ms (1.2%)

simplify72.0ms (0.9%)

prune9.0ms (0.1%)

localize83.0ms (1.1%)

rewrite234.0ms (3.1%)

series340.0ms (4.5%)

simplify183.0ms (2.4%)

prune86.0ms (1.1%)

localize87.0ms (1.1%)

rewrite437.0ms (5.7%)

series145.0ms (1.9%)

simplify273.0ms (3.6%)

prune150.0ms (2%)

regimes554.0ms (7.3%)

simplify6.0ms (0.1%)

end33.0ms (0.4%)

sample2.5s (33.5%)

Profiling