Details

Time bar (total: 10.5s)

analyze3.2s (30.8%)

Algorithm
search
Search
TrueOtherFalseIter
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%1.5%98.5%11
0%1.5%98.5%12
0%1.5%98.5%13
0%1.5%98.5%14
Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.9s (27.3%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results
2.8s8256×body128valid
44.0ms138×body128invalid
Compiler

Compiled 99 to 73 computations (26.3% saved)

simplify51.0ms (0.5%)

Algorithm
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)

IterNodesCost
02235
15333
214531
353229
4211929
5443129
6497529

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
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
(*.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)

localize73.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.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
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
7.7b
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
7.7b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series306.0ms (2.9%)

Counts
4 → 84
Calls

4 calls:

243.0ms
(+.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))))
34.0ms
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
14.0ms
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
14.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite61.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity_binary32
57×times-frac_binary32
49×prod-diff_binary32
45×add-sqr-sqrt_binary32
43×add-cube-cbrt_binary32
Counts
4 → 174
Calls

4 calls:

27.0ms
(+.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))))
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)

simplify174.0ms (1.7%)

Algorithm
egg-herbie
Rules
963×times-frac_binary32
573×fma-neg_binary32
137×associate-*l*_binary32
117×associate-/l*_binary32
112×associate-*l/_binary32
Counts
258 → 229
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03056557
17295637
226215212
349505212
451675212

prune235.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2290229
Fresh011
Picked011
Done000
Total2292231
Error
0.1b
Counts
231 → 2
Alt Table
StatusErrorProgram
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
(*.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 8673 to 3837 computations (55.8% saved)

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.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 (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)

series256.0ms (2.4%)

Counts
4 → 180
Calls

4 calls:

143.0ms
(*.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)))))
55.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
46.0ms
(-.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)

rewrite38.0ms (0.4%)

Algorithm
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)))))
5.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms
(-.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)

simplify181.0ms (1.7%)

Algorithm
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 → 237
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044111185
1120310395
2515610395

prune432.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2334237
Fresh000
Picked101
Done011
Total2345239
Error
0.0b
Counts
239 → 5
Alt Table
StatusErrorProgram
3.0b
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
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)))))
12.3b
(*.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 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v)) (*.f32 (/.f32 (cbrt.f32 1/2) (sqrt.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 1/2 v) (pow.f32 (E.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 11285 to 6508 computations (42.3% saved)

localize79.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)
0.3b
(/.f32 (cbrt.f32 1/2) (sqrt.f32 v))
0.3b
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v))

series52.0ms (0.5%)

Counts
2 → 0
Calls

2 calls:

30.0ms
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v))
22.0ms
(/.f32 (cbrt.f32 1/2) (sqrt.f32 v))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
42×times-frac_binary32
34×*-un-lft-identity_binary32
34×add-sqr-sqrt_binary32
34×add-cube-cbrt_binary32
27×sqrt-prod_binary32
Counts
2 → 91
Calls

2 calls:

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

simplify183.0ms (1.7%)

Algorithm
egg-herbie
Rules
989×div-sub_binary32
790×fma-neg_binary32
618×unswap-sqr_binary32
401×associate-/l*_binary32
394×distribute-rgt-neg-out_binary32
Counts
91 → 100
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01071619
11881483
24071479
38391479
411621479
512471479
616711479
720701479
822241479
926801479
1038791479
1137301479
1252951479

prune512.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1761177
Fresh123
Picked011
Done011
Total1775182
Error
0.0b
Counts
182 → 5
Alt Table
StatusErrorProgram
3.0b
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
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)))))
12.3b
(*.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 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v)) (*.f32 (/.f32 (cbrt.f32 1/2) (sqrt.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 1/2) (cbrt.f32 1/2)) (sqrt.f32 v)) (*.f32 (/.f32 (cbrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (E.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 8961 to 5450 computations (39.2% saved)

localize97.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f32 (E.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)
0.3b
(/.f32 (cbrt.f32 1/2) (sqrt.f32 v))
0.3b
(/.f32 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v))

series70.0ms (0.7%)

Counts
1 → 60
Calls

1 calls:

69.0ms
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×unpow-prod-up_binary32
12×*-un-lft-identity_binary32
12×add-sqr-sqrt_binary32
10×add-cube-cbrt_binary32
prod-diff_binary32
Counts
1 → 37
Calls

1 calls:

8.0ms
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify108.0ms (1%)

Algorithm
egg-herbie
Rules
782×fma-def_binary32
252×times-frac_binary32
220×associate-/l/_binary32
167×associate-*r*_binary32
166×associate-/l*_binary32
Counts
97 → 75
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02624140
16854037
228263929
349273929

prune449.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1901191
Fresh022
Picked101
Done022
Total1915196
Error
0.0b
Counts
196 → 5
Alt Table
StatusErrorProgram
3.0b
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
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
(*.f32 (*.f32 (cbrt.f32 1/2) (/.f32 (cbrt.f32 1/2) (sqrt.f32 v))) (*.f32 (/.f32 (cbrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
12.3b
(*.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 (*.f32 (cbrt.f32 1/2) (cbrt.f32 1/2)) (sqrt.f32 v)) (*.f32 (/.f32 (cbrt.f32 1/2) (sqrt.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 9533 to 5658 computations (40.6% saved)

regimes777.0ms (7.4%)

Accuracy

Total 0.1b remaining (52.1%)

Threshold costs 0.1b (52.1%)

Counts
68 → 1
Compiler

Compiled 18246 to 12913 computations (29.2% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary32
*-commutative_binary32
sub-neg_binary32
neg-sub0_binary32
neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02135
13135
24235
35435
46235
56735
66935
76735

end190.0ms (1.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 402 to 271 computations (32.6% saved)

Profiling

Loading profile data...