Details

Time bar (total: 20.2s)

analyze4.1s (20.3%)

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
0.6%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)

sample144.0ms (0.7%)

Algorithm
intervals
Results
53.0ms256×body128valid
25.0ms259×pre128true
1.0msbody128nan
Compiler

Compiled 104 to 78 computations (25% saved)

simplify57.0ms (0.3%)

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

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
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
(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)

localize92.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0b
(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
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

series164.0ms (0.8%)

Counts
3 → 120
Calls

3 calls:

78.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
68.0ms
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
17.0ms
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity_binary32
23×add-sqr-sqrt_binary32
19×add-cube-cbrt_binary32
18×prod-diff_binary32
14×exp-sum_binary32
Counts
3 → 73
Calls

3 calls:

7.0ms
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
5.0ms
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
1.0ms
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

simplify237.0ms (1.2%)

Algorithm
egg-herbie
Rules
369×distribute-rgt-in_binary32
248×times-frac_binary32
210×fma-neg_binary32
176×cancel-sign-sub-inv_binary32
174×associate-*r*_binary32
Counts
193 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02626006
16965386
230144645
348014645
449124645

prune371.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1363139
Fresh101
Picked101
Done000
Total1383141
Error
0.0b
Counts
141 → 3
Alt Table
StatusErrorProgram
0.1b
(*.f32 (/.f32 1/2 v) (pow.f32 (E.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 1/2 v) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 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))))))
1.4b
(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
Compiler

Compiled 6154 to 3555 computations (42.2% saved)

localize111.0ms (0.6%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.1b
(pow.f32 (E.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
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)

series98.0ms (0.5%)

Counts
1 → 60
Calls

1 calls:

98.0ms
(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite15.0ms (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) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify208.0ms (1%)

Algorithm
egg-herbie
Rules
807×fma-def_binary32
248×times-frac_binary32
213×associate-/l/_binary32
161×associate-*r*_binary32
160×associate-/l*_binary32
Counts
97 → 72
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02484144
16804033
227823899
349493899
449323899

prune346.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1450145
Fresh022
Picked011
Done000
Total1453148
Error
0.0b
Counts
148 → 3
Alt Table
StatusErrorProgram
0.1b
(*.f32 (/.f32 1/2 v) (pow.f32 (E.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 1/2 v) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 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))))))
1.4b
(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
Compiler

Compiled 6483 to 3615 computations (44.2% saved)

localize189.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)
0.2b
(cbrt.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
(cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
0.5b
(*.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

series3.2s (15.7%)

Counts
3 → 180
Calls

3 calls:

1.7s
(*.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
747.0ms
(cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
747.0ms
(cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))

rewrite70.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod_binary32
31×*-un-lft-identity_binary32
23×add-sqr-sqrt_binary32
16×cbrt-div_binary32
13×add-cube-cbrt_binary32
Counts
3 → 88
Calls

3 calls:

33.0ms
(*.f32 (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))) (cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
13.0ms
(cbrt.f32 (+.f32 3121444901730491/4503599627370496 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
5.0ms
(cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify1.1s (5.3%)

Algorithm
egg-herbie
Rules
582×fma-def_binary32
366×associate-/l*_binary32
344×associate-/r*_binary32
296×times-frac_binary32
100×sub-neg_binary32
Counts
268 → 280
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0240554550
1530254550

prune2.6s (12.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New4061407
Fresh011
Picked101
Done101
Total4082410
Error
0.0b
Counts
410 → 2
Alt Table
StatusErrorProgram
1.4b
(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2))) (cbrt.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 76811 to 44368 computations (42.2% saved)

localize186.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(cbrt.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
(pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2)
7.9b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
15.2b
(cbrt.f32 (pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2))

series449.0ms (2.2%)

Counts
3 → 72
Calls

3 calls:

368.0ms
(cbrt.f32 (pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2))
52.0ms
(pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2)
28.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

rewrite60.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity_binary32
14×unpow-prod-down_binary32
13×add-sqr-sqrt_binary32
12×cbrt-prod_binary32
add-cube-cbrt_binary32
Counts
3 → 69
Calls

3 calls:

22.0ms
(pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2)
22.0ms
(cbrt.f32 (pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2))
9.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify307.0ms (1.5%)

Algorithm
egg-herbie
Rules
646×times-frac_binary32
562×associate-/r*_binary32
438×fma-def_binary32
371×associate-/l*_binary32
150×*-commutative_binary32
Counts
141 → 148
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05369406
117008856
250188856

prune588.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1660166
Fresh011
Picked011
Done000
Total1662168
Error
0.0b
Counts
168 → 2
Alt Table
StatusErrorProgram
1.4b
(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 3121444901730491/4503599627370496)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (-.f32 3121444901730491/4503599627370496 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) 2))) (cbrt.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 13282 to 8104 computations (39% saved)

regimes917.0ms (4.5%)

Accuracy

Total 0.0b remaining (3.7%)

Threshold costs 0.0b (3.7%)

Counts
51 → 1
Compiler

Compiled 12624 to 9117 computations (27.8% saved)

simplify5.0ms (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
01929
12629
23029
33229
43329
53229

end46.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 120 to 90 computations (25% saved)

sample4.6s (22.9%)

Algorithm
intervals
Results
2.0s8000×body128valid
874.0ms8148×pre128true
32.0ms148×body128nan
Compiler

Compiled 165 to 121 computations (26.7% saved)

Profiling

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