Details

Time bar (total: 12.9s)

analyze1.9s (14.4%)

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)

sample131.0ms (1%)

Algorithm
intervals
Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results
31.0ms256×body128valid
13.0ms263×pre128true
1.0msbody128nan
Compiler

Compiled 104 to 78 computations (25% saved)

simplify51.0ms (0.4%)

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
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
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)))))
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)))))
Compiler

Compiled 160 to 112 computations (30% saved)

localize64.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
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))))
7.1b
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.1b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series279.0ms (2.2%)

Counts
4 → 120
Calls

4 calls:

216.0ms
(+.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))))
38.0ms
(+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
13.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

rewrite108.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
203×*-un-lft-identity_binary32
150×associate-+l+_binary32
137×add-sqr-sqrt_binary32
127×prod-diff_binary32
119×times-frac_binary32
Counts
4 → 273
Calls

4 calls:

30.0ms
(+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)
24.0ms
(+.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))))
3.0ms
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify188.0ms (1.5%)

Algorithm
egg-herbie
Rules
834×times-frac_binary32
697×fma-neg_binary32
136×associate-*l*_binary32
127×+-commutative_binary32
120×associate-/l*_binary32
Counts
393 → 404
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031510843
18087972
228067736
352517736

prune422.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New4031404
Fresh011
Picked101
Done000
Total4042406
Error
0.0b
Counts
406 → 2
Alt Table
StatusErrorProgram
0.0b
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 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 18679 to 8600 computations (54% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log.f32 (/.f32 1/2 v))
0.0b
(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
0.0b
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
0.1b
(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))

series181.0ms (1.4%)

Counts
4 → 76
Calls

4 calls:

110.0ms
(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
25.0ms
(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
23.0ms
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
22.0ms
(log.f32 (/.f32 1/2 v))

rewrite34.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity_binary32
43×add-sqr-sqrt_binary32
39×add-cube-cbrt_binary32
30×prod-diff_binary32
26×log-prod_binary32
Counts
4 → 142
Calls

4 calls:

8.0ms
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
6.0ms
(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
4.0ms
(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
2.0ms
(log.f32 (/.f32 1/2 v))

simplify192.0ms (1.5%)

Algorithm
egg-herbie
Rules
392×fma-neg_binary32
253×sub-neg_binary32
252×cancel-sign-sub-inv_binary32
179×times-frac_binary32
135×associate-*r*_binary32
Counts
218 → 210
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03326102
17605420
230594722
345314722
449944722
548964722

prune259.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2073210
Fresh101
Picked101
Done000
Total2093212
Error
0.0b
Counts
212 → 3
Alt Table
StatusErrorProgram
0.1b
(*.f32 (exp.f32 6931/10000) (/.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(pow.f32 (exp.f32 (+.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
Compiler

Compiled 7139 to 4829 computations (32.4% saved)

localize45.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log.f32 (/.f32 1/2 v))
0.0b
(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
0.0b
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
0.1b
(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))

series27.0ms (0.2%)

Counts
1 → 36
Calls

1 calls:

26.0ms
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary32
20×unpow-prod-up_binary32
15×prod-diff_binary32
14×add-sqr-sqrt_binary32
12×add-cube-cbrt_binary32
Counts
1 → 45
Calls

1 calls:

7.0ms
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

simplify90.0ms (0.7%)

Algorithm
egg-herbie
Rules
760×associate-/r*_binary32
551×fma-def_binary32
270×associate-/r/_binary32
174×times-frac_binary32
164×associate-/l/_binary32
Counts
81 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02273311
15633157
221852801
355462801

prune415.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2131214
Fresh022
Picked101
Done000
Total2143217
Error
0.0b
Counts
217 → 3
Alt Table
StatusErrorProgram
0.0b
(*.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2)) (pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2)))
0.1b
(*.f32 (exp.f32 6931/10000) (/.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
0.0b
(pow.f32 (exp.f32 (+.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
Compiler

Compiled 7476 to 4917 computations (34.2% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log.f32 (/.f32 1/2 v))
0.0b
(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
0.0b
(pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2))
0.1b
(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))

series29.0ms (0.2%)

Counts
1 → 36
Calls

1 calls:

29.0ms
(pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity_binary32
25×pow-unpow_binary32
21×times-frac_binary32
19×add-sqr-sqrt_binary32
13×add-cube-cbrt_binary32
Counts
1 → 43
Calls

1 calls:

8.0ms
(pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2))

simplify116.0ms (0.9%)

Algorithm
egg-herbie
Rules
529×fma-def_binary32
294×associate-/r/_binary32
273×fma-neg_binary32
200×associate-/l/_binary32
166×cancel-sign-sub-inv_binary32
Counts
79 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02043625
16113512
222853286
348093286
449783286

prune966.0ms (7.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New4262428
Fresh202
Picked101
Done000
Total4292431
Error
0.0b
Counts
431 → 2
Alt Table
StatusErrorProgram
0.2b
(*.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2)) (cbrt.f32 (pow.f32 (pow.f32 (E.f32) (*.f32 1/2 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 3)))
15.8b
(*.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2)) (pow.f32 (E.f32) (/.f32 (/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) (pow.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) 3)) (+.f32 (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 6) (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) 2)))
Compiler

Compiled 24007 to 16229 computations (32.4% saved)

regimes5.0s (38.7%)

Accuracy

Total 0.0b remaining (9.9%)

Threshold costs 0.0b (9.9%)

Counts
338 → 1
Compiler

Compiled 127178 to 95712 computations (24.7% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary32
*-commutative_binary32
distribute-rgt-neg-in_binary32
sub-neg_binary32
neg-sub0_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028104
141104
244104
345104
443104

end28.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 365 to 250 computations (31.5% saved)

sample2.3s (17.9%)

Algorithm
intervals
Results
968.0ms8000×body128valid
419.0ms8147×pre128true
15.0ms147×body128nan
Compiler

Compiled 277 to 200 computations (27.8% saved)

Profiling

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