Details

Time bar (total: 15.9s)

analyze9.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
Compiler

Compiled 66 to 48 computations (27.3% saved)

sample121.0ms (0.8%)

Algorithm
1×intervals
Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results
29.0ms256×body128valid
13.0ms256×pre128true
Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify47.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
913×times-frac_binary32
551×associate-/l*_binary32
460×associate-/l/_binary32
362×associate-*l/_binary32
312×associate-/r/_binary32
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02034
15434
217132
371032
4363132
5462732
6526132

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
Compiler

Compiled 154 to 104 computations (32.5% saved)

localize52.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓0.4b
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
✓0.7b
(sinh.f32 (/.f32 1 v))

series543.0ms (3.4%)

Counts
4 → 96
Calls

4 calls:

452.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
73.0ms
(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
12.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
5.0ms
(sinh.f32 (/.f32 1 v))

rewrite35.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
50×add-cbrt-cube_binary32
44×add-exp-log_binary32
34×times-frac_binary32
21×*-un-lft-identity_binary32
21×add-sqr-sqrt_binary32
Counts
4 → 114
Calls

4 calls:

11.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
9.0ms
(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
3.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms
(sinh.f32 (/.f32 1 v))

simplify133.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
584×times-frac_binary32
466×associate-/r*_binary32
456×associate-/l*_binary32
371×associate-*l*_binary32
150×fma-def_binary32
Counts
210 → 218
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04199291
112978518
250438518

prune383.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New20711218
Fresh101
Picked101
Done000
Total20911220
Error
0.1b
Counts
220 → 11
Alt Table
StatusErrorProgram
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
▶0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.6b
(*.f32 cosTheta_O (/.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.6b
(*.f32 cosTheta_O (/.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 cosTheta_i (cbrt.f32 v)))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 1 (/.f32 cosTheta_i (-.f32 (*.f32 (*.f32 v v) (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.6b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
Compiler

Compiled 9052 to 4881 computations (46.1% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓0.3b
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓0.4b
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.7b
(sinh.f32 (/.f32 1 v))

series772.0ms (4.8%)

Counts
2 → 96
Calls

2 calls:

439.0ms
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
333.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

rewrite49.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
126×add-exp-log_binary32
88×add-cbrt-cube_binary32
64×times-frac_binary32
59×div-exp_binary32
58×prod-exp_binary32
Counts
2 → 143
Calls

2 calls:

18.0ms
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
9.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

simplify227.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
655×associate-/r*_binary32
646×associate-/l*_binary32
347×associate-*r/_binary32
331×associate-*l/_binary32
293×fma-def_binary32
Counts
239 → 263
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
046813962
1154812405
2496212283
3505612283

prune609.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3103313
Fresh2810
Picked101
Done000
Total31311324
Error
0.1b
Counts
324 → 11
Alt Table
StatusErrorProgram
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.6b
(*.f32 cosTheta_O (/.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.6b
(*.f32 cosTheta_O (/.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 cosTheta_i (cbrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
▶0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.4b
(*.f32 cosTheta_O (*.f32 1 (/.f32 cosTheta_i (-.f32 (*.f32 (*.f32 v v) (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 cosTheta_i (sqrt.f32 v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
Compiler

Compiled 13990 to 7748 computations (44.6% saved)

localize58.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))
✓0.4b
(/.f32 (/.f32 1 v) (sqrt.f32 v))
✓0.4b
(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
0.7b
(sinh.f32 (/.f32 1 v))

series844.0ms (5.3%)

Counts
3 → 80
Calls

3 calls:

454.0ms
(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
377.0ms
(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))
13.0ms
(/.f32 (/.f32 1 v) (sqrt.f32 v))

rewrite132.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
381×times-frac_binary32
211×add-sqr-sqrt_binary32
191×*-un-lft-identity_binary32
189×add-cube-cbrt_binary32
189×add-exp-log_binary32
Counts
3 → 377
Calls

3 calls:

47.0ms
(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
12.0ms
(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))
6.0ms
(/.f32 (/.f32 1 v) (sqrt.f32 v))

simplify375.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
893×times-frac_binary32
668×associate-/l*_binary32
584×fma-def_binary32
214×associate-/l/_binary32
172×*-commutative_binary32
Counts
457 → 507
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
058522108
1186419471
2495919299
3533219299

prune1.3s (8.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New5208528
Fresh4610
Picked101
Done000
Total52514539
Error
0.0b
Counts
539 → 14
Alt Table
StatusErrorProgram
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.6b
(*.f32 cosTheta_O (/.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (*.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 (*.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (fabs.f32 (cbrt.f32 v))) (/.f32 (cbrt.f32 (/.f32 1 v)) (sqrt.f32 (cbrt.f32 v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (exp.f32 (-.f32 (neg.f32 (log.f32 v)) (log.f32 (sqrt.f32 v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 (cbrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
0.4b
(*.f32 cosTheta_O (*.f32 1 (/.f32 cosTheta_i (-.f32 (*.f32 (*.f32 v v) (exp.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O (/.f32 1 v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v))) (/.f32 (/.f32 1 v) (sqrt.f32 (cbrt.f32 v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (*.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v)))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
▶0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
Compiler

Compiled 24506 to 12535 computations (48.8% saved)

localize60.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓0.4b
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.7b
(sinh.f32 (/.f32 1 v))
✓0.7b
(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

series793.0ms (5%)

Counts
3 → 108
Calls

3 calls:

459.0ms
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
328.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
6.0ms
(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

rewrite49.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
127×add-exp-log_binary32
89×add-cbrt-cube_binary32
64×times-frac_binary32
59×div-exp_binary32
58×prod-exp_binary32
Counts
3 → 152
Calls

3 calls:

16.0ms
(*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
8.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
0.0ms
(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

simplify196.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
950×times-frac_binary32
637×associate-/r*_binary32
636×associate-/l*_binary32
203×fma-def_binary32
148×*-commutative_binary32
Counts
260 → 285
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048614533
1157912587
2540712587

prune645.0ms (4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3024306
Fresh4913
Picked101
Done000
Total30713320
Error
0.0b
Counts
320 → 13
Alt Table
StatusErrorProgram
0.6b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (/.f32 (*.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2)) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v))) (/.f32 (/.f32 1 v) (sqrt.f32 (cbrt.f32 v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (*.f32 (cbrt.f32 (/.f32 1 v)) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 1 v) (/.f32 cosTheta_i (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (exp.f32 (-.f32 (neg.f32 (log.f32 v)) (log.f32 (sqrt.f32 v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 1 (fabs.f32 (cbrt.f32 v))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 (cbrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (exp.f32 (log.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (*.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.4b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (*.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v)))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
Compiler

Compiled 14037 to 7974 computations (43.2% saved)

regimes5.9s (37.1%)

Accuracy

Total 0.3b remaining (73.2%)

Threshold costs 0.3b (73.2%)

Counts
520 → 1
Compiler

Compiled 143594 to 100088 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
5×*-commutative_binary32
1×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01935
12635
22535

end35.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 196 to 140 computations (28.6% saved)

sample2.5s (15.7%)

Algorithm
1×intervals
Results
971.0ms8000×body128valid
451.0ms8000×pre128true
Compiler

Compiled 599 to 409 computations (31.7% saved)

Profiling

Loading profile data...