Details

Time bar (total: 40.8s)

analyze103.0ms (0.3%)

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

Compiled 50 to 36 computations (28% saved)

sample171.0ms (0.4%)

Algorithm
1×intervals
Results
62.0ms256×body128valid
25.0ms256×pre128true
Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify64.0ms (0.2%)

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 → 1
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02034
15434
217132
371032
4362432
5457132
6500932

prune17.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.4b
(/.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 132 to 92 computations (30.3% saved)

localize137.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(*.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)
0.3b
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.9b
(sinh.f32 (/.f32 1 v))

rewrite618.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
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 → 106
Calls

4 calls:

29.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
18.0ms
(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
7.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 3186 to 1444 computations (54.7% saved)

series713.0ms (1.7%)

Error
0.3b
Counts
4 → 41
Calls

4 calls:

311.0ms
(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
166.0ms
(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
116.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
49.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 2749 to 1906 computations (30.7% saved)

simplify313.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
597×associate-/r/_binary32
307×associate-/r*_binary32
269×associate-*l*_binary32
241×associate-*r*_binary32
223×distribute-rgt-in_binary32
Counts
147 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02954906
17984065
228993957
348283949
449753949
549703949

prune435.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10913122
Fresh011
Picked101
Done000
Total11014124
Error
0.1b
Counts
124 → 14
Alt Table
StatusErrorProgram
0.4b
(/.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))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.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 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i 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) (*.f32 (sqrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (*.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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 cosTheta_i v) (-.f32 (*.f32 (exp.f32 (/.f32 1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 (sqrt.f32 v) (*.f32 (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 (*.f32 (cbrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (*.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 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.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 cosTheta_i (*.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 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 v (/.f32 (/.f32 cosTheta_i (cbrt.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) v) (/.f32 (cbrt.f32 cosTheta_i) (*.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 (cbrt.f32 cosTheta_i) (pow.f32 v 3/2)) (cbrt.f32 cosTheta_i)) (/.f32 (/.f32 (cbrt.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) (exp.f32 (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
Compiler

Compiled 2729 to 1447 computations (47% saved)

localize140.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.3b
(/.f32 cosTheta_i (*.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) (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.9b
(sinh.f32 (/.f32 1 v))

rewrite826.0ms (2%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
98×add-exp-log_binary32
68×add-cbrt-cube_binary32
51×prod-exp_binary32
32×div-exp_binary32
29×cbrt-unprod_binary32
Counts
4 → 121
Calls

4 calls:

36.0ms
(*.f32 (/.f32 1 v) (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
20.0ms
(/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
7.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 4073 to 2174 computations (46.6% saved)

series892.0ms (2.2%)

Error
0.1b
Counts
4 → 42
Calls

4 calls:

343.0ms
(*.f32 (/.f32 1 v) (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
322.0ms
(/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
81.0ms
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
55.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 3079 to 2173 computations (29.4% saved)

simplify300.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
434×times-frac_binary32
403×associate-*r*_binary32
333×associate-*l*_binary32
286×distribute-rgt-in_binary32
284×associate-/r*_binary32
Counts
163 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03085661
18464472
234764448
348534448
449474448

prune380.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1245129
Fresh6713
Picked101
Done000
Total13112143
Error
0.1b
Counts
143 → 12
Alt Table
StatusErrorProgram
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 v))))
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (*.f32 (exp.f32 (/.f32 1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.4b
(/.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))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 (/.f32 1 v) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.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) (*.f32 (sqrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (*.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.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 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (sqrt.f32 (/.f32 1 v)) (*.f32 (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (/.f32 1 v)))))
23.7b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (sqrt.f32 cosTheta_i) (/.f32 v (/.f32 (sqrt.f32 cosTheta_i) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 v (/.f32 (cbrt.f32 cosTheta_i) (*.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) (exp.f32 (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
Compiler

Compiled 2314 to 1331 computations (42.5% saved)

localize150.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
0.4b
(*.f32 (/.f32 1 v) (/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
0.9b
(sinh.f32 (/.f32 1 v))
0.9b
(/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

rewrite3.7s (9.1%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
478×times-frac_binary32
320×add-exp-log_binary32
240×add-sqr-sqrt_binary32
204×*-un-lft-identity_binary32
194×div-exp_binary32
Counts
4 → 425
Calls

4 calls:

95.0ms
(*.f32 (/.f32 1 v) (/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
90.0ms
(/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
24.0ms
(/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
4.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 16742 to 9425 computations (43.7% saved)

series1.1s (2.7%)

Error
0.1b
Counts
4 → 47
Calls

4 calls:

343.0ms
(*.f32 (/.f32 1 v) (/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
297.0ms
(/.f32 1 (/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
291.0ms
(/.f32 v (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
59.0ms
(sinh.f32 (/.f32 1 v))
Compiler

Compiled 3888 to 2729 computations (29.8% saved)

simplify946.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
445×associate-*r*_binary32
399×associate-/r/_binary32
352×associate-*r/_binary32
343×associate-*l/_binary32
319×associate-*l*_binary32
Counts
472 → 431
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
050518942
1127915932
2469015922
3490415922
4495715922

prune1.6s (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New4238431
Fresh5611
Picked101
Done000
Total42914443
Error
0.1b
Counts
443 → 14
Alt Table
StatusErrorProgram
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 1 (*.f32 (/.f32 (sqrt.f32 v) cosTheta_i) (*.f32 (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 1 v) (*.f32 (/.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (*.f32 (cbrt.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (*.f32 (/.f32 1 v) (cbrt.f32 (/.f32 cosTheta_i (*.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (*.f32 v (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 (/.f32 v (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.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) (*.f32 (sqrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (*.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 1 v) (sqrt.f32 v)) (/.f32 1 (/.f32 (sqrt.f32 v) (/.f32 cosTheta_i (*.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 (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (*.f32 (exp.f32 (/.f32 1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
0.4b
(/.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 1 v) (-.f32 (+.f32 (/.f32 (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O)) cosTheta_i) (/.f32 (exp.f32 (/.f32 1 v)) (/.f32 cosTheta_i v))) (+.f32 (*.f32 (/.f32 sinTheta_i cosTheta_i) (*.f32 sinTheta_O (exp.f32 (/.f32 -1 v)))) (*.f32 (/.f32 v cosTheta_i) (exp.f32 (/.f32 -1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (sqrt.f32 (/.f32 1 v)) (*.f32 (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (/.f32 1 v)))))
0.6b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (/.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (sqrt.f32 v)) (/.f32 1 (/.f32 (sqrt.f32 v) (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
Compiler

Compiled 8483 to 4413 computations (48% saved)

localize196.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))
0.4b
(*.f32 (/.f32 1 v) (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v)))
0.8b
(exp.f32 (/.f32 -1 v))
0.8b
(exp.f32 (/.f32 1 v))

rewrite1.6s (4%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
193×add-exp-log_binary32
129×add-cbrt-cube_binary32
106×prod-exp_binary32
68×div-exp_binary32
60×cbrt-unprod_binary32
Counts
4 → 179
Calls

4 calls:

47.0ms
(*.f32 (/.f32 1 v) (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v)))
45.0ms
(*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))
6.0ms
(exp.f32 (/.f32 1 v))
6.0ms
(exp.f32 (/.f32 -1 v))
Compiler

Compiled 7772 to 4710 computations (39.4% saved)

series787.0ms (1.9%)

Error
0.1b
Counts
4 → 42
Calls

4 calls:

286.0ms
(*.f32 (/.f32 1 v) (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v)))
254.0ms
(*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))
51.0ms
(exp.f32 (/.f32 1 v))
51.0ms
(exp.f32 (/.f32 -1 v))
Compiler

Compiled 2926 to 2054 computations (29.8% saved)

simplify568.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
443×associate-*r*_binary32
421×times-frac_binary32
383×associate-*l*_binary32
378×associate-*r/_binary32
378×associate-*l/_binary32
Counts
221 → 179
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038110110
110546890
244236798
346176798
450006798
550006798
649916798

prune650.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1736179
Fresh4913
Picked101
Done000
Total17815193
Error
0.1b
Counts
193 → 15
Alt Table
StatusErrorProgram
0.4b
(/.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))
0.7b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (pow.f32 (exp.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (cbrt.f32 1) (sqrt.f32 v))) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))))
0.4b
(*.f32 cosTheta_O (/.f32 cosTheta_i (*.f32 (*.f32 v v) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (/.f32 1 (*.f32 (/.f32 (sqrt.f32 v) cosTheta_i) (*.f32 (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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (*.f32 v (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 (/.f32 v (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (*.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (*.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 1 v) (*.f32 (/.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 2 (cbrt.f32 v)))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 (sqrt.f32 (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (*.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 1 v) (sqrt.f32 v)) (/.f32 1 (/.f32 (sqrt.f32 v) (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (pow.f32 E.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 2 v))))
0.5b
(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
0.4b
(*.f32 cosTheta_O (/.f32 (/.f32 1 v) (-.f32 (+.f32 (/.f32 (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O)) cosTheta_i) (/.f32 (exp.f32 (/.f32 1 v)) (/.f32 cosTheta_i v))) (+.f32 (*.f32 (/.f32 sinTheta_i cosTheta_i) (*.f32 sinTheta_O (exp.f32 (/.f32 -1 v)))) (*.f32 (/.f32 v cosTheta_i) (exp.f32 (/.f32 -1 v)))))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (*.f32 (/.f32 cosTheta_i (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (*.f32 (cbrt.f32 2) (cbrt.f32 2))) (/.f32 (cbrt.f32 2) v))))
0.5b
(*.f32 cosTheta_O (*.f32 (sqrt.f32 (/.f32 1 v)) (*.f32 (/.f32 cosTheta_i (*.f32 v (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (/.f32 1 v)))))
0.5b
(*.f32 cosTheta_O (*.f32 (/.f32 1 v) (*.f32 (/.f32 (*.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 2 v) (/.f32 (cbrt.f32 cosTheta_i) (*.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))))))
Compiler

Compiled 3023 to 1811 computations (40.1% saved)

regimes21.0s (51.5%)

Accuracy

Total 0.3b remaining (76.5%)

Threshold costs 0.3b (76.5%)

Compiler

Compiled 181378 to 127768 computations (29.6% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02037
13237
24237
34937
45437
55637
65537

end40.0ms (0.1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 145 to 105 computations (27.6% saved)

sample3.3s (8%)

Algorithm
1×intervals
Results
1.0s8000×body128valid
407.0ms8000×pre128true
Compiler

Compiled 671 to 466 computations (30.6% saved)

Profiling

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