Details

Time bar (total: 5.8s)

analyze1.0ms (0%)

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

Compiled 66 to 48 computations (27.3% saved)

sample2.6s (44%)

Results
2.5s8256×body128valid

preprocess31.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
696×associate-/l*_binary32
691×associate-/l/_binary32
677×times-frac_binary32
373×associate-/r/_binary32
359×associate-/r*_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0102374
1361374
21272352
055
155
Stop Event
1×unsound
1×node limit
Calls
Call 1
Inputs
0
1
2
3
4
Outputs
0
1
0
2
3
2
4
Call 2
Inputs
(/.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))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 cosTheta_i sinTheta_O) v))) (/.f32 (*.f32 sinTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i cosTheta_i) v))) (/.f32 (*.f32 sinTheta_O cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_i))) (/.f32 (*.f32 v cosTheta_O) cosTheta_i)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_i)) 2) cosTheta_i))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 cosTheta_O sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i sinTheta_i) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i cosTheta_O) v))) (/.f32 (*.f32 cosTheta_i sinTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_O))) (/.f32 (*.f32 cosTheta_i v) cosTheta_O)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) 2) cosTheta_O))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 v sinTheta_O) sinTheta_i))) (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) 2) sinTheta_i))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i v) sinTheta_O))) (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_O)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) 2) sinTheta_O))
Outputs
(/.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))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (*.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (*.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 cosTheta_i sinTheta_O) v))) (/.f32 (*.f32 sinTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O cosTheta_i)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 sinTheta_i (/.f32 v cosTheta_O)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 cosTheta_i) (/.f32 v sinTheta_O))) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (*.f32 sinTheta_i cosTheta_O) (*.f32 v v)))
(/.f32 (/.f32 (/.f32 (/.f32 cosTheta_O (/.f32 v sinTheta_i)) (exp.f32 (*.f32 (/.f32 sinTheta_O v) cosTheta_i))) (sinh.f32 (/.f32 1 v))) (*.f32 v 2))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i cosTheta_i) v))) (/.f32 (*.f32 sinTheta_O cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(*.f32 (/.f32 (exp.f32 (neg.f32 (/.f32 cosTheta_i (/.f32 v sinTheta_i)))) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 sinTheta_O (/.f32 v cosTheta_O)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 cosTheta_i) (/.f32 v sinTheta_i))) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (*.f32 v (/.f32 v sinTheta_O))))
(/.f32 (/.f32 (*.f32 (/.f32 sinTheta_O v) cosTheta_O) (*.f32 v (exp.f32 (*.f32 (/.f32 cosTheta_i v) sinTheta_i)))) (*.f32 (sinh.f32 (/.f32 1 v)) 2))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_i))) (/.f32 (*.f32 v cosTheta_O) cosTheta_i)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_i)) 2) cosTheta_i))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) cosTheta_i)) (*.f32 2 (sinh.f32 (/.f32 1 cosTheta_i)))) (/.f32 (/.f32 v (/.f32 cosTheta_i cosTheta_O)) cosTheta_i))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 cosTheta_i sinTheta_O))) (*.f32 2 (sinh.f32 (/.f32 1 cosTheta_i)))) (/.f32 (*.f32 (/.f32 v cosTheta_i) cosTheta_O) cosTheta_i))
(/.f32 (/.f32 (*.f32 v cosTheta_O) (pow.f32 (exp.f32 (/.f32 sinTheta_i cosTheta_i)) sinTheta_O)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_i)) (*.f32 cosTheta_i 2)) cosTheta_i))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 cosTheta_O sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i sinTheta_i) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O cosTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v sinTheta_i)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (*.f32 cosTheta_O (neg.f32 sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 sinTheta_i (*.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (*.f32 (/.f32 cosTheta_i v) sinTheta_i) (*.f32 2 (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) cosTheta_O))) (*.f32 (sinh.f32 (/.f32 1 v)) v))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i cosTheta_O) v))) (/.f32 (*.f32 cosTheta_i sinTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i cosTheta_O)) v)) (/.f32 (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_i (/.f32 v sinTheta_O))))
(/.f32 (/.f32 sinTheta_O (/.f32 v cosTheta_i)) (/.f32 (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 cosTheta_O)) v))))
(/.f32 (/.f32 (/.f32 (*.f32 (/.f32 sinTheta_O v) cosTheta_i) (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) cosTheta_O)) (sinh.f32 (/.f32 1 v))) (*.f32 v 2))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) cosTheta_O))) (/.f32 (*.f32 cosTheta_i v) cosTheta_O)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) 2) cosTheta_O))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) cosTheta_O)) (*.f32 2 (sinh.f32 (/.f32 1 cosTheta_O)))) (/.f32 (/.f32 cosTheta_i (/.f32 cosTheta_O v)) cosTheta_O))
(/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) cosTheta_O)) (*.f32 (/.f32 (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) (*.f32 cosTheta_O 2)) cosTheta_i) (/.f32 cosTheta_O v)))
(/.f32 (/.f32 (/.f32 cosTheta_i (/.f32 cosTheta_O v)) (pow.f32 (exp.f32 (/.f32 sinTheta_i cosTheta_O)) sinTheta_O)) (*.f32 (sinh.f32 (/.f32 1 cosTheta_O)) (*.f32 cosTheta_O 2)))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) v))
(*.f32 (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_O (*.f32 v (/.f32 v cosTheta_i))))
(/.f32 (/.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (exp.f32 (/.f32 sinTheta_O v)) sinTheta_i))) v)
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 v sinTheta_O) sinTheta_i))) (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) 2) sinTheta_i))
(/.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O v)) sinTheta_i)) (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_i)) (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) (*.f32 2 sinTheta_i)))
(*.f32 (/.f32 (*.f32 (/.f32 cosTheta_i sinTheta_i) cosTheta_O) (sinh.f32 (/.f32 1 sinTheta_i))) (/.f32 (exp.f32 (/.f32 (*.f32 v (neg.f32 sinTheta_O)) sinTheta_i)) (*.f32 sinTheta_i 2)))
(/.f32 (*.f32 (/.f32 cosTheta_i sinTheta_i) cosTheta_O) (*.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_i)) (*.f32 sinTheta_i 2)) (pow.f32 (exp.f32 (/.f32 v sinTheta_i)) sinTheta_O)))
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i v) sinTheta_O))) (/.f32 (*.f32 cosTheta_i cosTheta_O) sinTheta_O)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) 2) sinTheta_O))
(/.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i v)) sinTheta_O)) (/.f32 cosTheta_i (/.f32 sinTheta_O cosTheta_O))) (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) (*.f32 2 sinTheta_O)))
(*.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i v)) sinTheta_O)) (*.f32 2 (sinh.f32 (/.f32 1 sinTheta_O)))) (/.f32 cosTheta_i (*.f32 sinTheta_O (/.f32 sinTheta_O cosTheta_O))))
(/.f32 (*.f32 (/.f32 cosTheta_i sinTheta_O) cosTheta_O) (*.f32 (*.f32 2 (*.f32 (sinh.f32 (/.f32 1 sinTheta_O)) sinTheta_O)) (exp.f32 (/.f32 sinTheta_i (/.f32 sinTheta_O v)))))
Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
914×times-frac_binary32
551×associate-/l*_binary32
460×associate-/l/_binary32
360×associate-*l/_binary32
311×associate-/r/_binary32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02034
15434
217332
380032
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(/.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))
Outputs
(/.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))
(/.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) v)) (/.f32 (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(*.f32 (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (sinh.f32 (/.f32 1 v))) (/.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (*.f32 v 2)))
(/.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)))
(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))

prune5.0ms (0.1%)

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 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
▶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))
Compiler

Compiled 154 to 106 computations (31.2% saved)

localize64.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓0.3b
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓0.8b
(sinh.f32 (/.f32 1 v))

series17.0ms (0.3%)

Counts
4 → 24
Calls

24 calls:

TimeVariablePointExpression
2.0ms
cosTheta_O
@0
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
1.0ms
v
@inf
(sinh.f32 (/.f32 1 v))
1.0ms
v
@0
(sinh.f32 (/.f32 1 v))
1.0ms
sinTheta_i
@inf
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms
v
@0
(*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v)

rewrite65.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
292×log1p-udef_binary32
166×add-sqr-sqrt_binary32
162×*-un-lft-identity_binary32
162×pow1_binary32
152×add-cbrt-cube_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
133232
2435932
Stop Event
1×node limit
Counts
4 → 131
Calls
Call 1
Inputs
(sinh.f32 (/.f32 1 v))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (exp.f32 (/.f32 1 v)) 2) (/.f32 (exp.f32 (/.f32 -1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (sinh.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 2 (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 v) (*.f32 sinTheta_i sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 sinTheta_i (/.f32 1 (/.f32 v sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 sinTheta_i (*.f32 sinTheta_O (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 sinTheta_O (*.f32 sinTheta_i (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 sinTheta_i sinTheta_O) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)) (cbrt.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (*.f32 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simplify27.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
509×unswap-sqr_binary32
478×times-frac_binary32
370×fma-def_binary32
327×associate-*l/_binary32
298×associate-/r*_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
050408
1121392
2270392
3624392
41896392
Stop Event
1×node limit
Counts
155 → 149
Calls
Call 1
Inputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 (*.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 (*.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
Outputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (/.f32 1 v) (+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5)))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (/.f32 1 v) (+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5)))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (/.f32 1/3 (*.f32 v v)))
(+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4)))
(+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 2 (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (*.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
(+.f32 (+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4)))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 (+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6)))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6))))
2
(+.f32 2 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))))
(+.f32 2 (/.f32 1/3 (*.f32 v v)))
(+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4)))))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4)))
(+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 2 (/.f32 1/60 (pow.f32 v 4))))
(+.f32 (*.f32 1/2520 (/.f32 1 (pow.f32 v 6))) (+.f32 2 (+.f32 (*.f32 1/3 (/.f32 1 (pow.f32 v 2))) (*.f32 1/60 (/.f32 1 (pow.f32 v 4))))))
(+.f32 (+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (/.f32 1/60 (pow.f32 v 4)))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 (+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (/.f32 1/60 (pow.f32 v 4))) (/.f32 1/2520 (pow.f32 v 6)))
(+.f32 2 (+.f32 (/.f32 1/3 (*.f32 v v)) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6)))))
(+.f32 (+.f32 2 (/.f32 1/3 (*.f32 v v))) (+.f32 (/.f32 1/60 (pow.f32 v 4)) (/.f32 1/2520 (pow.f32 v 6))))

prune470.0ms (8.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New13415149
Fresh011
Picked101
Done000
Total13516151
Error
0.1b
Counts
151 → 16
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 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
0.5b
(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (/.f32 1 (/.f32 2 (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (expm1.f32 (log1p.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
0.4b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 1 v) (*.f32 cosTheta_i cosTheta_O))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 cosTheta_O (cbrt.f32 (*.f32 v v))) (/.f32 cosTheta_i (cbrt.f32 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶0.4b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 3))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
Compiler

Compiled 4990 to 2543 computations (49% saved)

localize64.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓0.3b
(*.f32 cosTheta_O (/.f32 1 v))
0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.8b
(sinh.f32 (/.f32 1 v))

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
cosTheta_O
@0
(*.f32 cosTheta_O (/.f32 1 v))
1.0ms
v
@-inf
(*.f32 cosTheta_O (/.f32 1 v))
1.0ms
cosTheta_O
@-inf
(*.f32 cosTheta_O (/.f32 1 v))
0.0ms
cosTheta_O
@inf
(*.f32 cosTheta_O (/.f32 1 v))
0.0ms
v
@0
(*.f32 cosTheta_O (/.f32 1 v))

rewrite34.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
537×pow1_binary32
495×add-log-exp_binary32
495×log1p-expm1-u_binary32
495×expm1-log1p-u_binary32
484×add-exp-log_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064
11204
214244
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(*.f32 cosTheta_O (/.f32 1 v))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (/.f32 cosTheta_O v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 cosTheta_O v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (cbrt.f32 cosTheta_O) 2) (/.f32 v (cbrt.f32 cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 cosTheta_O) (/.f32 v (sqrt.f32 cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 cosTheta_O) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 cosTheta_O (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 cosTheta_O 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 cosTheta_O (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1 cosTheta_O) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta_O -1) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 cosTheta_O v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 cosTheta_O v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 cosTheta_O v) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 cosTheta_O v) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v -2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (/.f32 (pow.f32 v -2) v) (pow.f32 cosTheta_O 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 cosTheta_O v)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0496
Stop Event
1×saturated
Counts
48 → 24
Calls
Call 1
Inputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
Outputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)

prune510.0ms (8.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1207127
Fresh51015
Picked101
Done000
Total12617143
Error
0.1b
Counts
143 → 17
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 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
0.5b
(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (expm1.f32 (log1p.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 3))
9.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (sqrt.f32 (/.f32 cosTheta_O v)) 2))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶0.4b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
10.0b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
8.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
Compiler

Compiled 4632 to 2819 computations (39.1% saved)

localize74.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓0.5b
(log.f32 (sinh.f32 (/.f32 1 v)))
✓0.6b
(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
0.8b
(sinh.f32 (/.f32 1 v))

series38.0ms (0.6%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
35.0ms
v
@0
(log.f32 (sinh.f32 (/.f32 1 v)))
1.0ms
v
@inf
(log.f32 (sinh.f32 (/.f32 1 v)))
1.0ms
v
@-inf
(log.f32 (sinh.f32 (/.f32 1 v)))
0.0ms
v
@0
(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
0.0ms
v
@inf
(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))

rewrite37.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
530×pow1_binary32
490×add-log-exp_binary32
488×log1p-expm1-u_binary32
488×expm1-log1p-u_binary32
478×add-exp-log_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
112614
2138614
Stop Event
1×node limit
Counts
2 → 44
Calls
Call 1
Inputs
(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
(log.f32 (sinh.f32 (/.f32 1 v)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 1 (-.f32 (sinh.f32 (/.f32 1 v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (sinh.f32 (/.f32 1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (exp.f32 (/.f32 1 v)) 2) (/.f32 (exp.f32 (/.f32 -1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (sinh.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 2 (*.f32 2 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 2 (sinh.f32 (/.f32 1 v)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sinh.f32 (/.f32 1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (log.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2)) (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x sinh.f32 (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v)))) (log.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) (log.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (log.f32 (sinh.f32 (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (*.f32 2 (sinh.f32 (/.f32 1 v)))) (log.f32 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (log.f32 (sinh.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) (pow.f32 (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log.f32 (sinh.f32 (/.f32 1 v))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (sinh.f32 (/.f32 1 v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))

simplify46.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
852×times-frac_binary32
643×fma-neg_binary32
336×associate-/r*_binary32
320×fma-def_binary32
266×associate-+l+_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
062472
1167450
2412450
31133444
43917444
Stop Event
1×node limit
Counts
68 → 70
Calls
Call 1
Inputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (/.f32 1 v))
(+.f32 (log.f32 (/.f32 1 v)) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))
(-.f32 (+.f32 (log.f32 (/.f32 1 v)) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(-.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 (*.f32 1/2835 (/.f32 1 (pow.f32 v 6))) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1))
(+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))))
(-.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(-.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (*.f32 1/2835 (/.f32 1 (pow.f32 v 6))) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
Outputs
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))
(*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1/120 (pow.f32 v 5)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(/.f32 1 v)
(+.f32 (/.f32 1 v) (*.f32 1/6 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (*.f32 1/120 (/.f32 1 (pow.f32 v 5)))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1 v) (+.f32 (/.f32 1/6 (pow.f32 v 3)) (/.f32 1/120 (pow.f32 v 5))))
(+.f32 (/.f32 1/120 (pow.f32 v 5)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (*.f32 1/6 (/.f32 1 (pow.f32 v 3))) (+.f32 (/.f32 1 v) (+.f32 (*.f32 1/5040 (/.f32 1 (pow.f32 v 7))) (*.f32 1/120 (/.f32 1 (pow.f32 v 5))))))
(+.f32 (/.f32 1/6 (pow.f32 v 3)) (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7)))))
(+.f32 (+.f32 (/.f32 1/120 (pow.f32 v 5)) (/.f32 1/5040 (pow.f32 v 7))) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3))))
(+.f32 (/.f32 1/5040 (pow.f32 v 7)) (+.f32 (/.f32 1/120 (pow.f32 v 5)) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v))))))
(log.f32 (*.f32 1/2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
(log.f32 (/.f32 1 v))
(neg.f32 (log.f32 v))
(+.f32 (log.f32 (/.f32 1 v)) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))
(+.f32 (neg.f32 (log.f32 v)) (/.f32 1/6 (*.f32 v v)))
(-.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 v))
(-.f32 (/.f32 (/.f32 1/6 v) v) (log.f32 v))
(-.f32 (+.f32 (log.f32 (/.f32 1 v)) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(+.f32 (neg.f32 (log.f32 v)) (-.f32 (/.f32 1/6 (*.f32 v v)) (/.f32 1/180 (pow.f32 v 4))))
(+.f32 (-.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 v)) (/.f32 -1/180 (pow.f32 v 4)))
(+.f32 (-.f32 (/.f32 (/.f32 1/6 v) v) (log.f32 v)) (/.f32 -1/180 (pow.f32 v 4)))
(-.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 (*.f32 1/2835 (/.f32 1 (pow.f32 v 6))) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(+.f32 (neg.f32 (log.f32 v)) (-.f32 (+.f32 (/.f32 1/6 (*.f32 v v)) (/.f32 1/2835 (pow.f32 v 6))) (/.f32 1/180 (pow.f32 v 4))))
(+.f32 (+.f32 (-.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 v)) (/.f32 1/2835 (pow.f32 v 6))) (/.f32 -1/180 (pow.f32 v 4)))
(+.f32 (-.f32 (/.f32 1/6 (*.f32 v v)) (-.f32 (log.f32 v) (/.f32 1/2835 (pow.f32 v 6)))) (/.f32 -1/180 (pow.f32 v 4)))
(+.f32 (/.f32 (/.f32 1/6 v) v) (-.f32 (/.f32 -1/180 (pow.f32 v 4)) (-.f32 (log.f32 v) (/.f32 1/2835 (pow.f32 v 6)))))
(+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1))
(+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))))
(+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 -1)))
(+.f32 (/.f32 1/6 (*.f32 v v)) (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1)))
(fma.f32 2 (log.f32 -1) (-.f32 (/.f32 (/.f32 1/6 v) v) (log.f32 v)))
(-.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(+.f32 (log.f32 (/.f32 -1 v)) (-.f32 (+.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 -1)) (/.f32 1/180 (pow.f32 v 4))))
(+.f32 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1)) (+.f32 (/.f32 1/6 (*.f32 v v)) (/.f32 -1/180 (pow.f32 v 4))))
(fma.f32 2 (log.f32 -1) (+.f32 (-.f32 (/.f32 (/.f32 1/6 v) v) (log.f32 v)) (/.f32 -1/180 (pow.f32 v 4))))
(-.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (*.f32 1/2835 (/.f32 1 (pow.f32 v 6))) (+.f32 (log.f32 -1) (*.f32 1/6 (/.f32 1 (pow.f32 v 2)))))) (*.f32 1/180 (/.f32 1 (pow.f32 v 4))))
(+.f32 (log.f32 (/.f32 -1 v)) (-.f32 (+.f32 (/.f32 1/2835 (pow.f32 v 6)) (+.f32 (/.f32 1/6 (*.f32 v v)) (log.f32 -1))) (/.f32 1/180 (pow.f32 v 4))))
(+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (+.f32 (/.f32 1/2835 (pow.f32 v 6)) (log.f32 -1)) (+.f32 (/.f32 1/6 (*.f32 v v)) (/.f32 -1/180 (pow.f32 v 4)))))
(+.f32 (/.f32 1/2835 (pow.f32 v 6)) (+.f32 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1)) (+.f32 (/.f32 1/6 (*.f32 v v)) (/.f32 -1/180 (pow.f32 v 4)))))
(+.f32 (/.f32 1/2835 (pow.f32 v 6)) (fma.f32 2 (log.f32 -1) (+.f32 (-.f32 (/.f32 (/.f32 1/6 v) v) (log.f32 v)) (/.f32 -1/180 (pow.f32 v 4)))))

prune553.0ms (9.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1453148
Fresh31316
Picked101
Done000
Total14916165
Error
0.0b
Counts
165 → 16
Alt Table
StatusErrorProgram
5.2b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
0.5b
(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (pow.f32 (E.f32) (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
▶0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (exp.f32 (-.f32 (log.f32 (*.f32 2 (sinh.f32 (/.f32 1 v)))) (log.f32 2))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
10.0b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
9.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (sqrt.f32 (/.f32 cosTheta_O v)) 2))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
8.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
Compiler

Compiled 5676 to 3594 computations (36.7% saved)

localize85.0ms (1.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓0.3b
(/.f32 1 (/.f32 v cosTheta_O))
0.3b
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.8b
(sinh.f32 (/.f32 1 v))

series2.0ms (0%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
v
@0
(/.f32 1 (/.f32 v cosTheta_O))
0.0ms
v
@inf
(/.f32 1 (/.f32 v cosTheta_O))
0.0ms
cosTheta_O
@inf
(/.f32 1 (/.f32 v cosTheta_O))
0.0ms
v
@-inf
(/.f32 1 (/.f32 v cosTheta_O))
0.0ms
cosTheta_O
@-inf
(/.f32 1 (/.f32 v cosTheta_O))

rewrite33.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
617×pow1_binary32
571×add-log-exp_binary32
571×log1p-expm1-u_binary32
571×expm1-log1p-u_binary32
62×add-sqr-sqrt_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067
11254
216074
Stop Event
1×node limit
Counts
1 → 37
Calls
Call 1
Inputs
(/.f32 1 (/.f32 v cosTheta_O))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 cosTheta_O v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 cosTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 cosTheta_O (pow.f32 v -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 cosTheta_O v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 cosTheta_O v)) (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 2) (cbrt.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 cosTheta_O v)) (sqrt.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 -1 (/.f32 1 (/.f32 (neg.f32 v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 v -1) cosTheta_O)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 v -1) (pow.f32 (/.f32 1 cosTheta_O) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (/.f32 v cosTheta_O)) 2) -1) (pow.f32 (cbrt.f32 (/.f32 v cosTheta_O)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (/.f32 v cosTheta_O)) -1) (pow.f32 (sqrt.f32 (/.f32 v cosTheta_O)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_O) 2) 1) (/.f32 (cbrt.f32 cosTheta_O) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 cosTheta_O) 1) (/.f32 (sqrt.f32 cosTheta_O) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_O (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_O) 2) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (cbrt.f32 cosTheta_O) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 cosTheta_O) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 cosTheta_O) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_O) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 cosTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 cosTheta_O) (sqrt.f32 v)) (/.f32 (sqrt.f32 cosTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (neg.f32 v)) (neg.f32 cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (pow.f32 v -1) 1) cosTheta_O)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (pow.f32 v -1) (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (pow.f32 v -1) (sqrt.f32 cosTheta_O)) (sqrt.f32 cosTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v cosTheta_O) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 cosTheta_O v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 cosTheta_O v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 cosTheta_O v) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 cosTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 cosTheta_O v) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 cosTheta_O v)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0496
Stop Event
1×saturated
Counts
61 → 38
Calls
Call 1
Inputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
Outputs
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)
(/.f32 cosTheta_O v)

prune525.0ms (9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1392141
Fresh01515
Picked011
Done000
Total13918157
Error
0.0b
Counts
157 → 18
Alt Table
StatusErrorProgram
5.2b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (log.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
0.5b
(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (pow.f32 (E.f32) (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
✓0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (exp.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
8.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (pow.f32 (/.f32 cosTheta_O v) 3) 1/3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)))) (*.f32 (*.f32 (exp.f32 (-.f32 (log.f32 (*.f32 2 (sinh.f32 (/.f32 1 v)))) (log.f32 2))) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) 3)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (*.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (*.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
10.0b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 cosTheta_O v))))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
9.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (sqrt.f32 (/.f32 cosTheta_O v)) 2))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.5b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
0.6b
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
Compiler

Compiled 4579 to 2565 computations (44% saved)

regimes282.0ms (4.8%)

Accuracy

Total -20.2b remaining (-4975.7%)

Threshold costs -20.2b (-4975.7%)

Counts
65 → 1
Compiler

Compiled 1771 to 871 computations (50.8% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
10×*-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
02237
13437
24437
35137
45637
55837
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (pow.f32 v -1)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
Outputs
(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (*.f32 cosTheta_i (*.f32 cosTheta_O (pow.f32 v -1)))) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
(/.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_i sinTheta_O)) v)) (*.f32 cosTheta_i (*.f32 cosTheta_O (pow.f32 v -1)))) (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))
(/.f32 (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (*.f32 cosTheta_i (*.f32 cosTheta_O (pow.f32 v -1)))) (*.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))

end268.0ms (4.6%)

Stop Event
1×fuel
Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 650 to 375 computations (42.3% saved)

Profiling

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