Details

Time bar (total: 7.9s)

analyze169.0ms (2.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0.6%99.4%0
0%0.6%99.4%1
0%0.6%99.4%2
0.3%0.3%99.4%3
0.3%0.3%99.4%4
0.5%0.2%99.4%5
0.5%0.2%99.4%6
0.6%0.1%99.4%7
0.6%0.1%99.4%8
0.6%0%99.4%9
0.6%0%99.4%10
0.6%0%99.4%11
0.6%0%99.4%12
0.6%0%99.4%13
0.6%0%99.4%14
Compiler

Compiled 35 to 23 computations (34.3% saved)

sample46.0ms (0.6%)

Algorithm
1×intervals
Results
25.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify53.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
608×associate-/l*_binary32
462×associate-*l*_binary32
382×associate-*l/_binary32
363×associate-*r*_binary32
360×distribute-lft-in_binary32
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01433
14531
216031
366131
4279131
5486631
6497831

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.5b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.5b
(/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 PI.f32 (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
▶0.5b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 PI.f32 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
Compiler

Compiled 121 to 77 computations (36.4% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
0.3b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 PI.f32 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.4b
(*.f32 PI.f32 (log.f32 (*.f32 alpha alpha)))

rewrite269.0ms (3.4%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
42×pow1_binary32
30×add-exp-log_binary32
28×add-sqr-sqrt_binary32
23×add-cube-cbrt_binary32
22×add-cbrt-cube_binary32
Counts
4 → 181
Calls

4 calls:

28.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 PI.f32 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
20.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
17.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
14.0ms
(*.f32 PI.f32 (log.f32 (*.f32 alpha alpha)))
Compiler

Compiled 5489 to 2520 computations (54.1% saved)

series154.0ms (1.9%)

Error
0.3b
Counts
4 → 34
Calls

4 calls:

65.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 PI.f32 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
20.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
16.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
12.0ms
(*.f32 PI.f32 (log.f32 (*.f32 alpha alpha)))
Compiler

Compiled 2964 to 2115 computations (28.6% saved)

simplify145.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
578×times-frac_binary32
449×associate-*l*_binary32
380×associate-/r*_binary32
303×associate-/l*_binary32
237×fma-neg_binary32
Counts
215 → 150
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03575129
110694467
248994467
350334467

prune170.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1419150
Fresh101
Picked101
Done000
Total1439152
Error
0.0b
Counts
152 → 9
Alt Table
StatusErrorProgram
0.7b
(*.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.8b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (cbrt.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))))) (cbrt.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
▶0.4b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
3.0b
(-.f32 (exp.f32 (log1p.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) 1)
0.6b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (pow.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (fma.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.7b
(*.f32 (/.f32 (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(/.f32 (*.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
Compiler

Compiled 4884 to 2667 computations (45.4% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
0.2b
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
0.3b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
3.2b
(pow.f32 (*.f32 alpha alpha) PI.f32)

rewrite445.0ms (5.6%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
33×pow1_binary32
26×add-exp-log_binary32
24×add-cube-cbrt_binary32
23×add-sqr-sqrt_binary32
20×add-cbrt-cube_binary32
Counts
4 → 173
Calls

4 calls:

152.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
26.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
17.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
15.0ms
(pow.f32 (*.f32 alpha alpha) PI.f32)
Compiler

Compiled 5132 to 2405 computations (53.1% saved)

series164.0ms (2.1%)

Error
0.0b
Counts
4 → 34
Calls

4 calls:

71.0ms
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
20.0ms
(*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
18.0ms
(*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta)
12.0ms
(pow.f32 (*.f32 alpha alpha) PI.f32)
Compiler

Compiled 3216 to 2367 computations (26.4% saved)

simplify162.0ms (2%)

Algorithm
1×egg-herbie
Rules
395×times-frac_binary32
354×associate-*l*_binary32
330×fma-neg_binary32
329×associate-*r*_binary32
252×associate-/r*_binary32
Counts
207 → 141
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03205002
18534411
243654404
350834404

prune158.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1401141
Fresh178
Picked011
Done000
Total1419150
Error
0.0b
Counts
150 → 9
Alt Table
StatusErrorProgram
▶0.6b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
✓0.4b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.7b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (/.f32 1 (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3))) (fma.f32 (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
3.0b
(-.f32 (exp.f32 (log1p.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) 1)
0.6b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (pow.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (fma.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.7b
(*.f32 (/.f32 (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(/.f32 (*.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
Compiler

Compiled 4928 to 2716 computations (44.9% saved)

localize104.0ms (1.3%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 PI.f32 (log.f32 alpha))
0.5b
(pow.f32 (fma.f32 alpha alpha -1) 2)
0.5b
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
1.0b
(pow.f32 PI.f32 2)

rewrite363.0ms (4.6%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
32×add-cube-cbrt_binary32
22×pow1_binary32
17×add-sqr-sqrt_binary32
16×add-exp-log_binary32
14×add-cbrt-cube_binary32
Counts
4 → 163
Calls

4 calls:

17.0ms
(*.f32 PI.f32 (log.f32 alpha))
16.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
16.0ms
(pow.f32 PI.f32 2)
14.0ms
(pow.f32 (fma.f32 alpha alpha -1) 2)
Compiler

Compiled 8199 to 5111 computations (37.7% saved)

series62.0ms (0.8%)

Error
0.0b
Counts
4 → 11
Calls

4 calls:

15.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
15.0ms
(pow.f32 (fma.f32 alpha alpha -1) 2)
13.0ms
(*.f32 PI.f32 (log.f32 alpha))
0.0ms
(pow.f32 PI.f32 2)
Compiler

Compiled 1924 to 1320 computations (31.4% saved)

simplify139.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
482×log-prod_binary32
359×fma-neg_binary32
346×*-commutative_binary32
270×exp-prod_binary32
244×cube-prod_binary32
Counts
174 → 89
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01611374
13351275
211191156
331891144
449041144
549761144
652191144

prune120.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New88189
Fresh167
Picked011
Done011
Total89998
Error
0.0b
Counts
98 → 9
Alt Table
StatusErrorProgram
✓0.6b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
✓0.4b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.7b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (/.f32 1 (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3))) (fma.f32 (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.6b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (pow.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (fma.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
▶0.5b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (log.f32 alpha) (cbrt.f32 PI.f32)))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.7b
(*.f32 (/.f32 (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(/.f32 (*.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
Compiler

Compiled 4396 to 2757 computations (37.3% saved)

localize168.0ms (2.1%)

Local error

Found 4 expressions with local error:

0.5b
(pow.f32 (fma.f32 alpha alpha -1) 2)
0.5b
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
0.5b
(*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (log.f32 alpha) (cbrt.f32 PI.f32)))
1.0b
(pow.f32 PI.f32 2)

rewrite373.0ms (4.7%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
23×add-cube-cbrt_binary32
20×add-exp-log_binary32
15×add-sqr-sqrt_binary32
15×pow1_binary32
14×add-cbrt-cube_binary32
Counts
4 → 154
Calls

4 calls:

21.0ms
(*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (log.f32 alpha) (cbrt.f32 PI.f32)))
16.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
14.0ms
(pow.f32 PI.f32 2)
12.0ms
(pow.f32 (fma.f32 alpha alpha -1) 2)
Compiler

Compiled 8508 to 4821 computations (43.3% saved)

series92.0ms (1.2%)

Error
0.0b
Counts
4 → 11
Calls

4 calls:

42.0ms
(pow.f32 (fma.f32 alpha alpha -1) 2)
16.0ms
(pow.f32 (*.f32 2 (log.f32 alpha)) 2)
15.0ms
(*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (log.f32 alpha) (cbrt.f32 PI.f32)))
0.0ms
(pow.f32 PI.f32 2)
Compiler

Compiled 2071 to 1366 computations (34% saved)

simplify96.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1040×fma-def_binary32
595×exp-prod_binary32
473×log-prod_binary32
442×unswap-sqr_binary32
278×*-commutative_binary32
Counts
165 → 86
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01471354
12891031
28431013
325721004
43927998
55063998

prune130.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New86086
Fresh066
Picked011
Done022
Total86995
Error
0.0b
Counts
95 → 9
Alt Table
StatusErrorProgram
0.6b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.4b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) PI.f32)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.7b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (/.f32 1 (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3))) (fma.f32 (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 1 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.6b
(/.f32 (-.f32 (/.f32 (pow.f32 alpha 6) (pow.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (pow.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) 3)) (fma.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 (/.f32 alpha (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) PI.f32) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (pow.f32 alpha 4) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.5b
(*.f32 (cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))) (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (log.f32 alpha) (cbrt.f32 PI.f32)))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
0.7b
(*.f32 (/.f32 (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (*.f32 2 (*.f32 PI.f32 (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
0.7b
(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (*.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32)) (*.f32 (*.f32 2 (log.f32 alpha)) (cbrt.f32 PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.6b
(/.f32 (*.f32 (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (pow.f32 PI.f32 2) (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (*.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))) (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 2 (*.f32 PI.f32 (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
Compiler

Compiled 3872 to 2297 computations (40.7% saved)

regimes2.5s (31.3%)

Accuracy

Total 0.4b remaining (95.6%)

Threshold costs 0.4b (95.6%)

Compiler

Compiled 66203 to 43133 computations (34.8% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary32
2×+-commutative_binary32
1×sub-neg_binary32
1×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01967
12867
22967
32767

end1.0ms (0%)

Compiler

Compiled 46 to 29 computations (37% saved)

sample1.8s (22.2%)

Algorithm
1×intervals
Results
790.0ms8000×body128valid
186.0ms8000×pre128true
Compiler

Compiled 686 to 434 computations (36.7% saved)

Profiling

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