Details

Time bar (total: 16.2s)

analyze1.4s (8.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14
Compiler

Compiled 39 to 31 computations (20.5% saved)

sample407.0ms (2.5%)

Algorithm
intervals
Results
123.0ms119×body1024nan
87.0ms132×body1024valid
34.0ms78×body512nan
32.0ms67×body512valid
15.0ms11×body2048valid
10.0ms36×body256nan
10.0ms29×body256valid
4.0ms17×body128valid
Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify55.0ms (0.3%)

Algorithm
egg-herbie
Rules
738×fma-neg_binary64
569×fma-def_binary64
365×div-sub_binary64
240×associate-/r*_binary64
202×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01764
14961
211759
329555
473655
5162555
6400355
7505355

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
62.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
62.6b
(*.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
Compiler

Compiled 136 to 100 computations (26.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (/.f64 (PI.f64) 4) f)
0.3b
(*.f64 (PI.f64) f)
0.8b
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
6.4b
(-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))

series48.0ms (0.3%)

Counts
4 → 48
Calls

4 calls:

34.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
9.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))
3.0ms
(*.f64 (/.f64 (PI.f64) 4) f)
2.0ms
(*.f64 (PI.f64) f)

rewrite137.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt_binary64
71×*-un-lft-identity_binary64
43×add-cube-cbrt_binary64
38×times-frac_binary64
21×prod-diff_binary64
Counts
4 → 159
Calls

4 calls:

102.0ms
(-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))
10.0ms
(/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))
5.0ms
(*.f64 (/.f64 (PI.f64) 4) f)
4.0ms
(*.f64 (PI.f64) f)

simplify200.0ms (1.2%)

Algorithm
egg-herbie
Rules
784×fma-def_binary64
588×times-frac_binary64
366×fma-neg_binary64
225×cancel-sign-sub-inv_binary64
196×exp-prod_binary64
Counts
207 → 258
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03128603
16527401
219966651
341696609
448406609

prune376.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3472349
Fresh000
Picked101
Done000
Total3482350
Error
1.6b
Counts
350 → 2
Alt Table
StatusErrorProgram
62.6b
(*.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
Compiler

Compiled 15856 to 10266 computations (35.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))
0.3b
(/.f64 4 (*.f64 f (PI.f64)))
0.3b
(*.f64 f (PI.f64))
0.5b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

series118.0ms (0.7%)

Counts
4 → 24
Calls

4 calls:

93.0ms
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
15.0ms
(log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))
7.0ms
(/.f64 4 (*.f64 f (PI.f64)))
2.0ms
(*.f64 f (PI.f64))

rewrite48.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
17×add-exp-log_binary64
16×associate-*r*_binary64
Counts
4 → 92
Calls

4 calls:

35.0ms
(/.f64 4 (*.f64 f (PI.f64)))
6.0ms
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
3.0ms
(*.f64 f (PI.f64))
1.0ms
(log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))

simplify127.0ms (0.8%)

Algorithm
egg-herbie
Rules
551×associate-/r*_binary64
454×fma-def_binary64
382×fma-neg_binary64
287×cancel-sign-sub-inv_binary64
274×times-frac_binary64
Counts
116 → 196
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02673005
16672698
221512681
348962673
450362673

prune263.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2189227
Fresh011
Picked101
Done000
Total21910229
Error
0.9b
Counts
229 → 10
Alt Table
StatusErrorProgram
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (exp.f64 (+.f64 (log.f64 f) (log.f64 (PI.f64))))))) (/.f64 -4 (PI.f64)))
1.5b
(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
1.9b
(*.f64 (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 f (*.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))))) (log.f64 (cbrt.f64 (fma.f64 f (*.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
2.7b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))) (cbrt.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64))))) (cbrt.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
1.8b
(*.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
2.0b
(*.f64 (sqrt.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) (*.f64 (sqrt.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64))))
62.6b
(*.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
2.1b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64))) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))) (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
63.0b
(log1p.f64 (expm1.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
Compiler

Compiled 5867 to 3593 computations (38.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12)
0.3b
(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
0.3b
(/.f64 (log.f64 f) (PI.f64))
2.0b
(log.f64 (/.f64 4 (PI.f64)))

series434.0ms (2.7%)

Counts
4 → 28
Calls

4 calls:

394.0ms
(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
34.0ms
(/.f64 (log.f64 f) (PI.f64))
4.0ms
(*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12)
0.0ms
(log.f64 (/.f64 4 (PI.f64)))

rewrite99.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
457×times-frac_binary64
315×*-un-lft-identity_binary64
313×add-sqr-sqrt_binary64
301×add-cube-cbrt_binary64
256×prod-diff_binary64
Counts
4 → 404
Calls

4 calls:

22.0ms
(-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
7.0ms
(*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12)
3.0ms
(/.f64 (log.f64 f) (PI.f64))
2.0ms
(log.f64 (/.f64 4 (PI.f64)))

simplify465.0ms (2.9%)

Algorithm
egg-herbie
Rules
421×associate-/l*_binary64
343×fma-neg_binary64
193×associate-/l/_binary64
185×exp-prod_binary64
179×associate-*l*_binary64
Counts
432 → 358
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043914223
193611573
2206210749
3435710748
4481410748

prune453.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3553358
Fresh459
Picked101
Done000
Total3608368
Error
0.9b
Counts
368 → 8
Alt Table
StatusErrorProgram
1.5b
(fma.f64 4 (/.f64 (*.f64 (PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64))))) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
1.5b
(fma.f64 4 (+.f64 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 4) (PI.f64))) (/.f64 (log.f64 (PI.f64)) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
1.8b
(*.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
62.6b
(*.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (exp.f64 (+.f64 (log.f64 f) (log.f64 (PI.f64))))))) (/.f64 -4 (PI.f64)))
1.4b
(fma.f64 4 (-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
63.0b
(log1p.f64 (expm1.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
Compiler

Compiled 18079 to 10009 computations (44.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12)
0.3b
(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
2.0b
(log.f64 (/.f64 4 (PI.f64)))
5.1b
(pow.f64 f (/.f64 1 (PI.f64)))

series726.0ms (4.5%)

Counts
2 → 24
Calls

2 calls:

694.0ms
(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
32.0ms
(pow.f64 f (/.f64 1 (PI.f64)))

rewrite29.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt_binary64
71×*-un-lft-identity_binary64
70×times-frac_binary64
69×add-cube-cbrt_binary64
64×prod-diff_binary64
Counts
2 → 137
Calls

2 calls:

12.0ms
(-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)))
3.0ms
(pow.f64 f (/.f64 1 (PI.f64)))

simplify163.0ms (1%)

Algorithm
egg-herbie
Rules
602×fma-def_binary64
448×associate-*l/_binary64
343×associate-/l*_binary64
238×fma-neg_binary64
179×exp-prod_binary64
Counts
161 → 160
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02505261
15874065
213602941
344352929
449832929
547602929

prune284.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2251226
Fresh167
Picked011
Done000
Total2268234
Error
0.9b
Counts
234 → 8
Alt Table
StatusErrorProgram
1.8b
(*.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
1.4b
(fma.f64 4 (+.f64 (/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64)))) (PI.f64)) 0) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
1.5b
(fma.f64 4 (/.f64 (*.f64 (PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 (PI.f64))))) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
1.8b
(*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (log1p.f64 (expm1.f64 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
1.5b
(fma.f64 4 (+.f64 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 4) (PI.f64))) (/.f64 (log.f64 (PI.f64)) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
62.6b
(*.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
1.4b
(fma.f64 4 (-.f64 (log.f64 (pow.f64 f (/.f64 1 (PI.f64)))) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 f f)) -1/12))
63.0b
(log1p.f64 (expm1.f64 (*.f64 (log.f64 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
Compiler

Compiled 9100 to 5816 computations (36.1% saved)

regimes581.0ms (3.6%)

Accuracy

Total 0.7b remaining (35.1%)

Threshold costs 0.7b (35.1%)

Counts
98 → 1
Compiler

Compiled 15486 to 11114 computations (28.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01737
12337
22937
33337
43637
53737
63637

end2.0ms (0%)

Compiler

Compiled 23 to 17 computations (26.1% saved)

sample9.7s (59.7%)

Algorithm
intervals
Results
3.2s3944×body1024valid
2.5s3882×body1024nan
1.0s1957×body512valid
894.0ms1963×body512nan
624.0ms488×body2048valid
320.0ms945×body256valid
318.0ms1038×body256nan
112.0ms666×body128valid
0.0msbody128overflowed
Compiler

Compiled 247 to 182 computations (26.3% saved)

Profiling

Loading profile data...