Details

Time bar (total: 6.2s)

analyze336.0ms (5.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.3s (21.1%)

Results
1.2s8256×body128valid
50.0ms369×body128invalid
Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify38.0ms (0.6%)

Algorithm
egg-herbie
Rules
693×div-sub_binary64
599×times-frac_binary64
519×associate-/l*_binary64
357×associate-/l/_binary64
274×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01632
13729
29429
334529
4120728
5346828
6502028

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
17.3b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
Compiler

Compiled 127 to 87 computations (31.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
0.2b
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.2b
(/.f64 (PI.f64) a)

series52.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

20.0ms
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
19.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
9.0ms
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))
3.0ms
(/.f64 (PI.f64) a)

rewrite42.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
55×times-frac_binary64
39×add-cube-cbrt_binary64
21×associate-*r*_binary64
Counts
4 → 143
Calls

4 calls:

15.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a)))
10.0ms
(/.f64 (PI.f64) a)
4.0ms
(/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (-.f64 b a))
0.0ms
(fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a))

simplify218.0ms (3.5%)

Algorithm
egg-herbie
Rules
425×times-frac_binary64
380×associate-/l/_binary64
318×fma-neg_binary64
291×fma-def_binary64
232×distribute-rgt-in_binary64
Counts
215 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02655404
16764819
221334749
346294748
449894748
549984748
649724748

prune271.0ms (4.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2289237
Fresh011
Picked101
Done000
Total22910239
Error
0b
Counts
239 → 10
Alt Table
StatusErrorProgram
0.3b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))))
0.5b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (*.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) a)) (cbrt.f64 (/.f64 (PI.f64) a))) (cbrt.f64 (/.f64 (PI.f64) a)))) (-.f64 b a)))
31.9b
(*.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (sqrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (sqrt.f64 (-.f64 b a))))
0.2b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (cbrt.f64 1/2) (+.f64 a b))))
17.3b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
29.7b
(*.f64 1/2 (/.f64 (PI.f64) (*.f64 a (pow.f64 b 2))))
0.7b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
Compiler

Compiled 7112 to 2754 computations (61.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.2b
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
0.2b
(/.f64 (PI.f64) a)
0.3b
(/.f64 (PI.f64) b)

series40.0ms (0.6%)

Counts
3 → 48
Calls

3 calls:

20.0ms
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
17.0ms
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
2.0ms
(/.f64 (PI.f64) b)

rewrite61.0ms (1%)

Algorithm
rewrite-expression-head
Rules
142×add-sqr-sqrt_binary64
133×times-frac_binary64
122×*-un-lft-identity_binary64
44×add-cube-cbrt_binary64
43×distribute-lft-out--_binary64
Counts
3 → 156
Calls

3 calls:

20.0ms
(/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))
20.0ms
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
2.0ms
(/.f64 (PI.f64) b)

simplify173.0ms (2.8%)

Algorithm
egg-herbie
Rules
663×times-frac_binary64
311×fma-def_binary64
299×fma-neg_binary64
273×distribute-rgt-in_binary64
248×distribute-lft-in_binary64
Counts
204 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03115679
17985327
222285259
349715259
451495259

prune310.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2352237
Fresh369
Picked011
Done000
Total2389247
Error
0b
Counts
247 → 9
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
0.2b
(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.3b
(/.f64 (*.f64 1/2 (*.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
31.9b
(*.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (sqrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (sqrt.f64 (-.f64 b a))))
0.5b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (*.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) a)) (cbrt.f64 (/.f64 (PI.f64) a))) (cbrt.f64 (/.f64 (PI.f64) a)))) (-.f64 b a)))
0.2b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
17.3b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
Compiler

Compiled 6821 to 1952 computations (71.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (PI.f64) a)
0.2b
(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
0.3b
(/.f64 (PI.f64) b)
0.7b
(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))

series56.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

36.0ms
(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))
19.0ms
(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))

rewrite125.0ms (2%)

Algorithm
rewrite-expression-head
Rules
761×times-frac_binary64
647×add-sqr-sqrt_binary64
543×*-un-lft-identity_binary64
213×add-cube-cbrt_binary64
191×distribute-lft-out--_binary64
Counts
2 → 391
Calls

2 calls:

22.0ms
(/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))
17.0ms
(/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)))

simplify386.0ms (6.2%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
419×associate-/r/_binary64
369×times-frac_binary64
325×associate-/r*_binary64
317×distribute-rgt-in_binary64
Counts
439 → 437
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030014610
166713806
2203613407
3456513407
4514813407

prune470.0ms (7.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5000500
Fresh077
Picked011
Done011
Total5009509
Error
0b
Counts
509 → 9
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (*.f64 (cbrt.f64 (-.f64 b a)) (cbrt.f64 (-.f64 b a)))) (cbrt.f64 (-.f64 b a))))
0.2b
(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.3b
(/.f64 (*.f64 1/2 (*.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
31.9b
(*.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (sqrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (sqrt.f64 (-.f64 b a))))
0.5b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (*.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) a)) (cbrt.f64 (/.f64 (PI.f64) a))) (cbrt.f64 (/.f64 (PI.f64) a)))) (-.f64 b a)))
0.2b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
17.3b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
Compiler

Compiled 17144 to 4859 computations (71.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a))
0.2b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
0.2b
(/.f64 (PI.f64) a)
0.3b
(/.f64 (PI.f64) b)

series38.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

19.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
18.0ms
(/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a))

rewrite87.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
217×*-un-lft-identity_binary64
172×times-frac_binary64
113×add-sqr-sqrt_binary64
69×distribute-lft-out_binary64
63×add-cube-cbrt_binary64
Counts
2 → 174
Calls

2 calls:

37.0ms
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a)))
21.0ms
(/.f64 (+.f64 (neg.f64 (/.f64 (PI.f64) b)) (/.f64 (PI.f64) a)) (-.f64 b a))

simplify183.0ms (3%)

Algorithm
egg-herbie
Rules
781×times-frac_binary64
600×div-sub_binary64
437×fma-def_binary64
270×fma-neg_binary64
234×associate-*r/_binary64
Counts
222 → 255
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02836484
18165753
226955716
344415715
456905715

prune314.0ms (5.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3171318
Fresh156
Picked101
Done022
Total3198327
Error
0b
Counts
327 → 8
Alt Table
StatusErrorProgram
31.9b
(*.f64 (*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 1 (sqrt.f64 (-.f64 b a)))) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (/.f64 (PI.f64) a)) (sqrt.f64 (-.f64 b a))))
0.5b
(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (fma.f64 (PI.f64) (/.f64 -1 b) (*.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) a)) (cbrt.f64 (/.f64 (PI.f64) a))) (cbrt.f64 (/.f64 (PI.f64) a)))) (-.f64 b a)))
0.2b
(/.f64 (*.f64 1/2 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a))) (+.f64 b a))
0.3b
(*.f64 (/.f64 1/2 (+.f64 b a)) (*.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a))))
17.3b
(*.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 1 (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.2b
(/.f64 (*.f64 1/2 (/.f64 1 (/.f64 (-.f64 b a) (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b))))) (+.f64 b a))
0.3b
(/.f64 (*.f64 1/2 (*.f64 (PI.f64) (/.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (-.f64 b a)))) (+.f64 b a))
0.4b
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (*.f64 (/.f64 (-.f64 (/.f64 (PI.f64) a) (/.f64 (PI.f64) b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 a b))))
Compiler

Compiled 9166 to 2501 computations (72.7% saved)

regimes1.5s (24.3%)

Accuracy

Total 0.3b remaining (91.2%)

Threshold costs 0.3b (91.2%)

Counts
214 → 1
Compiler

Compiled 15868 to 10122 computations (36.2% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01327
11927
22927
33527
43927
54027
64027

end129.0ms (2.1%)

Compiler

Compiled 227 to 148 computations (34.8% saved)

Profiling

Loading profile data...