Details

Time bar (total: 9.6s)

analyze656.0ms (6.9%)

Algorithm
1×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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.2s (23.4%)

Results
696.0ms5333×body128valid
622.0ms1169×body2048valid
329.0ms761×body1024valid
263.0ms413×body4096valid
137.0ms1094×body128invalid
122.0ms363×body512valid
53.0ms217×body256valid
Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess15.0ms (0.2%)

Algorithm
2×egg-herbie
Rules
4×fma-neg_binary64
4×fma-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039104
147104
251104
033
Stop Event
1×saturated
1×saturated
Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×fma-neg_binary64
1×fma-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01526
11726
21826
Stop Event
1×saturated
Counts
1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
35.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶35.9b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
Compiler

Compiled 60 to 42 computations (30% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
✓1.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
✓1.7b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
✓25.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series122.0ms (1.3%)

Counts
4 → 96
Calls

36 calls:

10.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
a
-inf
9.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
a
inf
8.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
c
-inf
7.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
c
inf
7.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
c
-inf

rewrite58.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
380×log-prod_binary64
278×expm1-udef_binary64
278×log1p-udef_binary64
276×log-pow_binary64
155×add-sqr-sqrt_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01574
129774
2322271
Stop Event
1×node limit
Counts
4 → 118

simplify408.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
1635×sqr-pow_binary64
777×pow-sqr_binary64
94×cube-mult_binary64
94×unpow3_binary64
93×cube-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01252134
11932134
22372134
32862134
43442134
54062134
64752134
75522134
86362134
97282134
108272134
119342134
1210482134
1311702134
1412992134
1514362134
1615802134
1717322134
1818912134
1920582134
2022322134
2124142134
2224262134
2324322134
2424322134
2526182134
2628092134
2730132134
2832252134
2934442134
3036712134
3139052134
3241472134
3342052134
3442562134
3542562134
3644542134
3747022134
3849652134
Stop Event
1×node limit
Counts
214 → 183

prune131.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1758183
Fresh000
Picked011
Done000
Total1759184
Error
5.8b
Counts
184 → 9
Alt Table
StatusErrorProgram
✓35.9b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
47.9b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)) 3))
54.7b
(/.f64 (-.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))
36.4b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
43.6b
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
37.2b
(*.f64 -1 (/.f64 c b))
48.1b
(-.f64 (/.f64 c b) (/.f64 b a))
47.9b
(*.f64 -1 (/.f64 b a))
▶34.9b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
Compiler

Compiled 5457 to 3213 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)))
✓0.3b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
✓0.6b
(-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c))))))
✓11.5b
(sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c))))

series3.6s (37.5%)

Counts
4 → 24
Calls

33 calls:

1.2s
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
a
inf
684.0ms
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
a
-inf
382.0ms
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)))
a
inf
247.0ms
(cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)))
a
-inf
191.0ms
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
c
inf

rewrite62.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
394×log-prod_binary64
295×log-pow_binary64
288×expm1-udef_binary64
288×log1p-udef_binary64
163×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01882
134382
2336282
Stop Event
1×node limit
Counts
4 → 94

simplify342.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
1600×sqr-pow_binary64
538×pow-sqr_binary64
64×cube-prod_binary64
64×cube-mult_binary64
64×unpow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01421437
12411372
23171372
33911372
44701372
55551372
66441372
77381372
88371372
99421372
1010511372
1111661372
1212851372
1314101372
1415391372
1516741372
1618131372
1719581372
1821071372
1922621372
2024211372
2125861372
2226221372
2326491372
2426491372
2527871372
2629551372
2731341372
2833171372
2935061372
3036991372
3138981372
3241011372
3343101372
3445231372
3547421372
3647501372
3747541372
3847541372
3949751372
Stop Event
1×node limit
Counts
118 → 133

prune115.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1303133
Fresh077
Picked011
Done011
Total13012142
Error
5.8b
Counts
142 → 12
Alt Table
StatusErrorProgram
48.4b
(pow.f64 (*.f64 (*.f64 (cbrt.f64 -1/2) (cbrt.f64 2)) (cbrt.f64 (/.f64 b a))) 3)
▶36.4b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
56.6b
(pow.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (+.f64 a a))))) (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (+.f64 a a))))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (+.f64 a a))))))) 3)
37.2b
(*.f64 -1 (/.f64 c b))
✓35.9b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
47.9b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)) 3))
54.7b
(/.f64 (-.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a))
42.6b
(pow.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (neg.f64 (*.f64 4 (*.f64 c a))) b)) (*.f64 a 2))) 3)
43.6b
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
48.1b
(-.f64 (/.f64 c b) (/.f64 b a))
47.9b
(*.f64 -1 (/.f64 b a))
✓34.9b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
Compiler

Compiled 4919 to 3291 computations (33.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
1.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
✓13.4b
(-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2))
✓26.5b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4)

series132.0ms (1.4%)

Counts
3 → 92
Calls

27 calls:

9.0ms
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
b
0
7.0ms
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
a
-inf
7.0ms
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
a
inf
7.0ms
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
c
inf
7.0ms
(pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)
c
-inf

rewrite50.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
369×log-prod_binary64
268×expm1-udef_binary64
268×log1p-udef_binary64
265×log-pow_binary64
155×log1p-expm1-u_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01553
131051
2329049
Stop Event
1×node limit
Counts
3 → 74

simplify271.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
1134×pow-sqr_binary64
923×sqr-pow_binary64
468×fma-neg_binary64
73×fma-def_binary64
44×rem-sqrt-square_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03194531
14624531
26034531
37894531
49904531
512284531
615964531
721404531
830984531
947044531
1049204531
1149344531
1249384531
1349384531
Stop Event
1×node limit
Counts
166 → 198

prune194.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2402242
Fresh459
Picked011
Done022
Total24410254
Error
0.9b
Counts
254 → 10
Alt Table
StatusErrorProgram
53.6b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
43.6b
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
52.1b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))
48.1b
(-.f64 (/.f64 c b) (/.f64 b a))
✓35.9b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
47.9b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)) 3))
✓36.4b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
42.6b
(pow.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (neg.f64 (*.f64 4 (*.f64 c a))) b)) (*.f64 a 2))) 3)
▶37.2b
(*.f64 -1 (/.f64 c b))
✓34.9b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
Compiler

Compiled 9785 to 6440 computations (34.2% saved)

localize3.0ms (0%)

prune6.0ms (0.1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done033
Total01010
Error
0.9b
Counts
10 → 10
Alt Table
StatusErrorProgram
53.6b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2)) (*.f64 2 a))
43.6b
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
52.1b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)) (*.f64 2 a))
48.1b
(-.f64 (/.f64 c b) (/.f64 b a))
✓35.9b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
47.9b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2)) 3))
✓36.4b
(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
42.6b
(pow.f64 (cbrt.f64 (/.f64 (*.f64 1/2 (/.f64 (neg.f64 (*.f64 4 (*.f64 c a))) b)) (*.f64 a 2))) 3)
✓37.2b
(*.f64 -1 (/.f64 c b))
✓34.9b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (neg.f64 (*.f64 4 (*.f64 a c)))))) (*.f64 a 2))) 3)
Compiler

Compiled 190 to 145 computations (23.7% saved)

regimes715.0ms (7.5%)

Accuracy

Total 9.0b remaining (90.9%)

Threshold costs 0b (0%)

Counts
40 → 3
Compiler

Compiled 3416 to 2534 computations (25.8% saved)

bsearch51.0ms (0.5%)

Algorithm
2×binary-search
Calls

2 calls:

26.0ms
b
24.0ms
b
Steps
ItersPointRange
8.202693601055587e+127
∈ [
2.8915325345551915e+122
, 
1.023616106515249e+128
]
-7.938665807053523e-52
∈ [
-2.2779147360256252e-51
, 
-6.694284446735352e-52
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02755
Stop Event
1×saturated

end366.0ms (3.8%)

Stop Event
1×fuel
Compiler

Compiled 270 to 195 computations (27.8% saved)

Profiling

Loading profile data...