Details

Time bar (total: 9.2s)

analyze747.0ms (8.1%)

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
0%74.9%25.1%5
0%74.9%25.1%6
0%74.9%25.1%7
6.2%56.2%37.6%8
7.8%53%39.2%9
10.9%45.6%43.4%10
18.3%31.4%50.3%11
19.1%29.5%51.3%12
21.4%24.8%53.8%13
25.8%16.7%57.5%14
Compiler

Compiled 28 to 21 computations (25% saved)

sample2.1s (23%)

Results
1.7s8256×body128valid
326.0ms2034×body128invalid
Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify75.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
703×fma-def_binary64
691×associate-/l*_binary64
673×sub-neg_binary64
568×fma-neg_binary64
439×div-sub_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02132
14332
29931
322330
452930
5101630
6191730
7300130
8339630
9483030
10511030

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.6b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
▶6.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
Compiler

Compiled 150 to 107 computations (28.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
✓0.1b
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
✓0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓6.1b
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series65.0ms (0.7%)

Counts
4 → 84
Calls

4 calls:

39.0ms
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
10.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
8.0ms
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
8.0ms
(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
9×prod-diff_binary64
9×times-frac_binary64
Counts
4 → 80
Calls

4 calls:

3.0ms
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)
2.0ms
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)
0.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
0.0ms
(fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)

simplify158.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
646×times-frac_binary64
501×fma-neg_binary64
456×distribute-rgt-in_binary64
422×distribute-lft-in_binary64
375×cancel-sign-sub-inv_binary64
Counts
164 → 176
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02003470
14453008
216162849
346502833
449932833
549902833
649042833

prune257.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New16313176
Fresh101
Picked101
Done000
Total16513178
Error
0.1b
Counts
178 → 13
Alt Table
StatusErrorProgram
10.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
7.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
20.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (*.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
6.6b
(+.f64 (-.f64 (+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 91893853320467/100000000000000) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
25.5b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000) x) 3)))
6.7b
(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
7.7b
(+.f64 (*.f64 -1 (*.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
7.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (-.f64 (+.f64 (*.f64 7936500793651/10000000000000000 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (*.f64 y (pow.f64 z 2)) x) (*.f64 83333333333333/1000000000000000 (/.f64 1 x)))) (*.f64 13888888888889/5000000000000000 (/.f64 z x))))
6.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x)) (sqrt.f64 x)))
10.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
38.4b
(+.f64 (log.f64 (/.f64 (exp.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (exp.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
▶0.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
Compiler

Compiled 5953 to 3811 computations (36% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)
✓0.4b
(/.f64 83333333333333/1000000000000000 x)
✓5.0b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series35.0ms (0.4%)

Counts
3 → 60
Calls

3 calls:

25.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
6.0ms
(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
4.0ms
(/.f64 83333333333333/1000000000000000 x)

rewrite18.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
19×add-cbrt-cube_binary64
Counts
3 → 93
Calls

3 calls:

7.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
6.0ms
(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms
(/.f64 83333333333333/1000000000000000 x)

simplify88.0ms (1%)

Algorithm
1×egg-herbie
Rules
701×fma-def_binary64
596×associate-*l/_binary64
452×associate-*r/_binary64
331×distribute-rgt-in_binary64
326×distribute-lft-in_binary64
Counts
153 → 140
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01911847
14491683
213431683
344911683
449851683

prune303.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1635168
Fresh4812
Picked101
Done000
Total16813181
Error
0.0b
Counts
181 → 13
Alt Table
StatusErrorProgram
10.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
7.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
20.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (*.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
1.0b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
7.7b
(+.f64 (*.f64 -1 (*.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
16.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 83333333333333/1000000000000000 x) 3)) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
▶0.9b
(+.f64 (-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
1.0b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
10.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
38.4b
(+.f64 (log.f64 (/.f64 (exp.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (exp.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
4.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
Compiler

Compiled 6788 to 3808 computations (43.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 z (/.f64 z x))
0.2b
(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
0.4b
(/.f64 83333333333333/1000000000000000 x)
5.0b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series9.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

9.0ms
(*.f64 z (/.f64 z x))

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
9×*-un-lft-identity_binary64
9×add-cube-cbrt_binary64
Counts
1 → 34
Calls

1 calls:

6.0ms
(*.f64 z (/.f64 z x))

simplify75.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
998×fma-neg_binary64
447×associate-/r*_binary64
409×*-commutative_binary64
353×associate-/r/_binary64
222×unswap-sqr_binary64
Counts
58 → 51
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
066565
1152499
2491499
31243491
42159491
53065491
64488491
75157491

prune356.0ms (3.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1910191
Fresh01212
Picked011
Done000
Total19113204
Error
0.0b
Counts
204 → 13
Alt Table
StatusErrorProgram
10.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
7.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
20.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (*.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
▶1.0b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
7.7b
(+.f64 (*.f64 -1 (*.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
16.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 83333333333333/1000000000000000 x) 3)) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
✓0.9b
(+.f64 (-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
1.0b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
10.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
38.4b
(+.f64 (log.f64 (/.f64 (exp.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (exp.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
4.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
Compiler

Compiled 7762 to 4309 computations (44.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.f64 83333333333333/1000000000000000 x)
✓0.4b
(*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))
5.0b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
✓16.7b
(cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))

series1.6s (16.9%)

Counts
2 → 72
Calls

2 calls:

875.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))
684.0ms
(cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))

rewrite25.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
70×associate-*r/_binary64
65×cbrt-div_binary64
51×frac-times_binary64
26×flip-+_binary64
26×flip3-+_binary64
Counts
2 → 84
Calls

2 calls:

7.0ms
(cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))
6.0ms
(*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))

simplify162.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
654×fma-def_binary64
217×distribute-rgt-in_binary64
212×fma-neg_binary64
203×distribute-lft-in_binary64
195×times-frac_binary64
Counts
156 → 199
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03285700
17645408
220314782
348024778
450004778

prune1.0s (11.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New5120512
Fresh01111
Picked011
Done011
Total51213525
Error
0.0b
Counts
525 → 13
Alt Table
StatusErrorProgram
10.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (expm1.f64 (log1p.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))) x))
7.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000))) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (*.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
20.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (fma.f64 z (/.f64 (*.f64 z (+.f64 7936500793651/10000000000000000 y)) x) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
✓1.0b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y)))) (cbrt.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
7.7b
(+.f64 (*.f64 -1 (*.f64 (+.f64 1 (log.f64 (/.f64 1 x))) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (fma.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
16.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 83333333333333/1000000000000000 x) 3)) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
✓0.9b
(+.f64 (-.f64 (+.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
1.0b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
10.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 z (+.f64 7936500793651/10000000000000000 y) -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
38.4b
(+.f64 (log.f64 (/.f64 (exp.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (exp.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
4.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
Compiler

Compiled 32431 to 17829 computations (45% saved)

regimes1.7s (18.8%)

Accuracy

Total 0.4b remaining (86%)

Threshold costs 0.4b (86%)

Counts
168 → 1
Compiler

Compiled 43257 to 29666 computations (31.4% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02548
14148
24648
34848
44948
54748

end310.0ms (3.4%)

Compiler

Compiled 521 to 357 computations (31.5% saved)

Profiling

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