Details

Time bar (total: 7.8s)

analyze591.0ms (7.6%)

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)

sample98.0ms (1.3%)

Algorithm
1×intervals
Results
25.0ms256×body128valid
4.0ms41×body128invalid
2.0ms23×body128nan
Compiler

Compiled 58 to 44 computations (24.1% saved)

simplify75.0ms (1%)

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

prune5.0ms (0.1%)

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 (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))
6.6b
(+.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))
Compiler

Compiled 150 to 107 computations (28.7% saved)

localize17.0ms (0.2%)

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)
✓0.2b
(-.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)
✓6.2b
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)

series74.0ms (0.9%)

Counts
4 → 84
Calls

4 calls:

47.0ms
(/.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)
9.0ms
(-.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)

rewrite10.0ms (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 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)
0.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)

simplify161.0ms (2.1%)

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

prune273.0ms (3.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New16214176
Fresh101
Picked101
Done000
Total16414178
Error
0.0b
Counts
178 → 14
Alt Table
StatusErrorProgram
7.0b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.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))
28.8b
(+.f64 (-.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000)) (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))
6.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
8.0b
(+.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))
▶0.6b
(+.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)))
9.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
6.6b
(+.f64 (+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 91893853320467/100000000000000 x)) (/.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))
6.8b
(+.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))
20.4b
(+.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 91893853320467/100000000000000 (*.f64 (log.f64 x) x)) (+.f64 (*.f64 1/2 (log.f64 x)) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x))))
7.0b
(+.f64 (fma.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)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
Compiler

Compiled 6087 to 3895 computations (36% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.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)
✓4.2b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series39.0ms (0.5%)

Counts
3 → 60
Calls

3 calls:

29.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))
8.0ms
(*.f64 (/.f64 z x) -13888888888889/5000000000000000)
2.0ms
(/.f64 83333333333333/1000000000000000 x)

rewrite20.0ms (0.3%)

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

simplify86.0ms (1.1%)

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

prune320.0ms (4.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1662168
Fresh21113
Picked011
Done000
Total16814182
Error
0.0b
Counts
182 → 14
Alt Table
StatusErrorProgram
7.0b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.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))
6.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
8.0b
(+.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))
9.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
▶0.7b
(+.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)))
6.6b
(+.f64 (+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 91893853320467/100000000000000 x)) (/.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))
6.8b
(+.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))
20.4b
(+.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 91893853320467/100000000000000 (*.f64 (log.f64 x) x)) (+.f64 (*.f64 1/2 (log.f64 x)) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
6.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x))))
✓0.6b
(+.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)))
7.0b
(+.f64 (fma.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)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
27.6b
(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000) 3)) 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 6804 to 3829 computations (43.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)
0.4b
(/.f64 83333333333333/1000000000000000 x)
✓0.4b
(*.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)))
4.2b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series16.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

8.0ms
(*.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)))
8.0ms
(fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)

rewrite11.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
18×sqrt-prod_binary64
17×pow1_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 63
Calls

2 calls:

6.0ms
(*.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)))
0.0ms
(fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)

simplify95.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
472×fma-def_binary64
460×fma-neg_binary64
446×unswap-sqr_binary64
434×times-frac_binary64
298×unsub-neg_binary64
Counts
87 → 71
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0831430
11561139
23911092
312801006
427811006
541491006
649491006

prune323.0ms (4.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1573160
Fresh11112
Picked011
Done101
Total15915174
Error
0.0b
Counts
174 → 15
Alt Table
StatusErrorProgram
7.0b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.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))
6.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
8.0b
(+.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))
6.6b
(+.f64 (-.f64 (+.f64 91893853320467/100000000000000 (*.f64 (log.f64 x) x)) (+.f64 (*.f64 1/2 (log.f64 x)) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
0.9b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
6.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x))))
▶0.8b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (sqrt.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)))
9.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
✓0.7b
(+.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)))
6.6b
(+.f64 (+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 91893853320467/100000000000000 x)) (/.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))
6.8b
(+.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))
20.4b
(+.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)))
1.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) (*.f64 (cbrt.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)))
7.0b
(+.f64 (fma.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)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
Compiler

Compiled 8155 to 4928 computations (39.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (sqrt.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))))
0.4b
(/.f64 83333333333333/1000000000000000 x)
✓0.4b
(*.f64 (sqrt.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)))
4.2b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))

series843.0ms (10.8%)

Counts
2 → 24
Calls

2 calls:

832.0ms
(*.f64 (sqrt.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)))
10.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (sqrt.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))))

rewrite30.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
51×sqrt-pow1_binary64
48×pow1_binary64
42×add-sqr-sqrt_binary64
37×sqrt-prod_binary64
36×pow-prod-up_binary64
Counts
2 → 100
Calls

2 calls:

11.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (sqrt.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))))
6.0ms
(*.f64 (sqrt.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)))

simplify208.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
889×associate-/l*_binary64
771×fma-def_binary64
303×*-commutative_binary64
190×+-commutative_binary64
171×associate-+r+_binary64
Counts
124 → 152
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
080214362
1291613231
2526713231

prune817.0ms (10.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New2352237
Fresh11213
Picked011
Done101
Total23715252
Error
0.0b
Counts
252 → 15
Alt Table
StatusErrorProgram
7.0b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x)) (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x))) (cbrt.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))
6.6b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 1 (/.f64 x (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000))))
8.0b
(+.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))
6.6b
(+.f64 (-.f64 (+.f64 91893853320467/100000000000000 (*.f64 (log.f64 x) x)) (+.f64 (*.f64 1/2 (log.f64 x)) x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
0.9b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) 3)) x) (+.f64 (+.f64 (/.f64 83333333333333/1000000000000000 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7936500793651/10000000000000000 y))) (*.f64 (/.f64 z x) -13888888888889/5000000000000000)))
6.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x))))
✓0.8b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (sqrt.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)))
9.9b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 91893853320467/100000000000000) x) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) (/.f64 x (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)))))
6.6b
(+.f64 (+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 91893853320467/100000000000000 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
1.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)) (cbrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.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)))
20.4b
(+.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)))
1.1b
(+.f64 (-.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (cbrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) (*.f64 (cbrt.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)))
7.0b
(+.f64 (fma.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)) (neg.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))
1.1b
(+.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000)))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 91893853320467/100000000000000))))) (*.f64 (cbrt.f64 (sqrt.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)))
6.8b
(+.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))
Compiler

Compiled 27784 to 20868 computations (24.9% saved)

regimes1.6s (20.9%)

Accuracy

Total 0.4b remaining (88.7%)

Threshold costs 0.4b (88.7%)

Counts
140 → 1
Compiler

Compiled 37735 to 26435 computations (29.9% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
5×*-commutative_binary64
3×sub-neg_binary64
1×*-lft-identity_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02543
14043
24543
34743
44843
54543

end1.0ms (0%)

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample2.0s (25.7%)

Algorithm
1×intervals
Results
987.0ms8000×body128valid
110.0ms1224×body128invalid
57.0ms683×body128nan
Compiler

Compiled 675 to 470 computations (30.4% saved)

Profiling

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