Details

Time bar (total: 10.5s)

analyze661.0ms (6.3%)

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%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)

sample1.8s (17.3%)

Results
1.4s8256×body128valid
335.0ms2017×body128invalid
Compiler

Compiled 83 to 62 computations (25.3% saved)

simplify78.0ms (0.7%)

Algorithm
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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
4.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
4.8b
(+.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))
4.8b
(+.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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.1b
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
4.5b
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)

series87.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

49.0ms
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)
14.0ms
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
13.0ms
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
11.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))

rewrite87.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
237×add-sqr-sqrt_binary64
229×log1p-expm1-u_binary64
229×expm1-log1p-u_binary64
224×add-log-exp_binary64
223×add-exp-log_binary64
Counts
4 → 109
Calls

4 calls:

84.0ms
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
84.0ms
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)
84.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
84.0ms
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02051
147351
2489651
3482651
000
100

simplify103.0ms (1%)

Algorithm
egg-herbie
Rules
797×div-sub_binary64
487×fma-neg_binary64
330×associate--l+_binary64
330×sub-neg_binary64
320×cancel-sign-sub-inv_binary64
Counts
181 → 145
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
0871593
12531476
26441358
31807960
44284960
54985952
65645952

prune243.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New13411145
Fresh101
Picked101
Done000
Total13611147
Error
1.4b
Counts
147 → 11
Alt Table
StatusErrorProgram
5.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) (sqrt.f64 x))))
9.7b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.2b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)) 2) (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))))
21.5b
(+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2) 8444480278083503881401098089/10000000000000000000000000000) (-.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))
4.8b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.3b
(+.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (cbrt.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))
9.5b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
4.9b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.3b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) 2) (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.0b
(+.f64 (pow.f64 (sqrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.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))))
Compiler

Compiled 5060 to 3419 computations (32.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)
0.1b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000)
0.2b
(fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x))
4.5b
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)

series28.0ms (0.3%)

Counts
3 → 48
Calls

3 calls:

10.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x))
9.0ms
(*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)
9.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000)

rewrite97.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
359×prod-diff_binary64
211×egg-rr
194×add-sqr-sqrt_binary64
186×log1p-expm1-u_binary64
186×expm1-log1p-u_binary64
Counts
3 → 211
Calls

3 calls:

91.0ms
(*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z)
91.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000)
91.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01738
138734
2455734
3505834
000
100

simplify95.0ms (0.9%)

Algorithm
egg-herbie
Rules
675×sub-neg_binary64
590×fma-def_binary64
552×distribute-neg-in_binary64
461×neg-mul-1_binary64
339×distribute-neg-out_binary64
Counts
259 → 235
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
062690
1163600
2431572
31122518
43277518
54076518
64746518
74865518

prune426.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2743277
Fresh1910
Picked101
Done000
Total27612288
Error
1.4b
Counts
288 → 12
Alt Table
StatusErrorProgram
9.5b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
16.2b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 3) -2679183813443137002743484225480109739369/125000000000000000000000000000000000000000000000) z) (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 2) (+.f64 192901234567904320987654321/25000000000000000000000000000000 (*.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000)))) 83333333333333/1000000000000000) x))
5.5b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (+.f64 7936500793651/10000000000000000 y) (pow.f64 z 2)) 83333333333333/1000000000000000) x))
4.9b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
9.7b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.3b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) 2) (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.2b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)) 2) (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))))
21.5b
(+.f64 (/.f64 (-.f64 (pow.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2) 8444480278083503881401098089/10000000000000000000000000000) (-.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))
9.7b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.0b
(+.f64 (pow.f64 (sqrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.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))))
5.3b
(+.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (cbrt.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 10515 to 6261 computations (40.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)))
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
0.4b
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
4.5b
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)

series117.0ms (1.1%)

Counts
2 → 10
Calls

2 calls:

89.0ms
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
28.0ms
(sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)))

rewrite104.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
471×log-prod_binary64
439×prod-diff_binary64
233×fma-def_binary64
203×egg-rr
196×expm1-udef_binary64
Counts
2 → 203
Calls

2 calls:

97.0ms
(sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)))
97.0ms
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01128
124324
2273024
3528724
000
100

simplify52.0ms (0.5%)

Algorithm
egg-herbie
Rules
708×fma-def_binary64
572×associate-/l/_binary64
346×cancel-sign-sub-inv_binary64
265×times-frac_binary64
248×unswap-sqr_binary64
Counts
213 → 216
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040274
1115246
2355231
31990222
44922222
55026222

prune751.0ms (7.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New3335338
Fresh11011
Picked101
Done000
Total33515350
Error
1.4b
Counts
350 → 15
Alt Table
StatusErrorProgram
9.5b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
16.2b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 3) -2679183813443137002743484225480109739369/125000000000000000000000000000000000000000000000) z) (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 2) (+.f64 192901234567904320987654321/25000000000000000000000000000000 (*.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000)))) 83333333333333/1000000000000000) x))
31.0b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (*.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.5b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (+.f64 7936500793651/10000000000000000 y) (pow.f64 z 2)) 83333333333333/1000000000000000) x))
47.4b
(+.f64 (+.f64 (fma.f64 (sqrt.f64 (log.f64 x)) (*.f64 (sqrt.f64 (log.f64 x)) (-.f64 x 1/2)) (neg.f64 (*.f64 (/.f64 1 (+.f64 x 91893853320467/100000000000000)) (fma.f64 x x -8444480278083503881401098089/10000000000000000000000000000)))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 x 91893853320467/100000000000000))) (fma.f64 x x -8444480278083503881401098089/10000000000000000000000000000) (*.f64 (/.f64 1 (+.f64 x 91893853320467/100000000000000)) (fma.f64 x x -8444480278083503881401098089/10000000000000000000000000000)))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
9.7b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.3b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) 2) (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
7.0b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.0b
(+.f64 (pow.f64 (sqrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
4.9b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.3b
(+.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (cbrt.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))
9.7b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.2b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)) 2) (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))))
5.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.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))))
5.2b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)))) 3) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
Compiler

Compiled 17348 to 12451 computations (28.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
0.4b
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
0.5b
(pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2)
4.5b
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x)

series127.0ms (1.2%)

Counts
2 → 18
Calls

2 calls:

96.0ms
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
30.0ms
(pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2)

rewrite104.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
439×prod-diff_binary64
246×fma-def_binary64
237×expm1-udef_binary64
237×log1p-udef_binary64
189×egg-rr
Counts
2 → 189
Calls

2 calls:

96.0ms
(fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2) (neg.f64 (-.f64 x 91893853320467/100000000000000)))
96.0ms
(pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01528
131524
2329324
3475324
000
100

simplify79.0ms (0.8%)

Algorithm
egg-herbie
Rules
398×fma-neg_binary64
376×cancel-sign-sub-inv_binary64
185×unswap-sqr_binary64
184×times-frac_binary64
176×div-sub_binary64
Counts
207 → 222
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01651913
15681724
225631232
345221052
451381052

prune1.5s (14.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New3062308
Fresh21214
Picked101
Done000
Total30914323
Error
1.4b
Counts
323 → 14
Alt Table
StatusErrorProgram
9.5b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) 1) (/.f64 (sqrt.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000)) x)))
16.2b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 3) -2679183813443137002743484225480109739369/125000000000000000000000000000000000000000000000) z) (+.f64 (pow.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 2) (+.f64 192901234567904320987654321/25000000000000000000000000000000 (*.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000)))) 83333333333333/1000000000000000) x))
31.0b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (*.f64 (sqrt.f64 (-.f64 x 1/2)) (sqrt.f64 (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
9.7b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 83333333333333/1000000000000000 x))
5.3b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) 2) (cbrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
31.1b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (*.f64 (pow.f64 (pow.f64 (-.f64 x 1/2) 1/4) 2) (pow.f64 (pow.f64 (log.f64 x) 1/4) 2)) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
7.0b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))))) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.0b
(+.f64 (pow.f64 (sqrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
5.5b
(+.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (neg.f64 x)) 91893853320467/100000000000000) (/.f64 (+.f64 (*.f64 (+.f64 7936500793651/10000000000000000 y) (pow.f64 z 2)) 83333333333333/1000000000000000) x))
5.2b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (*.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x)) 2) (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7936500793651/10000000000000000) z -13888888888889/5000000000000000) 83333333333333/1000000000000000) x))))
5.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000) (-.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))))
5.3b
(+.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 91893853320467/100000000000000)) 2) (cbrt.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))
5.2b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)))) 3) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7936500793651/10000000000000000) z) 13888888888889/5000000000000000) z) 83333333333333/1000000000000000) x))
9.9b
(+.f64 (fma.f64 (sqrt.f64 (*.f64 (-.f64 x 1/2) (log.f64 x))) (pow.f64 (pow.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) 1/4) 2) (neg.f64 (-.f64 x 91893853320467/100000000000000))) (/.f64 83333333333333/1000000000000000 x))
Compiler

Compiled 17200 to 12539 computations (27.1% saved)

regimes3.5s (33.1%)

Accuracy

Total 0.6b remaining (18%)

Threshold costs 0.6b (18%)

Counts
224 → 3
Compiler

Compiled 56582 to 41852 computations (26% saved)

bsearch12.0ms (0.1%)

Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
038113
156113
261113
362113
460113

end374.0ms (3.5%)

Compiler

Compiled 664 to 488 computations (26.5% saved)

Profiling

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