Details

Time bar (total: 7.8s)

sample56.0ms

Algorithm
intervals
Results
20.0ms44×body1280valid
10.0ms40×body640valid
7.0ms174×body80valid
4.0ms25×body320valid
3.0ms89×body80nan
2.0ms18×body160valid

simplify111.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (8.0ms)

IterNodesCost
0156
1246
2516
31086
43104
57924
641924
750024

prune4.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 11.5b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow (/ x (+ x y)) x) x)
0.0b
(/ x (+ x y))
7.6b
(pow (/ x (+ x y)) x)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
118×*-un-lft-identity
90×unpow-prod-down
80×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
19×distribute-lft-out
16×add-exp-log
12×associate-/r/
7×div-exp associate-/r* add-cbrt-cube div-inv
6×flip3-+ flip-+
5×sqr-pow
4×pow1 pow-exp
3×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
2×cbrt-undiv pow-to-exp frac-2neg clear-num
1×pow-pow
Counts
3 → 178
Calls
3 calls:
11.0ms
(/ (pow (/ x (+ x y)) x) x)
5.0ms
(/ x (+ x y))
7.0ms
(pow (/ x (+ x y)) x)

series406.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(/ (pow (/ x (+ x y)) x) x)
44.0ms
(/ x (+ x y))
231.0ms
(pow (/ x (+ x y)) x)

simplify82.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
05541456
127261426
250021426

prune409.0ms

Filtered
187 candidates to 137 candidates (73.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1816187
Fresh000
Picked101
Done000
Total1826188

Merged error: 0.3b

Counts
188 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.1b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
61×unpow-prod-down
51×cbrt-prod
48×*-un-lft-identity
43×times-frac
36×add-sqr-sqrt add-cube-cbrt
20×add-exp-log
14×cbrt-div
10×associate-/r/
7×flip3-+ pow-exp flip-+
6×pow1 pow-unpow distribute-lft-out
5×div-exp
4×expm1-log1p-u frac-times prod-exp add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow pow1/3 associate-*r/ associate-*l/ div-inv sqr-pow
Counts
4 → 124
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
11.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
20.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series902.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt x)
185.0ms
(cbrt x)
265.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
276.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify62.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
07081370
122441300
250021271

prune439.0ms

Filtered
136 candidates to 98 candidates (72.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1333136
Fresh325
Picked101
Done000
Total1375142

Merged error: 0.0b

Counts
142 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.1b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.1b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.1b
(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
54×unpow-prod-down
48×cbrt-prod
47×*-un-lft-identity
42×times-frac
35×add-sqr-sqrt add-cube-cbrt
9×add-exp-log
7×pow1
6×distribute-lft-out
5×pow-unpow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow sqr-pow
2×cbrt-div associate-/r/
1×flip3-+ pow1/3 div-exp flip-+ div-inv
Counts
4 → 112
Calls
4 calls:
1.0ms
(cbrt x)
2.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
2.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
11.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series536.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(cbrt x)
26.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
26.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
269.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify57.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05551252
119821220
250011155

prune447.0ms

Filtered
124 candidates to 91 candidates (73.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1240124
Fresh044
Picked011
Done000
Total1245129

Merged error: 0.0b

Counts
129 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt x))
1.1b
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
1.1b
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
2.0b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
198×cbrt-prod
122×unpow-prod-down
92×times-frac
87×*-un-lft-identity
69×add-sqr-sqrt add-cube-cbrt
40×cbrt-div
33×add-exp-log
18×associate-/r/
13×flip3-+ flip-+
12×pow-exp
9×pow-unpow div-exp distribute-lft-out
8×frac-times prod-exp
7×pow1
4×expm1-log1p-u associate-*r/ associate-*l/ add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow div-inv sqr-pow
1×pow1/3
Counts
4 → 195
Calls
4 calls:
2.0ms
(cbrt (cbrt x))
17.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
21.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
15.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.2s

Counts
4 → 12
Calls
4 calls:
413.0ms
(cbrt (cbrt x))
256.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
275.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
274.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify94.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
011903102
134902979
250012889

prune817.0ms

Filtered
207 candidates to 134 candidates (64.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2061207
Fresh123
Picked101
Done011
Total2084212

Merged error: 0.0b

Counts
212 → 4

regimes85.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.7b

bsearch71.0ms

Steps
ItersRangePoint
8
3.458388425568309
13523.20185778739
3518.8334927999977
6
-2.370921026105228e+23
-2.691452647283223e+22
-2.830648860129908e+22

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03327
13327

end0.0ms

sample1.8s

Algorithm
intervals
Results
665.0ms1515×body1280valid
366.0ms1469×body640valid
211.0ms4842×body80valid
134.0ms837×body320valid
96.0ms2978×body80nan
49.0ms477×body160valid