Details

Time bar (total: 8.6s)

sample55.0ms

Algorithm
intervals
Results
15.0ms35×body1280valid
11.0ms47×body640valid
6.0ms157×body80valid
5.0ms31×body320valid
3.0ms92×body80nan
2.0ms20×body160valid

simplify116.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (9.0ms)

IterNodesCost
0156
1246
2516
31086
43104
57924
641924
750024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x y))
0.0b
(/ (pow (/ x (+ x y)) x) x)
8.3b
(pow (/ x (+ x y)) x)

rewrite74.0ms

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:
10.0ms
(/ x (+ x y))
42.0ms
(/ (pow (/ x (+ x y)) x) x)
13.0ms
(pow (/ x (+ x y)) x)

series373.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ x (+ x y))
122.0ms
(/ (pow (/ x (+ x y)) x) x)
213.0ms
(pow (/ x (+ x y)) x)

simplify76.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05541456
127261426
250031426

prune385.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ x y))
0.6b
(cbrt (+ x y))
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.2b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
61×unpow-prod-down
53×cbrt-prod
52×*-un-lft-identity
43×times-frac
36×add-sqr-sqrt add-cube-cbrt
20×add-exp-log
18×cbrt-div
10×associate-/r/
9×flip3-+ flip-+
8×distribute-lft-out
7×pow-exp
6×pow1 pow-unpow
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 → 130
Calls
4 calls:
4.0ms
(cbrt (+ x y))
4.0ms
(cbrt (+ x y))
18.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
29.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series755.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(cbrt (+ x y))
123.0ms
(cbrt (+ x y))
247.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
256.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify68.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
07461470
123311394
250011363

prune462.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ x y))
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
144×unpow-prod-down
139×cbrt-prod
127×*-un-lft-identity
126×times-frac
89×add-sqr-sqrt add-cube-cbrt
19×distribute-lft-out
13×add-exp-log
9×pow-unpow
8×cbrt-div
7×pow1
6×pow-exp associate-/r/
4×expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow div-exp div-inv sqr-pow
1×pow1/3
Counts
4 → 211
Calls
4 calls:
4.0ms
(cbrt (+ x y))
18.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
22.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
19.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series895.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (+ x y))
259.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
257.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
254.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify64.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05092400
116882373
250012303

prune644.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
0.7b
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
279×cbrt-prod
205×unpow-prod-down
175×times-frac
163×*-un-lft-identity
121×add-sqr-sqrt add-cube-cbrt
32×cbrt-div
26×add-exp-log
21×distribute-lft-out
14×associate-/r/
12×pow-unpow
11×pow-exp
9×flip3-+ flip-+
8×pow1
7×div-exp
4×expm1-log1p-u frac-times pow-to-exp pow-pow prod-exp add-cbrt-cube log1p-expm1-u div-inv add-log-exp sqr-pow
2×associate-*r/ associate-*l/
Counts
4 → 276
Calls
4 calls:
31.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
30.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
18.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
19.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series1.0s

Counts
4 → 12
Calls
4 calls:
269.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
258.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
256.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
252.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify112.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
012134043
137283935
250023804

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

95.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 6.1b

bsearch108.0ms

Steps
ItersRangePoint
6
8.43303239383745e-08
7.803840110207806e-07
7.683820352854433e-07
9
-5.3299012796639375e+97
-6.787168950808416e+90
-6.878253153357071e+90

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03738
13738

end0.0ms

sample1.9s

Algorithm
intervals
Results
684.0ms1580×body1280valid
365.0ms1463×body640valid
208.0ms4762×body80valid
143.0ms860×body320valid
86.0ms2996×body80nan
49.0ms481×body160valid