Details

Time bar (total: 7.8s)

sample60.0ms

Algorithm
intervals
Results
22.0ms48×body1280valid
10.0ms39×body640valid
7.0ms167×body80valid
4.0ms23×body320valid
4.0ms122×body80nan
2.0ms18×body160valid

simplify119.0ms

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: 10.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow (/ x (+ x y)) x) x)
0.0b
(/ x (+ x y))
5.6b
(pow (/ x (+ x y)) x)

rewrite49.0ms

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:
27.0ms
(/ (pow (/ x (+ x y)) x) x)
5.0ms
(/ x (+ x y))
8.0ms
(pow (/ x (+ x y)) x)

series406.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(/ (pow (/ x (+ x y)) x) x)
38.0ms
(/ x (+ x y))
233.0ms
(pow (/ x (+ x y)) x)

simplify74.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05541456
127251426
250011426

prune590.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite34.0ms

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:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
13.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
16.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series886.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt x)
176.0ms
(cbrt x)
260.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
268.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify73.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
07081370
122441300
250021271

prune440.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
4.1b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
96×cbrt-prod
85×*-un-lft-identity
84×times-frac
61×add-sqr-sqrt add-cube-cbrt
48×unpow-prod-down log-prod
12×distribute-lft-out
10×add-exp-log
6×pow1
4×expm1-log1p-u cbrt-div associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow
2×flip3-+ pow1/3 div-exp rem-log-exp pow-exp flip-+ div-inv
1×pow-to-exp log-div pow-pow log-pow sqr-pow
Counts
4 → 152
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
13.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
7.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt x)
176.0ms
(cbrt x)
267.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
75.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify58.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06121563
119281530
250021462

prune547.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.0b
(pow (* (cbrt (/ (cbrt x) (cbrt (+ x y)))) (cbrt (/ (cbrt x) (cbrt (+ x y))))) x)
1.0b
(pow (cbrt (/ (cbrt x) (cbrt (+ x y)))) x)
4.1b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
141×cbrt-prod
86×*-un-lft-identity
84×times-frac
62×add-sqr-sqrt add-cube-cbrt
52×unpow-prod-down
48×log-prod
14×pow1
12×distribute-lft-out
11×add-exp-log pow-pow
8×pow1/3
6×pow-unpow
4×expm1-log1p-u cbrt-div associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-exp
2×pow-to-exp flip3-+ rem-log-exp pow-prod-down pow-sqr pow-prod-up flip-+ div-inv sqr-pow
1×pow2 log-div pow-plus div-exp prod-exp log-pow
Counts
4 → 168
Calls
4 calls:
1.0ms
(cbrt x)
17.0ms
(pow (* (cbrt (/ (cbrt x) (cbrt (+ x y)))) (cbrt (/ (cbrt x) (cbrt (+ x y))))) x)
16.0ms
(pow (cbrt (/ (cbrt x) (cbrt (+ x y)))) x)
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series799.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt x)
271.0ms
(pow (* (cbrt (/ (cbrt x) (cbrt (+ x y)))) (cbrt (/ (cbrt x) (cbrt (+ x y))))) x)
266.0ms
(pow (cbrt (/ (cbrt x) (cbrt (+ x y)))) x)
73.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify73.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
07921945
124271884
250021818

prune743.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 6.2b

bsearch127.0ms

Steps
ItersRangePoint
11
1.7382738099505427e-22
8982319.97820102
18.0707144555821
9
-1.3447839841174185e+67
-6.096508117060729e+60
-9.605913011761164e+60

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03732
13732

end0.0ms

sample1.8s

Algorithm
intervals
Results
677.0ms1560×body1280valid
366.0ms1430×body640valid
210.0ms4840×body80valid
134.0ms822×body320valid
88.0ms3004×body80nan
44.0ms434×body160valid