Details

Time bar (total: 9.8s)

sample89.0ms

Algorithm
intervals
Results
29.0ms48×body1280valid
15.0ms167×body80valid
15.0ms39×body640valid
8.0ms122×body80nan
6.0ms23×body320valid
3.0ms18×body160valid

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (8.0ms)

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

localize9.0ms

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)

rewrite45.0ms

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:
24.0ms
(/ (pow (/ x (+ x y)) x) x)
5.0ms
(/ x (+ x y))
7.0ms
(pow (/ x (+ x y)) x)

series415.0ms

Counts
3 → 9
Calls
3 calls:
141.0ms
(/ (pow (/ x (+ x y)) x) x)
39.0ms
(/ x (+ x y))
235.0ms
(pow (/ x (+ x y)) x)

simplify76.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
05541456
127261426
250021426

prune423.0ms

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)

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:
0.0ms
(cbrt x)
4.0ms
(cbrt x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
15.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series925.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt x)
184.0ms
(cbrt x)
271.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
283.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify61.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
07081370
122441300
250021271

prune439.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
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)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
144×unpow-prod-down
138×cbrt-prod
126×times-frac
125×*-un-lft-identity
89×add-sqr-sqrt add-cube-cbrt
18×distribute-lft-out
13×add-exp-log
9×pow-unpow
7×pow1
6×cbrt-div pow-exp associate-/r/
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow flip3-+ div-exp flip-+ div-inv sqr-pow
1×pow1/3
Counts
4 → 208
Calls
4 calls:
0.0ms
(cbrt x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series986.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt x)
268.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
265.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
266.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify58.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04712350
115432326
250022257

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

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:
17.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
24.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)

series1.1s

Counts
4 → 12
Calls
4 calls:
283.0ms
(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)
271.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
272.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
268.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)

simplify115.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
012134043
137283935
250013804

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

98.3% (0.1b remaining)

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

bsearch174.0ms

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
03738
13738

end0.0ms

sample2.7s

Algorithm
intervals
Results
934.0ms1560×body1280valid
550.0ms1430×body640valid
455.0ms4840×body80valid
224.0ms822×body320valid
188.0ms3004×body80nan
82.0ms434×body160valid