Details

Time bar (total: 8.3s)

sample89.0ms

Algorithm
intervals
Results
29.0ms48×body1280valid
16.0ms167×body80valid
15.0ms39×body640valid
7.0ms122×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
31066
43044
57744
641424
750014

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×pow-unpow add-log-exp
2×cbrt-undiv pow-to-exp frac-2neg clear-num
1×pow-pow
Counts
3 → 172
Calls
3 calls:
24.0ms
(/ (pow (/ x (+ x y)) x) x)
5.0ms
(/ x (+ x y))
8.0ms
(pow (/ x (+ x y)) x)

series410.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(/ (pow (/ x (+ x y)) x) x)
43.0ms
(/ x (+ x y))
233.0ms
(pow (/ x (+ x y)) x)

simplify72.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05371436
126401406
250011406

prune397.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

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)

rewrite35.0ms

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×frac-times prod-exp add-cbrt-cube add-log-exp
2×pow-to-exp pow-pow pow1/3 associate-*r/ associate-*l/ div-inv sqr-pow
Counts
4 → 116
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)

series896.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt x)
177.0ms
(cbrt x)
263.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
279.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify64.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06911334
121641266
250011235

prune402.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.0b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b
(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite20.0ms

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×pow-exp add-cbrt-cube 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 → 104
Calls
4 calls:
0.0ms
(cbrt x)
1.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
13.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

series496.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt x)
28.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
31.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
262.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify54.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05401207
119151176
250011108

prune419.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (/ (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)
1.0b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
197×cbrt-prod
130×unpow-prod-down
106×times-frac
93×*-un-lft-identity
75×add-sqr-sqrt add-cube-cbrt
24×cbrt-div
12×add-exp-log
10×associate-/r/
9×distribute-lft-out
8×pow1 pow-unpow
7×flip3-+ flip-+
6×pow-exp
4×frac-times pow-to-exp pow-pow add-cbrt-cube add-log-exp sqr-pow
2×associate-*r/ div-exp associate-*l/ div-inv
Counts
4 → 184
Calls
4 calls:
13.0ms
(pow (/ (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)
1.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
22.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)

series600.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(pow (/ (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)
30.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
27.0ms
(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
266.0ms
(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)

simplify89.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
010343158
133283115
250023022

prune976.0ms

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

bsearch190.0ms

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
04442
14442

end0.0ms

sample2.7s

Algorithm
intervals
Results
937.0ms1560×body1280valid
553.0ms1430×body640valid
462.0ms4840×body80valid
224.0ms822×body320valid
198.0ms3004×body80nan
80.0ms434×body160valid