Details

Time bar (total: 6.7s)

sample60.0ms

Algorithm
intervals
Results
21.0ms48×body1280valid
13.0ms45×body640valid
7.0ms159×body80valid
6.0ms36×body320valid
2.0ms82×body80nan
1.0ms6×body160valid

simplify114.0ms

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: 9.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x y))
0.1b
(* x (log (/ x (+ x y))))
8.0b
(log (/ x (+ x y)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
54×log-prod
48×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt
18×distribute-rgt-in distribute-lft-in
13×distribute-lft-out
10×add-exp-log
8×associate-/r/
7×pow1 add-cbrt-cube
4×flip3-+ associate-*r* associate-/r* flip-+ div-inv
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp
2×div-exp rem-log-exp log-pow
1×cbrt-undiv log-div frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 123
Calls
3 calls:
6.0ms
(/ x (+ x y))
11.0ms
(* x (log (/ x (+ x y))))
4.0ms
(log (/ x (+ x y)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ x (+ x y))
75.0ms
(* x (log (/ x (+ x y))))
49.0ms
(log (/ x (+ x y)))

simplify104.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0302874
11266813
24974783
35001783

prune271.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
96×cbrt-prod log-prod
84×*-un-lft-identity times-frac
60×add-sqr-sqrt add-cube-cbrt
12×distribute-lft-out
10×add-exp-log
6×pow1
4×expm1-log1p-u cbrt-div rem-log-exp associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
2×log-div flip3-+ pow1/3 div-exp log-pow flip-+ div-inv
Counts
4 → 148
Calls
4 calls:
0.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series497.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
175.0ms
(cbrt x)
71.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
72.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify82.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03181502
17721456
223601424
350021350

prune556.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt x))
0.6b
(cbrt (* (cbrt x) (cbrt x)))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
14.3b
(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
61×log-prod
59×cbrt-prod
50×*-un-lft-identity
49×times-frac
36×add-sqr-sqrt add-cube-cbrt
13×add-exp-log
7×distribute-lft-out
6×pow1
5×rem-log-exp
4×expm1-log1p-u cbrt-div associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×div-exp
2×log-div flip3-+ pow1/3 log-pow flip-+ div-inv
1×prod-exp
Counts
4 → 115
Calls
4 calls:
1.0ms
(cbrt (cbrt x))
3.0ms
(cbrt (* (cbrt x) (cbrt x)))
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms
(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

series674.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (cbrt x))
278.0ms
(cbrt (* (cbrt x) (cbrt x)))
73.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms
(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify140.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 3 (128.0ms)

IterNodesCost
04031257
19991188
241351169
350011164

prune606.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt x))
3.0b
(log (/ (cbrt x) (cbrt (+ x y))))
4.4b
(pow (* (cbrt x) (cbrt x)) 1/3)
40.3b
(log (/ (* (pow (* (cbrt x) (cbrt x)) 1/3) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
61×log-prod
58×cbrt-prod
51×*-un-lft-identity
49×times-frac
37×add-sqr-sqrt add-cube-cbrt
25×add-exp-log
14×pow1
9×pow-pow
8×rem-log-exp
7×pow1/3 distribute-lft-out
6×div-exp prod-exp
4×expm1-log1p-u cbrt-div pow-exp associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-to-exp log-div flip3-+ pow-prod-down pow-sqr log-pow pow-prod-up flip-+ div-inv
1×pow2 unpow-prod-down pow-plus unpow1/3 sqr-pow
Counts
4 → 134
Calls
4 calls:
1.0ms
(cbrt (cbrt x))
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
4.0ms
(pow (* (cbrt x) (cbrt x)) 1/3)
6.0ms
(log (/ (* (pow (* (cbrt x) (cbrt x)) 1/3) (cbrt (cbrt x))) (cbrt (+ x y))))

series735.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(cbrt (cbrt x))
74.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
344.0ms
(pow (* (cbrt x) (cbrt x)) 1/3)
76.0ms
(log (/ (* (pow (* (cbrt x) (cbrt x)) 1/3) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify57.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04881286
114171199
250011138

prune641.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes53.0ms

Accuracy

49.1% (2.2b remaining)

Error of 3.6b against oracle of 1.3b and baseline of 5.7b

bsearch61.0ms

Steps
ItersRangePoint
7
50024088429.266525
12169712469967.395
51088118733.37021

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03636
13636

end0.0ms

sample1.7s

Algorithm
intervals
Results
675.0ms1582×body1280valid
356.0ms1425×body640valid
203.0ms4873×body80valid
129.0ms812×body320valid
93.0ms2981×body80nan
44.0ms453×body160valid