Details

Time bar (total: 7.5s)

sample91.0ms

Algorithm
intervals
Results
30.0ms50×body1280valid
19.0ms49×body640valid
13.0ms140×body80valid
7.0ms23×body320valid
6.0ms100×body80nan
4.0ms22×body160valid

simplify117.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (9.0ms)

IterNodesCost
0156
1246
2516
31066
43044
57744
641424
750014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b
(/ x (+ x y))
0.1b
(* x (log (/ x (+ x y))))
7.4b
(log (/ x (+ x y)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
261×times-frac
221×*-un-lft-identity
198×log-prod
149×add-sqr-sqrt
147×add-cube-cbrt
144×exp-sum
90×distribute-rgt-in distribute-lft-in
42×associate-/l*
37×distribute-lft-out
24×associate-/r/
13×div-inv
12×add-exp-log flip3-+ flip-+
10×add-cbrt-cube
8×pow1
7×associate-/r*
4×associate-*r* add-log-exp
3×div-exp associate-*l*
2×cbrt-undiv frac-2neg rem-log-exp clear-num log-pow
1×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 288
Calls
4 calls:
33.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
9.0ms
(/ x (+ x y))
11.0ms
(* x (log (/ x (+ x y))))
4.0ms
(log (/ x (+ x y)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
39.0ms
(/ x (+ x y))
80.0ms
(* x (log (/ x (+ x y))))
53.0ms
(log (/ x (+ x y)))

simplify85.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
08243036
128352608
250022592

prune559.0ms

Pruning

5 alts after pruning (5 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)
2.5b
(log (/ (cbrt x) (cbrt (+ x y))))
3.2b
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
61×log-prod
51×cbrt-prod
46×*-un-lft-identity
43×times-frac
34×add-sqr-sqrt add-cube-cbrt
20×add-exp-log
14×cbrt-div
10×associate-/r/
7×flip3-+ rem-log-exp flip-+
6×pow1 distribute-lft-out
5×div-exp
4×frac-times prod-exp add-cbrt-cube add-log-exp
2×log-div pow1/3 associate-*r/ associate-*l/ log-pow div-inv
Counts
4 → 108
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
11.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt x)
177.0ms
(cbrt x)
71.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
84.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
04391158
111011086
235331043
350021001

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
2.5b
(log (/ (cbrt x) (cbrt (+ x y))))
2.5b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite22.0ms

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×cbrt-div rem-log-exp associate-/r/ add-cbrt-cube add-log-exp
2×log-div flip3-+ pow1/3 div-exp log-pow flip-+ div-inv
Counts
4 → 140
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series505.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(cbrt x)
186.0ms
(cbrt x)
73.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
67.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify73.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
03111470
17571424
223191392
350011324

prune519.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cbrt x) (cbrt (+ x y)))
0.5b
(cbrt (+ x y))
0.6b
(cbrt x)
2.5b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
104×cbrt-prod
91×*-un-lft-identity
84×times-frac
63×add-sqr-sqrt add-cube-cbrt
48×log-prod
14×distribute-lft-out
9×add-exp-log
7×associate-/r*
6×cbrt-div associate-/l*
5×pow1
4×associate-/r/ add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×pow1/3 div-exp rem-log-exp div-inv
1×cbrt-undiv log-div frac-2neg clear-num log-pow
Counts
4 → 153
Calls
4 calls:
7.0ms
(/ (cbrt x) (cbrt (+ x y)))
2.0ms
(cbrt (+ x y))
0.0ms
(cbrt x)
6.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (cbrt x) (cbrt (+ x y)))
128.0ms
(cbrt (+ x y))
183.0ms
(cbrt x)
68.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify44.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03861444
111191407
250021386

prune611.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

98.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.5b

bsearch155.0ms

Steps
ItersRangePoint
9
0.000431479263060677
213.0826250665956
7.835280933943446
10
-3.44962383690743e+67
-9.704786708557082e+56
-1.0107557422829784e+57

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13920
23920

end0.0ms

sample2.7s

Algorithm
intervals
Results
903.0ms1514×body1280valid
563.0ms1455×body640valid
448.0ms4856×body80valid
225.0ms843×body320valid
190.0ms3064×body80nan
76.0ms422×body160valid