Details

Time bar (total: 3.9s)

sample56.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results
28.0ms62×body1280valid
12.0ms52×body640valid
3.0ms26×body320valid
3.0ms101×body80valid
1.0ms15×body160valid
0.0ms7×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052
152

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.7b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

4.4b
(log (+ 1.0 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
3.0ms
(log (+ 1.0 x))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(log (+ 1.0 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
012897
135487
2128081
3500178

prune39.0ms

Filtered
13 candidates to 18 candidates (-38.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New16218
Fresh000
Picked011
Done000
Total16319

Merged error: 0.0b

Counts
19 → 3

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
69×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
35×add-cube-cbrt *-un-lft-identity
24×add-exp-log unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 110
Calls
1 calls:
21.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series9.0ms

Counts
1 → 3
Calls
1 calls:
8.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify54.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0531638
12305526
25001525

prune180.0ms

Filtered
68 candidates to 113 candidates (-66.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1130113
Fresh011
Picked011
Done011
Total1133116

Merged error: 0.0b

Counts
116 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(- (log (+ (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
16.1b
(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
17.3b
(log (+ (pow 1.0 3) (pow x 3)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
24×log-prod
10×distribute-lft-out
9×pow1 add-sqr-sqrt associate--l+
8×unpow-prod-down log-div cube-prod
7×add-cube-cbrt
6×log-pow
5×add-exp-log
4×flip3-+ flip-+ distribute-lft-out--
3×add-cbrt-cube associate--r+ add-log-exp
2×associate--l- rem-log-exp sum-cubes associate--r-
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
3 → 67
Calls
3 calls:
19.0ms
(- (log (+ (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
5.0ms
(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
11.0ms
(log (+ (pow 1.0 3) (pow x 3)))

series30.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(- (log (+ (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
5.0ms
(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
14.0ms
(log (+ (pow 1.0 3) (pow x 3)))

simplify47.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404876
11479828
25002788

prune184.0ms

Filtered
57 candidates to 76 candidates (-33.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New74276
Fresh000
Picked101
Done022
Total75479

Merged error: 0b

Counts
79 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow x 2) (/ (pow x 3) (pow 1.0 2)))
0.0b
(+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2)))))
0.1b
(* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3)))
13.1b
(+ (+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2))))) (* 1.0 (- x (+ (pow x 2) (/ (pow x 3) (pow 1.0 2))))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
148×associate-*r*
120×add-sqr-sqrt
80×unpow-prod-down *-un-lft-identity cube-prod
78×add-cube-cbrt
32×sqr-pow
27×add-exp-log
24×cube-mult unpow3
20×add-log-exp
17×unswap-sqr
15×associate-*r/
14×frac-add
10×prod-exp sum-log
9×div-exp add-cbrt-cube
8×flip3-+ flip-+
6×pow1 pow-to-exp pow-exp
5×associate-+r+
4×flip3-- flip--
3×+-commutative associate-*l*
2×distribute-rgt-in sub-neg distribute-lft-in cbrt-unprod
1×cbrt-undiv associate-+l+ pow-prod-down *-commutative div-inv distribute-lft-out
Counts
4 → 243
Calls
4 calls:
44.0ms
(+ (pow x 2) (/ (pow x 3) (pow 1.0 2)))
19.0ms
(+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2)))))
40.0ms
(* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3)))
23.0ms
(+ (+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2))))) (* 1.0 (- x (+ (pow x 2) (/ (pow x 3) (pow 1.0 2))))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow x 2) (/ (pow x 3) (pow 1.0 2)))
23.0ms
(+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2)))))
7.0ms
(* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3)))
12.0ms
(+ (+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2))))) (* 1.0 (- x (+ (pow x 2) (/ (pow x 3) (pow 1.0 2))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012302766
150012564

prune942.0ms

Filtered
135 candidates to 255 candidates (-88.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2550255
Fresh011
Picked011
Done022
Total2554259

Merged error: 0b

Counts
259 → 4

regimes120.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
13623

end0.0ms

sample1.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results
1.0s2220×body1280valid
386.0ms1682×body640valid
98.0ms811×body320valid
80.0ms2841×body80valid
31.0ms446×body160valid
3.0ms174×body80nan

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