Details

Time bar (total: 3.9s)

sample57.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.99593%

Results
27.0ms59×body1280valid
14.0ms62×body640valid
3.0ms25×body320valid
3.0ms95×body80valid
1.0ms15×body160valid

simplify4.0ms

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: 37.9b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

4.2b
(log (+ 1.0 x))

rewrite7.0ms

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:
7.0ms
(log (+ 1.0 x))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(log (+ 1.0 x))

simplify43.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
012897
135487
2128081
3500178

prune41.0ms

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

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
2×diff-log associate-*r/ frac-sub
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity flip3-+ associate--l+ sum-log add-cbrt-cube flip-- flip-+
Counts
1 → 16
Calls
1 calls:
6.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series5.0ms

Counts
1 → 3
Calls
1 calls:
5.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify137.0ms

Algorithm
egg-herbie
Counts
19 → 19
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0181250
1733231
24310220
35001220

prune45.0ms

Filtered
14 candidates to 19 candidates (-35.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New19019
Fresh011
Picked011
Done011
Total19322

Merged error: 0.0b

Counts
22 → 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)))))
14.0b
(log (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
15.6b
(log (+ (pow 1.0 3) (pow x 3)))

rewrite40.0ms

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:
21.0ms
(- (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:
9.0ms
(- (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))))
16.0ms
(log (+ (pow 1.0 3) (pow x 3)))

simplify51.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0404876
11479828
25002788

prune182.0ms

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

localize25.0ms

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)))
12.2b
(+ (+ (* 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))))))

rewrite138.0ms

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:
38.0ms
(+ (pow x 2) (/ (pow x 3) (pow 1.0 2)))
22.0ms
(+ (* 0.3333333333333333 (/ (pow x 3) (pow 1.0 3))) (+ (* 1.0 (pow x 3)) (* 0.5 (/ (pow x 2) (pow 1.0 2)))))
36.0ms
(* 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))))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow x 2) (/ (pow x 3) (pow 1.0 2)))
20.0ms
(+ (* 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))))))

simplify65.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012302766
150012564

prune921.0ms

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

regimes113.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
13623

end0.0ms

sample1.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.99593%

Results
1.1s2336×body1280valid
388.0ms1676×body640valid
95.0ms792×body320valid
77.0ms2787×body80valid
30.0ms409×body160valid

Profiling

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