Details

Time bar (total: 22.0s)

sample66.0ms

Algorithm
intervals
Results
33.0ms84×body1280valid
12.0ms49×body640valid
6.0ms23×body2560valid
2.0ms17×body320valid
2.0ms68×body80valid
1.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
095
195

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.0b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.7b
(sqrt (+ (* x x) 1.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt sqrt-prod add-log-exp
4×add-exp-log log-prod distribute-lft-out
3×flip3-+ add-cbrt-cube flip-+
2×log-div sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp associate-*l* sum-log log-pow
Counts
3 → 44
Calls
3 calls:
10.0ms
(+ x (sqrt (+ (* x x) 1.0)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series291.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(+ x (sqrt (+ (* x x) 1.0)))
178.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms
(sqrt (+ (* x x) 1.0))

simplify131.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (125.0ms)

IterNodesCost
0304401
1987372
24427356
35003353

prune118.0ms

Filtered
53 candidates to 42 candidates (79.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New49453
Fresh000
Picked101
Done000
Total50454

Merged error: 0.0b

Counts
54 → 4

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
100×unpow-prod-down times-frac
92×associate-*r*
85×add-sqr-sqrt
55×*-un-lft-identity
54×add-cube-cbrt
30×sqrt-prod
28×sqr-pow
24×add-exp-log
22×associate-*r/
21×unpow3
13×unswap-sqr
11×associate-/r*
10×prod-exp
9×div-exp associate-/l*
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×clear-num un-div-inv cbrt-unprod
1×cbrt-undiv frac-2neg pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 153
Calls
1 calls:
34.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series146.0ms

Counts
1 → 3
Calls
1 calls:
146.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify80.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
0687921
13319855
25001855

prune318.0ms

Filtered
156 candidates to 94 candidates (60.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1560156
Fresh033
Picked011
Done000
Total1564160

Merged error: 0.0b

Counts
160 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.2b
(/ 0.125 (pow x 3))
9.2b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
39×add-sqr-sqrt
36×frac-sub
29×add-cube-cbrt
26×times-frac
20×log-div flip3-- associate-/r* flip--
15×associate-/l*
12×unpow-prod-down
10×distribute-lft-out--
9×add-exp-log
8×log-prod add-log-exp
5×frac-2neg clear-num add-cbrt-cube
4×pow1 unpow3 difference-of-squares sqr-pow
3×diff-log div-exp
2×sub-neg associate-*l* associate--r+
1×cbrt-undiv pow-to-exp rem-log-exp pow-exp log-pow div-inv associate--r-
Counts
3 → 125
Calls
3 calls:
35.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
5.0ms
(/ 0.125 (pow x 3))
39.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series246.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
42.0ms
(/ 0.125 (pow x 3))
159.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify112.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08091926
140081840
250021840

prune267.0ms

Filtered
134 candidates to 90 candidates (67.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1340134
Fresh022
Picked011
Done011
Total1344138

Merged error: 0.0b

Counts
138 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.4b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
10136×frac-sub
6371×associate-/r*
5305×associate-/l*
3574×*-un-lft-identity
3560×add-sqr-sqrt
3540×add-cube-cbrt
2550×log-div
1895×unpow-prod-down
1178×frac-2neg clear-num
782×distribute-rgt-neg-in
780×distribute-lft-neg-in
633×sqr-pow
368×unpow3
260×neg-mul-1
112×times-frac
30×flip3-- flip--
15×add-exp-log
14×distribute-lft-out--
11×log-prod
9×add-log-exp
8×add-cbrt-cube difference-of-squares
6×div-exp
5×pow1
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg div-sub pow-exp div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 5295
Calls
4 calls:
7.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
340.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
212.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (- 0.0625) (pow x 5))
37.0ms
(/ 0.125 (pow x 3))
193.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
68.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify1.6s

Algorithm
egg-herbie
Counts
5307 → 5307
Iterations

Useful iterations: 0 (111.0ms)

IterNodesCost
010029153087

prune14.6s

Filtered
5307 candidates to 3477 candidates (65.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New530705307
Fresh011
Picked011
Done022
Total530745311

Merged error: 0.0b

Counts
5311 → 4

regimes28.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.2b

bsearch84.0ms

Steps
ItersRangePoint
10
1.0482644148039984e-06
3857898261607.3584
0.8788979276681737
10
-1556119314.230081
-0.05767290693153419
-1.0189304134151242

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
930.0ms2277×body1280valid
398.0ms1634×body640valid
203.0ms737×body2560valid
112.0ms812×body320valid
70.0ms2093×body80valid
35.0ms447×body160valid