Details

Time bar (total: 5.2s)

sample66.0ms

Algorithm
intervals
Results
34.0ms80×body1280valid
9.0ms38×body640valid
8.0ms30×body2560valid
5.0ms36×body320valid
2.0ms63×body80valid
1.0ms9×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.8b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.6b
(sqrt (+ (* x x) 1.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series309.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x x) 1.0)
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0333450
11163414
25001398

prune170.0ms

Filtered
65 candidates to 53 candidates (81.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
12.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
52.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series297.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
140.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify113.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08542089
146421654
250011654

prune422.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.4b
(/ 0.125 (pow x 3))
11.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
21.1b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
7.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
67.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
71.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
188.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
52.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify95.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08402002
138201923
250011915

prune565.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.4b
(/ 0.125 (pow x 3))
9.7b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
33×*-un-lft-identity
29×add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
8×add-log-exp
6×log-prod
5×add-cbrt-cube
4×pow1 cube-mult log-div flip3-- unpow3 frac-sub flip-- difference-of-squares sqr-pow
3×diff-log div-exp associate-/l*
2×sub-neg associate--r+ distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv associate--r-
Counts
3 → 105
Calls
3 calls:
20.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
5.0ms
(/ 0.125 (pow x 3))
15.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series237.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
35.0ms
(/ 0.125 (pow x 3))
153.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify65.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0475884
12181836
25002836

prune210.0ms

Filtered
114 candidates to 70 candidates (61.4%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.3b

bsearch75.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
0.8851102844894212
8
-1.0806682141483241
-0.0004106978961831668
-1.013880423339445

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.8s

Algorithm
intervals
Results
927.0ms2308×body1280valid
364.0ms1569×body640valid
213.0ms782×body2560valid
107.0ms820×body320valid
69.0ms2147×body80valid
28.0ms374×body160valid