Details

Time bar (total: 5.6s)

sample70.0ms

Algorithm
intervals
Results
30.0ms63×body1280valid
15.0ms53×body640valid
8.0ms22×body2560valid
4.0ms27×body320valid
3.0ms74×body80valid
2.0ms17×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.5b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ x (sqrt (+ (* x x) 1.0)))
5.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.2b
(sqrt (+ (* x x) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series399.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
299.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify140.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune125.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0b

Counts
52 → 5

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)))

rewrite86.0ms

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)))

series278.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
130.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify117.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08542089
146421654
250011654

prune382.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh044
Picked011
Done000
Total2925297

Merged error: 0b

Counts
297 → 5

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.3b
(/ 0.125 (pow x 3))
7.5b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×add-sqr-sqrt
40×times-frac
29×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
9×add-exp-log
8×add-log-exp
6×log-prod
5×add-cbrt-cube distribute-lft-out difference-of-squares sqr-pow
4×pow1 cube-mult unpow3 distribute-lft-out--
3×div-exp associate-/l*
2×log-div flip3-+ diff-log frac-sub flip-+
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num sum-log log-pow flip-- div-inv
Counts
3 → 105
Calls
3 calls:
24.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
9.0ms
(/ 0.125 (pow x 3))
34.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series228.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
35.0ms
(/ 0.125 (pow x 3))
152.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0469784
12133747
25001747

prune176.0ms

Filtered
114 candidates to 67 candidates (58.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh033
Picked011
Done011
Total1145119

Merged error: 0b

Counts
119 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
9.7b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite163.0ms

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:
6.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
70.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
72.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
186.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
59.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify101.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371970
138171891
250021883

prune497.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh022
Picked011
Done022
Total2355240

Merged error: 0b

Counts
240 → 5

regimes34.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.8b

bsearch99.0ms

Steps
ItersRangePoint
10
8.416769919470913e-17
1.2368608357549227
0.8954688172587604
11
-55383.34621353126
-7.66540900750845e-16
-1.0204783204586885

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2303×body1280valid
429.0ms1511×body640valid
286.0ms829×body2560valid
134.0ms766×body320valid
98.0ms2159×body80valid
46.0ms432×body160valid