Details

Time bar (total: 6.1s)

sample63.0ms

Algorithm
intervals
Results
28.0ms71×body1280valid
12.0ms47×body640valid
8.0ms27×body2560valid
4.0ms26×body320valid
2.0ms74×body80valid
1.0ms11×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: 52.8b

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
1.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.6b
(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))

series268.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
163.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify141.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (136.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune146.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite88.0ms

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:
13.0ms
(- (+ (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)))

series291.0ms

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))))
133.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146421654
250011654

prune460.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.5b
(- (/ 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))
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))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- 0.0625) (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
186.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
54.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify94.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08371970
138171891
250021883

prune594.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

8.8b
(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
8.8b
(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
17.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
17.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
60×add-sqr-sqrt
40×times-frac
30×log-prod
28×distribute-lft-out--
24×sqrt-prod
20×difference-of-squares
16×frac-sub
14×add-log-exp
10×log-div sqrt-div
8×pow1 add-cube-cbrt flip3-- flip--
6×add-exp-log diff-log log-pow associate--r+
4×sub-neg unpow-prod-down distribute-rgt-neg-in cube-prod add-cbrt-cube associate--r- sqr-pow
2×neg-sub0 sqrt-pow1 pow1/2 div-sub rem-log-exp
Counts
4 → 120
Calls
4 calls:
71.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
71.0ms
(log (sqrt (- (/ 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))))
73.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
94.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
56.0ms
(- (/ 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))))

simplify52.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04062180
113192034
250011978

prune484.0ms

Filtered
132 candidates to 92 candidates (69.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.3b

bsearch99.0ms

Steps
ItersRangePoint
10
9.598072339636849e-08
814.2255113159289
0.8916223552936648
11
-402.67606408878214
-1.1015269942960052e-19
-1.030140799834648

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04339
14339

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.0s2374×body1280valid
383.0ms1550×body640valid
226.0ms780×body2560valid
118.0ms763×body320valid
73.0ms2157×body80valid
32.0ms376×body160valid