Details

Time bar (total: 5.4s)

sample71.0ms

Algorithm
intervals
Results
32.0ms71×body1280valid
12.0ms44×body640valid
10.0ms32×body2560valid
4.0ms25×body320valid
3.0ms71×body80valid
1.0ms13×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: 53.2b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.3b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series263.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
164.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify137.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (132.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune132.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New47451
Fresh000
Picked101
Done000
Total48452

Merged error: 0b

Counts
52 → 4

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
60.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series132.0ms

Counts
1 → 3
Calls
1 calls:
132.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify93.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07251757
138321368
250021368

prune320.0ms

Filtered
273 candidates to 95 candidates (34.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh033
Picked011
Done000
Total2734277

Merged error: 0b

Counts
277 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b
(/ 0.125 (pow x 3))
7.0b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite55.0ms

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:
20.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))
25.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series222.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
35.0ms
(/ 0.125 (pow x 3))
148.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0469784
12133747
25001747

prune187.0ms

Filtered
114 candidates to 67 candidates (58.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh022
Picked011
Done011
Total1144118

Merged error: 0b

Counts
118 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.1b
(/ 0.125 (pow x 3))
8.0b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
18.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite188.0ms

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))
6.0ms
(/ 0.125 (pow x 3))
81.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
81.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (- 0.0625) (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
234.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
53.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify98.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08371970
138171891
250021883

prune509.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh011
Picked011
Done022
Total2354239

Merged error: 0b

Counts
239 → 4

regimes26.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch101.0ms

Steps
ItersRangePoint
11
3.029362037509861e-19
14.716166499582775
0.8986488386268908
11
-2193661101726697.2
-1.4639597033977343e-08
-0.9978403496791813

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s2305×body1280valid
418.0ms1533×body640valid
279.0ms847×body2560valid
262.0ms2088×body80valid
137.0ms780×body320valid
43.0ms447×body160valid