Details

Time bar (total: 6.2s)

sample72.0ms

Algorithm
intervals
Results
34.0ms72×body1280valid
16.0ms56×body640valid
5.0ms19×body2560valid
3.0ms25×body320valid
2.0ms71×body80valid
1.0ms13×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.5b
(sqrt (+ (* x x) 1.0))

rewrite46.0ms

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:
19.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series272.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ x (sqrt (+ (* x x) 1.0)))
172.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
40.0ms
(sqrt (+ (* x x) 1.0))

simplify140.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune144.0ms

Pruning

5 alts after pruning (5 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)))

rewrite272.0ms

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:
164.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
89.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series287.0ms

Counts
2 → 6
Calls
2 calls:
149.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify117.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146421654
250011654

prune433.0ms

Pruning

5 alts after pruning (4 fresh and 1 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)))
0.2b
(/ 0.125 (pow x 3))
10.0b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite179.0ms

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:
84.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
8.0ms
(/ 0.125 (pow x 3))
83.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series229.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
33.0ms
(/ 0.125 (pow x 3))
150.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify63.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0475884
12181836
25002836

prune217.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite468.0ms

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:
10.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
211.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
229.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- 0.0625) (pow x 5))
33.0ms
(/ 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

prune570.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch76.0ms

Steps
ItersRangePoint
11
1.661404138935296e-22
2.5556453819330236
0.8921071852910252
7
-5.56536991933885
-0.04331797882383785
-1.0106802036626215

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s2317×body1280valid
421.0ms1626×body640valid
233.0ms810×body2560valid
115.0ms754×body320valid
64.0ms2091×body80valid
35.0ms402×body160valid