Details

Time bar (total: 5.6s)

sample66.0ms

Algorithm
intervals
Results
33.0ms75×body1280valid
10.0ms46×body640valid
6.0ms24×body2560valid
4.0ms29×body320valid
2.0ms61×body80valid
2.0ms21×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: 54.8b

localize7.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ x (sqrt (+ (* x x) 1.0)))
4.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite21.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series294.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(+ x (sqrt (+ (* x x) 1.0)))
181.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms
(sqrt (+ (* x x) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune138.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite89.0ms

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:
71.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series149.0ms

Counts
1 → 3
Calls
1 calls:
148.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify89.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07251757
138321368
250021368

prune364.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.5b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite380.0ms

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))
4.0ms
(/ 0.125 (pow x 3))
172.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
189.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (- 0.0625) (pow x 5))
43.0ms
(/ 0.125 (pow x 3))
187.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
60.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify99.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371970
138171891
250021883

prune582.0ms

Pruning

3 alts after pruning (1 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)))
0.2b
(/ 0.125 (pow x 3))
7.5b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite116.0ms

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:
54.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
4.0ms
(/ 0.125 (pow x 3))
55.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series240.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
36.0ms
(/ 0.125 (pow x 3))
156.0ms
(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

prune213.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.6b

bsearch89.0ms

Steps
ItersRangePoint
10
4.555257425893614e-05
47183757994.54101
0.8947439006781924
9
-13600.963204601821
-0.00047371797307045637
-1.020862079458779

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.0s

Algorithm
intervals
Results
937.0ms2309×body1280valid
566.0ms1601×body640valid
209.0ms769×body2560valid
101.0ms742×body320valid
68.0ms2176×body80valid
33.0ms403×body160valid