Details

Time bar (total: 5.8s)

sample71.0ms

Algorithm
intervals
Results
37.0ms85×body1280valid
11.0ms47×body640valid
9.0ms34×body2560valid
2.0ms59×body80valid
2.0ms13×body320valid
1.0ms18×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: 55.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
4.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(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:
20.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series252.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
160.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
39.0ms
(sqrt (+ (* x x) 1.0))

simplify135.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
0309394
11021364
24731348
35002347

prune140.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite98.0ms

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:
80.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series128.0ms

Counts
1 → 3
Calls
1 calls:
128.0ms
(* 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

prune366.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.2b
(/ (- 0.0625) (pow x 5))
11.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.3b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite443.0ms

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:
8.0ms
(/ 0.125 (pow x 3))
10.0ms
(/ (- 0.0625) (pow x 5))
197.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
219.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ 0.125 (pow x 3))
50.0ms
(/ (- 0.0625) (pow x 5))
175.0ms
(log (- (/ 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))))

simplify99.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08402002
138201923
250011915

prune567.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.1b
(/ 0.125 (pow x 3))
10.0b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube distribute-lft-out--
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult diff-log unpow3
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×sub-neg log-div associate--l+ frac-sub
1×cbrt-undiv +-commutative pow-to-exp associate-+r- flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 125
Calls
4 calls:
91.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
173.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
8.0ms
(/ 0.125 (pow x 3))
147.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series255.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
45.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
33.0ms
(/ 0.125 (pow x 3))
144.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0505968
12345912
25002912

prune234.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes66.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch78.0ms

Steps
ItersRangePoint
9
1.3330246063773173e-09
3.618674152218468
0.8781417519921209
9
-28256763.0897718
-0.23317146499959118
-1.0391662476697119

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
962.0ms2378×body1280valid
375.0ms1590×body640valid
208.0ms778×body2560valid
100.0ms750×body320valid
71.0ms2118×body80valid
29.0ms386×body160valid