Details

Time bar (total: 5.6s)

sample69.0ms

Algorithm
intervals
Results
35.0ms88×body1280valid
13.0ms53×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms58×body80valid
1.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series319.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x x) 1.0)
61.0ms
(+ x (sqrt (+ (* x x) 1.0)))
178.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0333450
11163414
25001398

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite86.0ms

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:
69.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series146.0ms

Counts
1 → 3
Calls
1 calls:
146.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify88.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07251757
138321368
250021368

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.8b
(/ 0.125 (pow x 3))
14.6b
(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))))

rewrite366.0ms

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))
4.0ms
(/ 0.125 (pow x 3))
166.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
180.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (- 0.0625) (pow x 5))
36.0ms
(/ 0.125 (pow x 3))
190.0ms
(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))))

simplify96.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08402002
138201923
250011915

prune572.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.8b
(/ 0.125 (pow x 3))
11.9b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite113.0ms

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:
53.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
4.0ms
(/ 0.125 (pow x 3))
53.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series244.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(- (/ 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))))

simplify65.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0475884
12181836
25002836

prune219.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.8b

bsearch89.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
0.9001758350297782
10
-64880754058.88788
-2.651420353119469e-05
-0.9989549344709008

simplify8.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s2398×body1280valid
402.0ms1535×body640valid
242.0ms806×body2560valid
116.0ms761×body320valid
76.0ms2126×body80valid
33.0ms374×body160valid