Details

Time bar (total: 6.2s)

sample113.0ms

Algorithm
intervals
Results
29.0ms63×body10240exit
27.0ms62×body1280valid
20.0ms351×body80valid
10.0ms38×body640valid
4.0ms25×body320valid
1.0ms11×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(* (+ 1.0 eps) x)
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
73×exp-neg
72×frac-times
55×neg-sub0 exp-diff
40×associate-*l/
36×associate-*r/
29×flip3-- flip--
28×flip3-+ flip-+
18×un-div-inv
15×add-sqr-sqrt
13×*-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
22.0ms
(* (- 1.0 eps) x)
9.0ms
(exp (- (* (- 1.0 eps) x)))
20.0ms
(* (+ 1.0 eps) x)
50.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (- 1.0 eps) x)
32.0ms
(exp (- (* (- 1.0 eps) x)))
27.0ms
(* (+ 1.0 eps) x)
204.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify135.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
012093667
146013404
250013393

prune386.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
5.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
13.0ms
(* 0.6666666666666667 (pow x 3))
60.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series82.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(* 0.6666666666666667 (pow x 3))
44.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0207273
1894245
25002241

prune109.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
4.9b
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
5.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
5.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div diff-log add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ sum-log
Counts
4 → 58
Calls
4 calls:
47.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
47.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
56.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
60.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
54.0ms
(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
43.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
40.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify103.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0171688
1611636
23106618
35003616

prune204.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
5.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
10.4b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.4b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div flip3-- diff-log add-cbrt-cube flip--
2×sub-neg pow1/3 associate--l+ sum-log
Counts
4 → 54
Calls
4 calls:
57.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
56.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
28.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
32.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
46.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
149.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
153.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify129.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0252862
1905800
24257736
35002736

prune278.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

regimes61.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.9b

bsearch182.0ms

Steps
ItersRangePoint
11
5.899922635698028e-18
1860724342265.0034
223.90795350971536

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06167
17367
27367

end0.0ms

sample2.9s

Algorithm
intervals
Results
727.0ms1863×body10240exit
722.0ms1706×body1280valid
555.0ms10124×body80valid
328.0ms1284×body640valid
98.0ms609×body320valid
31.0ms303×body160valid