Details

Time bar (total: 6.0s)

sample101.0ms

Algorithm
intervals
Results
28.0ms61×body10240exit
18.0ms44×body1280valid
18.0ms321×body80valid
14.0ms58×body640valid
4.0ms26×body320valid
1.0ms11×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
2.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
31×flip3-- flip--
27×flip3-+ flip-+
19×un-div-inv
15×add-sqr-sqrt
12×exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 associate-*l* add-cbrt-cube
5×add-exp-log
4×rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log difference-of-squares
1×sub-neg times-frac diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 157
Calls
4 calls:
16.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
30.0ms
(exp (- (* (+ 1.0 eps) x)))
27.0ms
(exp (- (* (- 1.0 eps) x)))
196.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify141.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
011693874
141983608
250023593

prune413.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
6.8b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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:
6.0ms
(* 0.6666666666666667 (pow x 3))
8.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune113.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

6.8b
(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
45.6b
(cbrt (* 0.6666666666666667 (pow x 3)))
45.6b
(cbrt (* 0.6666666666666667 (pow x 3)))
45.6b
(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cbrt-prod pow1/3
2×diff-log
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
4 → 41
Calls
4 calls:
15.0ms
(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
4.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
3.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
4.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))

series182.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
35.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
41.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
36.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))

simplify72.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0133470
1484391
22180346
35001327

prune170.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(pow (* 1.0 (pow x 2)) 3)
10.2b
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
10.9b
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
40×difference-of-squares
39×times-frac
37×*-un-lft-identity
33×sqr-pow
27×add-cube-cbrt
17×add-exp-log
15×unpow-prod-down cube-prod
13×associate-/l*
12×associate-*r*
11×add-cbrt-cube
6×pow-exp prod-exp add-log-exp
5×pow1 difference-cubes distribute-lft-out--
4×unswap-sqr
3×pow-to-exp pow-unpow associate-*l* associate-/r*
2×cube-mult flip3-- unpow3 associate-/r/ flip-- cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-undiv sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp clear-num *-commutative flip-+ div-inv
Counts
4 → 148
Calls
4 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
5.0ms
(pow (* 1.0 (pow x 2)) 3)
14.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
35.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* 0.6666666666666667 (pow x 3))
52.0ms
(pow (* 1.0 (pow x 2)) 3)
97.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
148.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06313439
129333295
250013294

prune583.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes98.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.4b

bsearch136.0ms

Steps
ItersRangePoint
9
1.5006309519768893e-05
674.2754902356271
295.27480666079055

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05538
16838
26838

end0.0ms

sample2.9s

Algorithm
intervals
Results
780.0ms1932×body10240exit
771.0ms1769×body1280valid
555.0ms9961×body80valid
321.0ms1255×body640valid
104.0ms602×body320valid
35.0ms328×body160valid