Details

Time bar (total: 5.6s)

sample105.0ms

Algorithm
intervals
Results
23.0ms351×body80valid
23.0ms61×body10240exit
23.0ms56×body1280valid
11.0ms47×body640valid
3.0ms17×body320valid
1.0ms9×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

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)))
2.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite140.0ms

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:
66.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
9.0ms
(exp (- (* (- 1.0 eps) x)))
6.0ms
(exp (- (* (+ 1.0 eps) x)))
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
25.0ms
(exp (- (* (- 1.0 eps) x)))
24.0ms
(exp (- (* (+ 1.0 eps) x)))
179.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify137.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
011693874
141983608
250023593

prune420.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
5.4b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite72.0ms

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:
12.0ms
(* 0.6666666666666667 (pow x 3))
57.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(* 0.6666666666666667 (pow x 3))
35.0ms
(- (+ (* 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

prune120.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (+ (* (* (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)))
41.3b
(cbrt (* 0.6666666666666667 (pow x 3)))
41.3b
(cbrt (* 0.6666666666666667 (pow x 3)))
41.3b
(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite219.0ms

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:
203.0ms
(- (+ (* (* (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)))
5.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
5.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
5.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (+ (* (* (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)))
39.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
34.0ms
(cbrt (* 0.6666666666666667 (pow x 3)))
38.0ms
(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

prune177.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0))
0.1b
(* (pow x 2) (- (* x 0.6666666666666667) 1.0))
0.2b
(log (exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log associate-*l*
6×exp-prod add-log-exp
5×add-cbrt-cube
4×pow1 unpow-prod-down log-prod log-pow unswap-sqr
3×associate-*r* prod-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ exp-sum rem-exp-log unpow2 sqr-pow
1×pow-to-exp flip3-- rem-log-exp pow-exp sum-log *-commutative flip-- cbrt-unprod
Counts
3 → 62
Calls
3 calls:
44.0ms
(exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0))
35.0ms
(* (pow x 2) (- (* x 0.6666666666666667) 1.0))
33.0ms
(log (exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0)))

series139.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0))
75.0ms
(* (pow x 2) (- (* x 0.6666666666666667) 1.0))
35.0ms
(log (exp (+ (* (pow x 2) (- (* x 0.6666666666666667) 1.0)) 2.0)))

simplify36.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0229491
1852426
25001423

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes53.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.7b

bsearch135.0ms

Steps
ItersRangePoint
9
1.5996814978684195e-06
74.54631513443616
10.817695361442519

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05237
16037
26037

end0.0ms

sample2.9s

Algorithm
intervals
Results
753.0ms1973×body10240exit
687.0ms1666×body1280valid
551.0ms10178×body80valid
323.0ms1338×body640valid
101.0ms633×body320valid
31.0ms303×body160valid