Details

Time bar (total: 5.8s)

sample105.0ms

Algorithm
intervals
Results
29.0ms74×body10240exit
24.0ms51×body1280valid
19.0ms357×body80valid
9.0ms36×body640valid
4.0ms21×body320valid
2.0ms17×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

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

rewrite86.0ms

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:
40.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
30.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms
(exp (- (* (+ 1.0 eps) x)))
29.0ms
(exp (- (* (- 1.0 eps) x)))
210.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify133.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
011693874
141983608
250023593

prune441.0ms

Filtered
169 candidates to 90 candidates (53.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

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)))

rewrite34.0ms

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))
26.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series110.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(* 0.6666666666666667 (pow x 3))
63.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0207270
1894242
25002238

prune121.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
8×pow-prod-down prod-exp cbrt-unprod
7×add-log-exp
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity diff-log
1×sub-neg flip3-- associate-*r* associate-*l* associate--l+ sum-log *-commutative flip--
Counts
2 → 36
Calls
2 calls:
10.0ms
(* (* 0.6666666666666667 x) (* x x))
87.0ms
(- (+ (* (* 0.6666666666666667 x) (* x x)) 2.0) (* 1.0 (pow x 2)))

series82.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(* (* 0.6666666666666667 x) (* x x))
40.0ms
(- (+ (* (* 0.6666666666666667 x) (* x x)) 2.0) (* 1.0 (pow x 2)))

simplify156.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0213283
1963225
24843218
35001218

prune87.0ms

Filtered
42 candidates to 22 candidates (52.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(* 0.6666666666666667 (pow x 3))
9.2b
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
11.1b
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
20×add-cube-cbrt *-un-lft-identity
16×add-exp-log
10×add-cbrt-cube
9×times-frac
8×unpow-prod-down cube-prod unswap-sqr
6×associate-*l* prod-exp add-log-exp
4×pow1 sqr-pow
3×flip3-+ associate-/r* flip-+ associate-/l*
2×cube-mult pow-to-exp associate-+r+ unpow3 pow-exp associate-/r/ *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-in frac-2neg distribute-lft-in div-exp clear-num sum-log div-inv
Counts
4 → 106
Calls
4 calls:
7.0ms
(* 0.6666666666666667 (pow x 3))
6.0ms
(* 0.6666666666666667 (pow x 3))
5.0ms
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
24.0ms
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series253.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(* 0.6666666666666667 (pow x 3))
50.0ms
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
123.0ms
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04121392
119941252
250011242

prune411.0ms

Filtered
118 candidates to 82 candidates (69.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes121.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch147.0ms

Steps
ItersRangePoint
10
0.0016736950671300647
38794610249.56377
3.591957276208114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05230
16530
26530

end0.0ms

sample2.8s

Algorithm
intervals
Results
774.0ms1929×body10240exit
743.0ms1728×body1280valid
556.0ms10048×body80valid
311.0ms1241×body640valid
110.0ms642×body320valid
35.0ms330×body160valid