Details

Time bar (total: 6.7s)

sample95.0ms

Algorithm
intervals
Results
27.0ms60×body10240exit
20.0ms46×body1280valid
17.0ms318×body80valid
9.0ms39×body640valid
4.0ms24×body320valid
1.0ms9×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.1b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac diff-log distribute-lft-out--
Counts
4 → 172
Calls
4 calls:
40.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
12.0ms
(* (+ 1.0 eps) x)
30.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
28.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms
(* (+ 1.0 eps) x)
46.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
200.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify147.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012574061
147723783
250013783

prune433.0ms

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

rewrite39.0ms

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:
10.0ms
(* 0.6666666666666667 (pow x 3))
27.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 0.6666666666666667 (pow x 3))
38.0ms
(- (+ (* 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

prune107.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(pow (* 1.0 (pow x 2)) 3)
10.0b
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
11.3b
(/ (- (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)))))

rewrite230.0ms

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:
7.0ms
(* 0.6666666666666667 (pow x 3))
3.0ms
(pow (* 1.0 (pow x 2)) 3)
60.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
154.0ms
(/ (- (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)))))

series335.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* 0.6666666666666667 (pow x 3))
53.0ms
(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))
149.0ms
(/ (- (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)))))

simplify122.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06313439
129333295
250013294

prune596.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1.666666666666667 (pow x 6))
0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(* 0.6666666666666667 (pow x 3))
12.2b
(/ (+ (* 1.666666666666667 (pow x 6)) (+ (* 8.0 (pow x 3)) 8.0)) (+ (* (+ (* 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)))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×associate-*r*
23×add-cube-cbrt *-un-lft-identity
21×add-exp-log
12×unpow-prod-down add-cbrt-cube
11×unswap-sqr
9×times-frac associate-*l* prod-exp
8×cube-prod
6×sqr-pow
4×pow1 add-log-exp
3×pow-to-exp pow-exp associate-/r* *-commutative cbrt-unprod associate-/l*
2×cube-mult flip3-+ unpow3 associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
5.0ms
(* 1.666666666666667 (pow x 6))
9.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(* 0.6666666666666667 (pow x 3))
67.0ms
(/ (+ (* 1.666666666666667 (pow x 6)) (+ (* 8.0 (pow x 3)) 8.0)) (+ (* (+ (* 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)))))

series265.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* 1.666666666666667 (pow x 6))
36.0ms
(* 0.6666666666666667 (pow x 3))
41.0ms
(* 0.6666666666666667 (pow x 3))
133.0ms
(/ (+ (* 1.666666666666667 (pow x 6)) (+ (* 8.0 (pow x 3)) 8.0)) (+ (* (+ (* 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)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
04661368
122921243
250031243

prune626.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes66.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch104.0ms

Steps
ItersRangePoint
7
10.298044827647965
488.5072251079851
80.0922900021786

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05129
16429
26429

end0.0ms

sample2.7s

Algorithm
intervals
Results
735.0ms1867×body10240exit
735.0ms1723×body1280valid
530.0ms10037×body80valid
298.0ms1237×body640valid
100.0ms618×body320valid
33.0ms324×body160valid