Details

Time bar (total: 6.0s)

sample110.0ms

Algorithm
intervals
Results
29.0ms72×body10240exit
21.0ms49×body1280valid
17.0ms311×body80valid
14.0ms52×body640valid
8.0ms20×body320valid
1.0ms9×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: 30.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(+ 1.0 (/ 1.0 eps))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.6b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip3-+ flip-- flip-+
20×un-div-inv
17×add-sqr-sqrt
14×*-un-lft-identity
10×associate-*l*
8×pow1 add-cube-cbrt add-cbrt-cube add-log-exp
6×add-exp-log associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out difference-of-squares unswap-sqr
1×+-commutative sub-neg times-frac diff-log sum-log distribute-lft-out--
Counts
4 → 163
Calls
4 calls:
65.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms
(+ 1.0 (/ 1.0 eps))
49.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
46.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms
(+ 1.0 (/ 1.0 eps))
47.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
181.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify139.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
011874036
143623762
250013749

prune425.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

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)))

rewrite69.0ms

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))
56.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series73.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(* 0.6666666666666667 (pow x 3))
39.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune111.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
0.1b
(* 0.6666666666666667 (pow x 3))
3.1b
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
6.8b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod associate-*r*
10×add-exp-log unpow-prod-down cube-prod
9×add-log-exp
7×add-cbrt-cube
5×pow1
4×cube-div unswap-sqr sqr-pow
3×cube-mult pow-unpow flip3-- unpow3 associate-*l* prod-exp flip--
2×pow-to-exp cbrt-div diff-log pow-exp
1×sub-neg pow-pow pow1/3 associate--l+ sum-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 93
Calls
4 calls:
55.0ms
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
12.0ms
(* 0.6666666666666667 (pow x 3))
46.0ms
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
55.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
39.0ms
(* 0.6666666666666667 (pow x 3))
37.0ms
(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
38.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify52.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0346862
11520806
25001799

prune245.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 8.0 (pow x 3))
0.2b
(* 12.0 (pow x 2))
7.0b
(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
10.0b
(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×associate-*r*
14×add-exp-log
12×add-cube-cbrt *-un-lft-identity
9×add-log-exp
8×unpow-prod-down add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sqr-pow
3×cbrt-prod
2×pow-to-exp cbrt-div flip3-- diff-log pow-exp *-commutative flip-- cbrt-unprod unpow2
1×cube-mult sub-neg pow1/3 unpow3 associate--l+ sum-log
Counts
4 → 85
Calls
4 calls:
13.0ms
(* 8.0 (pow x 3))
12.0ms
(* 12.0 (pow x 2))
56.0ms
(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
26.0ms
(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

series242.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 8.0 (pow x 3))
23.0ms
(* 12.0 (pow x 2))
41.0ms
(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
138.0ms
(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0420643
11692587
25001569

prune228.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

regimes74.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 17.1b

bsearch103.0ms

Steps
ItersRangePoint
7
345.8824083588705
6330.810310882262
417.18899044172827

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05834
17134
27134

end0.0ms

sample3.0s

Algorithm
intervals
Results
807.0ms1953×body10240exit
755.0ms1715×body1280valid
564.0ms9905×body80valid
336.0ms1284×body640valid
110.0ms633×body320valid
35.0ms317×body160valid