Details

Time bar (total: 6.6s)

sample103.0ms

Algorithm
intervals
Results
31.0ms69×body10240exit
23.0ms55×body1280valid
16.0ms307×body80valid
11.0ms43×body640valid
4.0ms23×body320valid
1.0ms8×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

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: 30.2b

localize20.0ms

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)))
2.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
106×times-frac
94×add-sqr-sqrt
36×add-cube-cbrt
26×distribute-lft-out--
17×difference-of-squares
11×distribute-lft-out
10×add-cbrt-cube associate-/l*
8×add-exp-log
6×pow1 associate-/r* add-log-exp
4×associate-*l* div-inv associate-/l/
3×div-sub associate-*r*
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp associate-*l/ clear-num flip-- flip-+
1×sub-neg distribute-rgt-out-- diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod sub-div associate--r- unswap-sqr
Counts
4 → 137
Calls
4 calls:
26.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
9.0ms
(* (+ 1.0 eps) x)
20.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
315.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series286.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
26.0ms
(* (+ 1.0 eps) x)
39.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
174.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify66.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06891986
122651877
250011876

prune447.0ms

Filtered
149 candidates to 109 candidates (73.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite48.0ms

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:
7.0ms
(* 0.33333333333333337 (pow x 3))
40.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 0.33333333333333337 (pow x 3))
37.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune112.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
9.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3
2×diff-log
1×sub-neg associate--l+ sum-log
Counts
4 → 53
Calls
4 calls:
29.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
12.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
13.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
146.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
142.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
149.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify134.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0253983
1904924
24251839
35001839

prune280.0ms

Filtered
65 candidates to 59 candidates (90.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

7.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.2b
(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
9.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div flip3-- diff-log add-cbrt-cube flip--
2×sub-neg pow1/3 associate--l+ sum-log
Counts
4 → 54
Calls
4 calls:
27.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
29.0ms
(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
12.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
13.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
38.0ms
(- (+ (* 0.1111111111111111 (pow x 3)) 1) (* 0.16666666666666666 (pow x 2)))
295.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
147.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify43.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0337862
11254804
25001748

prune287.0ms

Filtered
66 candidates to 52 candidates (78.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes86.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.7b

bsearch154.0ms

Steps
ItersRangePoint
10
0.3394070361140097
2696347712.967018
199.93447332075127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05371
15371

end0.0ms

sample2.8s

Algorithm
intervals
Results
789.0ms1923×body10240exit
741.0ms1721×body1280valid
536.0ms9984×body80valid
315.0ms1276×body640valid
106.0ms645×body320valid
35.0ms334×body160valid