Details

Time bar (total: 9.1s)

sample108.0ms

Algorithm
intervals
Results
23.0ms46×body10240exit
21.0ms309×body80valid
21.0ms42×body1280valid
18.0ms48×body640valid
6.0ms26×body320valid
1.0ms11×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* (- 1.0 eps) x))
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.4b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
106×times-frac
90×add-sqr-sqrt
34×add-cube-cbrt
26×distribute-lft-out--
17×difference-of-squares
10×distribute-lft-out associate-/l* add-log-exp
8×add-cbrt-cube
6×add-exp-log associate-/r*
4×pow1 div-inv associate-/l/
3×div-sub
2×cbrt-undiv flip3-- exp-to-pow frac-2neg diff-log div-exp clear-num flip--
1×sub-neg exp-prod distribute-rgt-out-- flip3-+ frac-sub flip-+ rem-exp-log sub-div associate--r-
Counts
4 → 127
Calls
4 calls:
9.0ms
(exp (* (- 1.0 eps) x))
44.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
42.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
295.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series267.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(exp (* (- 1.0 eps) x))
40.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
165.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
06171951
118601845
250011835

prune749.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
7.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (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:
13.0ms
(* 0.33333333333333337 (pow x 3))
58.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series72.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(* 0.33333333333333337 (pow x 3))
38.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

7.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
11.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.6b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite141.0ms

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:
55.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
27.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
29.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
28.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
138.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
134.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
141.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify145.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0253983
1904924
24251839
35001839

prune676.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
0.0b
(/ 1.0 (exp (* (+ 1.0 eps) x)))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.4b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
123×add-sqr-sqrt
112×*-un-lft-identity
69×add-cube-cbrt
20×associate-/l*
13×add-cbrt-cube
12×difference-of-squares
10×distribute-lft-out--
9×add-exp-log associate-/r* div-inv
7×distribute-lft-out
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1
3×frac-2neg clear-num associate-/l/
1×sub-neg flip3-- distribute-rgt-out-- flip3-+ diff-log frac-sub flip-- flip-+ sub-div
Counts
4 → 167
Calls
4 calls:
16.0ms
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
9.0ms
(/ 1.0 (exp (* (+ 1.0 eps) x)))
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
371.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

series187.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x)))
23.0ms
(/ 1.0 (exp (* (+ 1.0 eps) x)))
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
93.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
07922363
127062248
250032248

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes112.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.5b

bsearch182.0ms

Steps
ItersRangePoint
8
0.007285382865895221
3.704765010127866
1.7465203117868437

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04745
14745

end0.0ms

sample3.4s

Algorithm
intervals
Results
982.0ms1936×body10240exit
851.0ms1702×body1280valid
681.0ms9996×body80valid
397.0ms1310×body640valid
136.0ms663×body320valid
44.0ms333×body160valid