Details

Time bar (total: 6.4s)

sample101.0ms

Algorithm
intervals
Results
25.0ms60×body1280valid
23.0ms58×body10240exit
17.0ms330×body80valid
10.0ms42×body640valid
8.0ms30×body320valid
1.0ms10×body160valid

simplify37.0ms

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: 33.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
3.9b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite279.0ms

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:
9.0ms
(* (+ 1.0 eps) x)
20.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
25.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
219.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series300.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (+ 1.0 eps) x)
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
48.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
180.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06891986
122651877
250031876

prune442.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
6.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp unswap-sqr
7×add-cbrt-cube
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×cube-mult sub-neg flip3-- unpow3 associate--l+ sum-log flip--
Counts
3 → 72
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
6.0ms
(* 0.33333333333333337 (pow x 3))
25.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* 0.5 (pow x 2))
37.0ms
(* 0.33333333333333337 (pow x 3))
43.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify44.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0281367
11210327
25001314

prune164.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
4.7b
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
14×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div diff-log add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ sum-log
Counts
4 → 58
Calls
4 calls:
21.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
22.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
28.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
25.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
58.0ms
(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
38.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
41.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify106.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0171688
1611636
23106618
35003616

prune224.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

6.0b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
9.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.2b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite66.0ms

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:
28.0ms
(- (+ (* 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))))
12.0ms
(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))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (+ (* 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))))
144.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
151.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify138.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0253983
1904924
24251839
35001839

prune269.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes59.0ms

Accuracy

95.8% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 15.6b

bsearch124.0ms

Steps
ItersRangePoint
9
0.003342748024832997
311.65670950425
174.4766212849145

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04222
14222

end0.0ms

sample3.0s

Algorithm
intervals
Results
925.0ms1991×body10240exit
749.0ms1773×body1280valid
533.0ms10064×body80valid
323.0ms1331×body640valid
107.0ms644×body320valid
32.0ms310×body160valid