Details

Time bar (total: 6.3s)

sample106.0ms

Algorithm
intervals
Results
29.0ms63×body1280valid
28.0ms70×body10240exit
18.0ms340×body80valid
9.0ms35×body640valid
3.0ms21×body320valid
1.0ms8×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
106×times-frac
96×add-sqr-sqrt
36×add-cube-cbrt
27×distribute-lft-out--
18×difference-of-squares
10×add-cbrt-cube distribute-lft-out associate-/l*
8×add-exp-log
6×pow1 associate-/r* add-log-exp
5×associate-*l*
4×div-inv associate-/l/
3×flip3-- div-sub associate-*r* flip--
2×cbrt-undiv frac-2neg div-exp associate-*l/ clear-num
1×sub-neg distribute-rgt-out-- flip3-+ diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod flip-+ sub-div associate--r- unswap-sqr
Counts
4 → 138
Calls
4 calls:
6.0ms
(* (- 1.0 eps) x)
11.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
10.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
131.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series294.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (- 1.0 eps) x)
43.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
43.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
176.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06841993
121761881
250021880

prune434.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
5.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite19.0ms

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:
5.0ms
(* 0.5 (pow x 2))
6.0ms
(* 0.33333333333333337 (pow x 3))
7.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series100.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(* 0.5 (pow x 2))
34.0ms
(* 0.33333333333333337 (pow x 3))
43.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0281367
11210327
25001314

prune169.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
8.5b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.5b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.5b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite27.0ms

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:
7.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (+ (* 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))))
149.0ms
(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))))

simplify132.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0253983
1904924
24251839
35001839

prune272.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
5.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
8.5b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.5b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite28.0ms

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:
7.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
45.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
143.0ms
(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))))

simplify133.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0253862
1904804
24251738
35001738

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes88.0ms

Accuracy

90.5% (1.5b remaining)

Error of 1.8b against oracle of 0.3b and baseline of 16.0b

bsearch84.0ms

Steps
ItersRangePoint
6
1.0380161377784092e-26
1.091895904028376e-25
1.0640289263225317e-25

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample2.8s

Algorithm
intervals
Results
761.0ms1891×body10240exit
755.0ms1749×body1280valid
560.0ms10040×body80valid
312.0ms1224×body640valid
115.0ms680×body320valid
35.0ms305×body160valid