Details

Time bar (total: 7.5s)

sample149.0ms

Algorithm
intervals
Results
48.0ms314×body80valid
41.0ms54×body1280valid
19.0ms39×body640valid
14.0ms71×body80overflowed
6.0ms16×body320valid
3.0ms13×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize18.0ms

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)))
3.0b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite287.0ms

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:
11.0ms
(* (+ 1.0 eps) x)
25.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
20.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
224.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series299.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ 1.0 eps) x)
51.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
42.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
178.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06891986
122651877
250031876

prune431.0ms

Pruning

2 alts after pruning (2 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))
6.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite36.0ms

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:
6.0ms
(* 0.33333333333333337 (pow x 3))
29.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series80.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(* 0.33333333333333337 (pow x 3))
40.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0207273
1894245
25002241

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))))
0.0b
(exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
0.1b
(* 0.33333333333333337 (pow x 3))
6.4b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-log-exp
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
9×add-exp-log
6×log-prod exp-prod exp-sum add-cbrt-cube
5×pow1
4×unpow-prod-down diff-log cube-prod log-pow unswap-sqr
3×sub-neg associate-*l* prod-exp associate--l+ rem-exp-log
2×exp-diff sum-log sqr-pow
1×cube-mult pow-to-exp log-div flip3-- unpow3 rem-log-exp pow-exp *-commutative flip-- cbrt-unprod
Counts
4 → 81
Calls
4 calls:
50.0ms
(log (exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))))
49.0ms
(exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 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)))

series158.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(log (exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))))
33.0ms
(exp (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
41.0ms
(* 0.33333333333333337 (pow x 3))
39.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0267616
11177552
25001539

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.33333333333333337 (* (exp 1.0) (pow x 3)))
0.2b
(* (exp 1.0) (pow x 2))
6.4b
(- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2))))
10.7b
(log (- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
14×add-exp-log
11×add-cbrt-cube
10×prod-exp
9×add-cube-cbrt *-un-lft-identity associate-*r* add-log-exp
7×pow1
6×associate-*l*
4×unpow-prod-down cbrt-unprod unswap-sqr
3×log-prod
2×pow-to-exp log-div flip3-- diff-log pow-exp *-commutative flip-- unpow2 sqr-pow
1×sub-neg rem-log-exp pow-prod-down associate--l+ sum-log log-pow
Counts
4 → 74
Calls
4 calls:
14.0ms
(* 0.33333333333333337 (* (exp 1.0) (pow x 3)))
8.0ms
(* (exp 1.0) (pow x 2))
25.0ms
(- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2))))
14.0ms
(log (- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2)))))

series408.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* 0.33333333333333337 (* (exp 1.0) (pow x 3)))
65.0ms
(* (exp 1.0) (pow x 2))
93.0ms
(- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2))))
154.0ms
(log (- (+ (exp 1.0) (* 0.33333333333333337 (* (exp 1.0) (pow x 3)))) (* 0.5 (* (exp 1.0) (pow x 2)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0396876
11697772
25002756

prune235.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes70.0ms

Accuracy

96.3% (0.6b remaining)

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

bsearch177.0ms

Steps
ItersRangePoint
8
0.000431479263060677
6.35199241072448
2.4226617870012475

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04732
14732

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s9782×body80valid
1.3s1727×body1280valid
633.0ms1254×body640valid
279.0ms1896×body80overflowed
241.0ms657×body320valid
85.0ms330×body160valid