Details

Time bar (total: 8.6s)

sample109.0ms

Algorithm
intervals
Results
28.0ms75×body10240exit
26.0ms62×body1280valid
21.0ms338×body80valid
10.0ms40×body640valid
2.0ms12×body320valid
1.0ms9×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: 28.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b
(* (- 1.0 eps) x)
1.7b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite376.0ms

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:
37.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
41.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
19.0ms
(* (- 1.0 eps) x)
269.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series269.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
39.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
30.0ms
(* (- 1.0 eps) x)
161.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06841993
121761881
250021880

prune443.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

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)))

rewrite77.0ms

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:
11.0ms
(* 0.5 (pow x 2))
12.0ms
(* 0.33333333333333337 (pow x 3))
53.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series93.0ms

Counts
3 → 9
Calls
3 calls:
22.0ms
(* 0.5 (pow x 2))
36.0ms
(* 0.33333333333333337 (pow x 3))
34.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0281367
11210327
25001314

prune165.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (* x (+ eps 1.0))) eps)
0.0b
(* x (- 1.0 eps))
0.0b
(* x (- 1.0 eps))
3.2b
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×*-un-lft-identity
13×associate-*r*
11×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×add-exp-log associate-*r/
8×distribute-rgt-in distribute-lft-in
6×sub-neg associate-+l+ frac-add add-log-exp
3×flip3-- pow-prod-down prod-exp *-commutative frac-sub flip-- cbrt-unprod unswap-sqr
2×flip3-+ exp-sum associate--l+ flip-+ distribute-lft-out-- difference-of-squares
1×+-commutative sum-log
Counts
4 → 94
Calls
4 calls:
17.0ms
(* (exp (* x (+ eps 1.0))) eps)
18.0ms
(* x (- 1.0 eps))
19.0ms
(* x (- 1.0 eps))
299.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

series240.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (exp (* x (+ eps 1.0))) eps)
31.0ms
(* x (- 1.0 eps))
35.0ms
(* x (- 1.0 eps))
146.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

simplify75.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05961321
124351221
250011221

prune458.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
0.2b
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
3.2b
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))
3.2b
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
24×frac-add
20×associate-*r/
14×sqrt-div
12×associate-+l+ frac-sub
8×add-sqr-sqrt flip3-+ flip-+ add-log-exp
6×pow1 distribute-rgt-in add-cube-cbrt *-un-lft-identity distribute-lft-in sqrt-prod
4×add-exp-log sub-neg flip3-- associate--l+ add-cbrt-cube flip--
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 84
Calls
4 calls:
423.0ms
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
426.0ms
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
298.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))
304.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

series639.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
172.0ms
(sqrt (+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps))))))
150.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))
147.0ms
(+ (* 0.5 (- (+ (/ 1 (exp (* x (+ eps 1.0)))) (/ 1 (exp (* x (- 1.0 eps))))) (/ 1 (* (exp (* x (+ eps 1.0))) eps)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05794450
124124276
250014274

prune467.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes66.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.0b

bsearch154.0ms

Steps
ItersRangePoint
10
1.3045330821618359e-08
1883.707833756068
468.3220261647266

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04753
14753

end0.0ms

sample2.9s

Algorithm
intervals
Results
761.0ms1974×body10240exit
728.0ms1733×body1280valid
530.0ms9965×body80valid
314.0ms1287×body640valid
99.0ms634×body320valid
31.0ms303×body160valid