Details

Time bar (total: 6.6s)

sample137.0ms

Algorithm
intervals
Results
39.0ms71×body5120exit
31.0ms60×body1280valid
29.0ms316×body80valid
14.0ms43×body640valid
4.0ms19×body320valid
1.0ms9×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0515127

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(exp (neg (* (+ 1.0 eps) x)))
0.0b
(* (+ 1.0 eps) x)
2.3b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
73×exp-neg
72×frac-times
55×neg-sub0 exp-diff
40×associate-*l/
36×associate-*r/
29×flip3-- flip--
28×flip3-+ flip-+
18×un-div-inv
15×add-sqr-sqrt
13×*-un-lft-identity
9×add-cube-cbrt associate-*l*
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
6.0ms
(* (- 1.0 eps) x)
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
6.0ms
(* (+ 1.0 eps) x)
16.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (- 1.0 eps) x)
6.0ms
(exp (neg (* (+ 1.0 eps) x)))
4.0ms
(* (+ 1.0 eps) x)
49.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049846282
149846282

prune292.0ms

Filtered
86 candidates to 165 candidates (-91.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1632165
Fresh101
Picked011
Done000
Total1643167

Merged error: 0.5b

Counts
167 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (pow x 3) 0.6666666666666667)
5.0b
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
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-*r* prod-exp
2×pow1 associate-+r+ sum-log sqr-pow
1×+-commutative cube-mult pow-to-exp associate-+r- sub-neg flip3-+ diff-log unpow3 pow-exp *-commutative cbrt-unprod flip-+
Counts
2 → 46
Calls
2 calls:
5.0ms
(* (pow x 3) 0.6666666666666667)
6.0ms
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(* (pow x 3) 0.6666666666666667)
4.0ms
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify37.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05139465

prune70.0ms

Filtered
33 candidates to 52 candidates (-57.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New51152
Fresh011
Picked101
Done011
Total52355

Merged error: 0.5b

Counts
55 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- 2.0 (* x (* x 1.0))) 3)
0.1b
(* x (+ 1.0 (* x 0.6666666666666667)))
11.2b
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
12.9b
(/ (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3)) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
9×add-exp-log times-frac add-cbrt-cube
7×pow1
6×add-log-exp
4×flip3-+ flip-+
3×unpow-prod-down pow-unpow cube-prod associate-*r* associate-*l* associate-/r* associate-/l*
2×cube-div associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-in cube-mult pow-to-exp flip3-- pow-pow frac-2neg distribute-lft-in unpow3 div-exp pow-prod-down pow-exp prod-exp clear-num sum-log *-commutative flip-- cbrt-unprod div-inv rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 89
Calls
4 calls:
3.0ms
(pow (- 2.0 (* x (* x 1.0))) 3)
5.0ms
(* x (+ 1.0 (* x 0.6666666666666667)))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
15.0ms
(/ (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3)) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (- 2.0 (* x (* x 1.0))) 3)
6.0ms
(* x (+ 1.0 (* x 0.6666666666666667)))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
14.0ms
(/ (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3)) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
061532823

prune339.0ms

Filtered
72 candidates to 101 candidates (-40.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New992101
Fresh011
Picked101
Done011
Total1004104

Merged error: 0.5b

Counts
104 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

11.2b
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
11.2b
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
11.2b
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
13.7b
(/ (cbrt (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
12×cbrt-prod
10×add-log-exp
6×add-exp-log associate-/l*
5×flip3-+ add-cbrt-cube flip-+
4×pow1
3×+-commutative associate-/r* sum-log
2×cbrt-div associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 76
Calls
4 calls:
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
14.0ms
(/ (cbrt (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

series47.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
8.0ms
(+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))
20.0ms
(/ (cbrt (+ (* (pow x 9) (pow 0.6666666666666667 3)) (pow (- 2.0 (* x (* x 1.0))) 3))) (+ (* 0.6666666666666667 (* 0.6666666666666667 (pow x 6))) (* (- 2.0 (* x (* x 1.0))) (- 2.0 (* x (* x (+ 1.0 (* x 0.6666666666666667))))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
049973974
149973974

prune754.0ms

Filtered
77 candidates to 88 candidates (-14.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New86288
Fresh022
Picked101
Done011
Total87592

Merged error: 0.5b

Counts
92 → 5

regimes307.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 15.5b

bsearch94.0ms

Steps
ItersRangePoint
9
0.41648793310771814
20979818.667232726
33.18728172540726

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
085121
185121

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.1s1938×body5120exit
977.0ms1763×body1280valid
777.0ms10014×body80valid
442.0ms1263×body640valid
150.0ms628×body320valid
53.0ms333×body160valid

Profiling

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