Details

Time bar (total: 5.5s)

analyze227.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%87.4%12.6%6
20.3%59.3%20.4%7
21.1%51.5%27.4%8
35.5%30.4%34%9
35.7%26.1%38.1%10
42.8%15.4%41.8%11
42.9%13.2%44%12
46.4%7.8%45.8%13
46.4%6.6%47%14

sample123.0ms

Algorithm
intervals
Results
24.0ms43×body1280valid
17.0ms52×body640valid
10.0ms137×body80valid
3.0ms15×body320valid
1.0ms9×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0572027

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: 27.8b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b
(* (+ 1.0 eps) x)
27.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac diff-log distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
13.0ms
(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms
(* (+ 1.0 eps) x)
19.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series73.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms
(* (+ 1.0 eps) x)
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify84.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049936927
149936927

prune363.0ms

Filtered
100 candidates to 183 candidates (-83.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1812183
Fresh101
Picked101
Done000
Total1832185

Merged error: 0.8b

Counts
185 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (pow x 3) 0.6666666666666667)
6.4b
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite13.0ms

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 sum-log sqr-pow
1×+-commutative cube-mult pow-to-exp associate-+r- sub-neg associate-+r+ flip3-+ diff-log unpow3 pow-exp *-commutative cbrt-unprod flip-+
Counts
2 → 45
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))))

simplify53.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
04959458
14959458

prune76.0ms

Filtered
33 candidates to 51 candidates (-54.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New47451
Fresh011
Picked101
Done000
Total48553

Merged error: 0.8b

Counts
53 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (* x (- (* x 0.6666666666666667) 1.0)))
0.1b
(* x (- (* x 0.6666666666666667) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×sub-neg associate-*r/ associate-*l*
5×distribute-rgt-in add-cube-cbrt *-un-lft-identity distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-- *-commutative flip-- add-log-exp
1×unswap-sqr
Counts
2 → 46
Calls
2 calls:
9.0ms
(* x (* x (- (* x 0.6666666666666667) 1.0)))
6.0ms
(* x (- (* x 0.6666666666666667) 1.0))

series12.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(* x (* x (- (* x 0.6666666666666667) 1.0)))
5.0ms
(* x (- (* x 0.6666666666666667) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05235490

prune64.0ms

Filtered
30 candidates to 52 candidates (-73.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New50252
Fresh134
Picked101
Done000
Total52557

Merged error: 0.8b

Counts
57 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b
(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b
(cbrt (- (* x 0.6666666666666667) 1.0))
0.2b
(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-- pow1/3 flip--
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
4.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
4.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
5.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
13.0ms
(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
9.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
9.0ms
(cbrt (- (* x 0.6666666666666667) 1.0))
12.0ms
(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
049691633
149691633

prune261.0ms

Filtered
80 candidates to 99 candidates (-23.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New97299
Fresh044
Picked101
Done000
Total986104

Merged error: 0.8b

Counts
104 → 6

regimes139.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch93.0ms

Steps
ItersRangePoint
8
26.996139422879125
16331.47228918433
120.7427870229541

simplify11.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
056556
156556

end0.0ms

sample3.6s

Algorithm
intervals
Results
885.0ms1703×body1280valid
422.0ms1310×body640valid
294.0ms4071×body80valid
133.0ms592×body320valid
47.0ms324×body160valid

Profiling

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