Details

Time bar (total: 5.5s)

sample79.0ms

Algorithm
intervals
Results
25.0ms46×body1280valid
21.0ms329×body80valid
9.0ms33×body640valid
3.0ms52×body80overflowed
3.0ms15×body320valid
1.0ms6×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 23.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
29×flip3-- flip--
27×flip3-+ flip-+
18×un-div-inv
12×add-sqr-sqrt exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
5×associate-*l*
4×rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 149
Calls
4 calls:
7.0ms
(* (- 1.0 eps) x)
4.0ms
(exp (neg (* (- 1.0 eps) x)))
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
21.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (- 1.0 eps) x)
30.0ms
(exp (neg (* (- 1.0 eps) x)))
26.0ms
(exp (neg (* (+ 1.0 eps) x)))
195.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify135.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
011753668
143233407
250023396

prune363.0ms

Filtered
161 candidates to 82 candidates (50.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1583161
Fresh000
Picked101
Done000
Total1593162

Merged error: 0.3b

Counts
162 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
23×exp-prod
20×add-log-exp
16×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
8×rem-exp-log
6×distribute-lft-neg-in distribute-rgt-neg-in
4×pow1 add-exp-log exp-diff exp-sum neg-log add-cbrt-cube
3×diff-log sum-log frac-sub
2×neg-sub0 exp-neg neg-mul-1 sub-neg distribute-neg-in distribute-lft-out-- difference-of-squares
1×flip3-- flip3-+ times-frac frac-add associate--l+ flip-- flip-+ distribute-lft-out
Counts
4 → 82
Calls
4 calls:
4.0ms
(exp (- (* x eps) (* 1.0 x)))
5.0ms
(exp (neg (+ (* x eps) (* 1.0 x))))
8.0ms
(exp (neg (+ (* x eps) (* 1.0 x))))
24.0ms
(- (+ (/ (exp (- (* x eps) (* 1.0 x))) eps) (exp (- (* x eps) (* 1.0 x)))) (/ (exp (neg (+ (* x eps) (* 1.0 x)))) eps))

series140.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(exp (- (* x eps) (* 1.0 x)))
18.0ms
(exp (neg (+ (* x eps) (* 1.0 x))))
17.0ms
(exp (neg (+ (* x eps) (* 1.0 x))))
86.0ms
(- (+ (/ (exp (- (* x eps) (* 1.0 x))) eps) (exp (- (* x eps) (* 1.0 x)))) (/ (exp (neg (+ (* x eps) (* 1.0 x)))) eps))

simplify109.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
02881023
1858958
23863910
35001908

prune304.0ms

Filtered
94 candidates to 73 candidates (77.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New93194
Fresh022
Picked101
Done000
Total94397

Merged error: 0.3b

Counts
97 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.6666666666666667 (pow x 3))
42.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0207270
1894242
25002238

prune95.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New50151
Fresh022
Picked011
Done000
Total50454

Merged error: 0.3b

Counts
54 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
0.1b
(pow (* 1.0 (pow x 2)) 3)
13.6b
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
14.9b
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
40×difference-of-squares
39×times-frac
37×*-un-lft-identity
33×sqr-pow
27×add-cube-cbrt
17×add-exp-log
15×unpow-prod-down cube-prod
13×associate-/l*
12×associate-*r*
11×add-cbrt-cube
6×pow-exp prod-exp add-log-exp
5×pow1 difference-cubes distribute-lft-out--
4×unswap-sqr
3×pow-to-exp pow-unpow associate-*l* associate-/r*
2×cube-mult flip3-- unpow3 associate-/r/ flip-- cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-undiv sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp clear-num *-commutative flip-+ div-inv
Counts
4 → 148
Calls
4 calls:
7.0ms
(* 0.6666666666666667 (pow x 3))
5.0ms
(pow (* 1.0 (pow x 2)) 3)
14.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
33.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 0.6666666666666667 (pow x 3))
51.0ms
(pow (* 1.0 (pow x 2)) 3)
95.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
145.0ms
(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06313439
129333295
250013294

prune526.0ms

Filtered
160 candidates to 111 candidates (69.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1582160
Fresh022
Picked101
Done101
Total1604164

Merged error: 0.3b

Counts
164 → 4

regimes80.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch143.0ms

Steps
ItersRangePoint
8
0.004314681149180372
4.41326808055529
1.1309056466216085

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06658
17858
27858

end0.0ms

sample2.5s

Algorithm
intervals
Results
831.0ms1683×body1280valid
664.0ms10070×body80valid
381.0ms1291×body640valid
124.0ms599×body320valid
120.0ms1843×body80overflowed
39.0ms305×body160valid

Profiling

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