Details

Time bar (total: 5.4s)

sample101.0ms

Algorithm
intervals
Results
28.0ms60×body10240exit
23.0ms54×body1280valid
17.0ms299×body80valid
12.0ms44×body640valid
4.0ms22×body320valid
1.0ms11×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (39.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

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: 30.1b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.1b
(exp (- (* (+ 1.0 eps) x)))
0.1b
(exp (- (* (- 1.0 eps) x)))
3.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
256×add-sqr-sqrt
199×*-un-lft-identity
195×prod-diff
176×associate-*l*
107×add-cube-cbrt
102×associate-*r*
81×frac-sub
78×exp-neg
76×frac-times
62×exp-prod
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/ unswap-sqr
34×*-commutative
32×difference-of-squares
30×flip3-+ flip-+
28×flip3-- flip--
27×distribute-lft-neg-in distribute-rgt-neg-in distribute-lft-out--
22×distribute-lft-out
19×un-div-inv
13×times-frac fma-neg
10×add-log-exp
7×add-exp-log
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u rem-exp-log
2×neg-mul-1 neg-log prod-exp
1×sub-neg diff-log pow-prod-down cbrt-unprod
Counts
4 → 435
Calls
4 calls:
24.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
10.0ms
(exp (- (* (+ 1.0 eps) x)))
10.0ms
(exp (- (* (- 1.0 eps) x)))
63.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
29.0ms
(exp (- (* (+ 1.0 eps) x)))
32.0ms
(exp (- (* (- 1.0 eps) x)))
218.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify145.0ms

Algorithm
egg-herbie
Counts
447 → 447
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0191814628
1500111301

prune745.0ms

Filtered
447 candidates to 180 candidates (59.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New4434447
Fresh101
Picked101
Done000
Total4454449

Merged error: 0.5b

Counts
449 → 4

localize9.0ms

Local error

Found 1 expressions with local error:

6.6b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series45.0ms

Counts
1 → 3
Calls
1 calls:
45.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify30.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04189
113078
267778
3500175

prune45.0ms

Filtered
13 candidates to 11 candidates (15.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New11213
Fresh033
Picked101
Done000
Total12517

Merged error: 0.5b

Counts
17 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

series42.0ms

Counts
1 → 3
Calls
1 calls:
42.0ms
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)

simplify110.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04882
112867
253367
3308367
4500167

prune38.0ms

Filtered
13 candidates to 10 candidates (23.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New12113
Fresh134
Picked011
Done000
Total13518

Merged error: 0.5b

Counts
18 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)
0.5b
(expm1 (log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)))
12.4b
(log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u log1p-expm1-u
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-log1p
1×log1p-udef log1p-expm1 fma-udef expm1-udef
Counts
3 → 33
Calls
3 calls:
1.0ms
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)
1.0ms
(expm1 (log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)))
1.0ms
(log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0))

series296.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)
151.0ms
(expm1 (log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0)))
98.0ms
(log1p (fma (pow x 2) (- (* x 0.6666666666666667) 1.0) 2.0))

simplify90.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0255339
1828298
23568272
35002268

prune89.0ms

Filtered
42 candidates to 34 candidates (19.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New39342
Fresh033
Picked101
Done011
Total40747

Merged error: 0.5b

Counts
47 → 7

regimes94.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 17.0b

bsearch131.0ms

Steps
ItersRangePoint
9
5.487422510167526e-06
1875.067688488174
210.23946370490975

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04621
15621
25621

end0.0ms

sample2.9s

Algorithm
intervals
Results
770.0ms1873×body10240exit
749.0ms1690×body1280valid
568.0ms10220×body80valid
317.0ms1222×body640valid
115.0ms654×body320valid
33.0ms287×body160valid