Details

Time bar (total: 4.1s)

sample88.0ms

Algorithm
intervals
Results
23.0ms107×body2560nan
16.0ms524×body80nan
12.0ms79×body1280nan
10.0ms256×body80valid
5.0ms43×body640nan
3.0ms31×body320nan
1.0ms10×body160nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.9b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) 1.0)
0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.7b
(sqrt (- (* x x) 1.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
4.0ms
(- (* x x) 1.0)
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series24.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (* x x) 1.0)
12.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

simplify132.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0327471
11087435
24892422
35002422

prune112.0ms

Filtered
68 candidates to 55 candidates (19.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh000
Picked101
Done000
Total66369

Merged error: 0b

Counts
69 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
0.0b
(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
0.6b
(/ 0.125 (pow x 3))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×times-frac
39×*-un-lft-identity
29×add-cube-cbrt
14×unpow-prod-down cube-prod
12×associate-/r*
10×difference-of-squares
9×add-exp-log
6×sqr-pow
5×add-cbrt-cube add-log-exp
4×pow1 cube-mult unpow3
3×log-prod div-exp associate-/l* distribute-lft-out--
2×log-div
1×cbrt-undiv associate--l- neg-sub0 pow-to-exp sub-neg flip3-- distribute-rgt-neg-in frac-2neg flip3-+ diff-log div-sub rem-log-exp pow-exp clear-num log-pow frac-sub flip-- flip-+ div-inv
Counts
3 → 106
Calls
3 calls:
80.0ms
(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
80.0ms
(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))

series20.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
7.0ms
(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0457837
12004799
25002799

prune159.0ms

Filtered
115 candidates to 71 candidates (38.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1150115
Fresh022
Picked011
Done000
Total1153118

Merged error: 0b

Counts
118 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (exp (log (sqrt (- (* x x) 1.0)))))
0.0b
(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
5.6b
(exp (log (sqrt (- (* x x) 1.0))))
30.7b
(sqrt (- (* x x) 1.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt
11×log-prod
9×add-cube-cbrt
8×pow1 sqrt-prod
7×exp-sum
6×exp-prod add-log-exp
5×add-exp-log
4×log-div sqrt-div log-pow add-cbrt-cube
2×flip3-- sqrt-pow1 flip3-+ pow1/2 exp-diff flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square rem-log-exp sum-log rem-exp-log
Counts
4 → 66
Calls
4 calls:
8.0ms
(+ x (exp (log (sqrt (- (* x x) 1.0)))))
7.0ms
(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
6.0ms
(exp (log (sqrt (- (* x x) 1.0))))
6.0ms
(sqrt (- (* x x) 1.0))

series22.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ x (exp (log (sqrt (- (* x x) 1.0)))))
9.0ms
(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
4.0ms
(exp (log (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

simplify137.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
0365649
11119581
24804558
35003552

prune141.0ms

Filtered
78 candidates to 65 candidates (16.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New78078
Fresh011
Picked011
Done011
Total78381

Merged error: 0b

Counts
81 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ x (cbrt (pow (sqrt (- (* x x) 1.0)) 3))))
0.0b
(pow (sqrt (- (* x x) 1.0)) 3)
30.7b
(sqrt (- (* x x) 1.0))
39.5b
(cbrt (pow (sqrt (- (* x x) 1.0)) 3))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×cbrt-prod sqrt-prod
18×*-un-lft-identity
16×add-cube-cbrt
14×unpow-prod-down cube-prod
8×pow1
6×add-exp-log sqrt-div
5×add-cbrt-cube difference-of-squares
4×cube-div log-prod add-log-exp
3×pow-unpow flip3-- pow-pow flip--
2×cube-mult log-div cbrt-div sqrt-pow1 pow1/2 unpow3 sqr-pow
1×pow-to-exp rem-sqrt-square flip3-+ pow1/3 rem-log-exp pow-exp log-pow sqrt-pow2 rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 98
Calls
4 calls:
10.0ms
(log (+ x (cbrt (pow (sqrt (- (* x x) 1.0)) 3))))
6.0ms
(pow (sqrt (- (* x x) 1.0)) 3)
4.0ms
(sqrt (- (* x x) 1.0))
6.0ms
(cbrt (pow (sqrt (- (* x x) 1.0)) 3))

series22.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(log (+ x (cbrt (pow (sqrt (- (* x x) 1.0)) 3))))
5.0ms
(pow (sqrt (- (* x x) 1.0)) 3)
4.0ms
(sqrt (- (* x x) 1.0))
4.0ms
(cbrt (pow (sqrt (- (* x x) 1.0)) 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0451792
11710741
25002727

prune150.0ms

Filtered
110 candidates to 69 candidates (37.3%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1100110
Fresh000
Picked011
Done022
Total1103113

Merged error: 0b

Counts
113 → 3

regimes28.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0178
1178

end0.0ms

sample2.7s

Algorithm
intervals
Results
609.0ms3105×body2560nan
570.0ms16610×body80nan
402.0ms2516×body1280nan
328.0ms8000×body80valid
163.0ms1256×body640nan
62.0ms628×body320nan
23.0ms312×body160nan

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