Details

Time bar (total: 5.2s)

sample74.0ms

Algorithm
intervals
Results
35.0ms74×body1280valid
13.0ms48×body640valid
7.0ms20×body2560valid
6.0ms80×body80valid
4.0ms21×body320valid
1.0ms13×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

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: 49.2b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b
(sqrt (+ (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series16.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms
(sqrt (+ (* x x) 1.0))

simplify134.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune105.0ms

Filtered
51 candidates to 42 candidates (17.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New48351
Fresh000
Picked101
Done000
Total49352

Merged error: 0.0b

Counts
52 → 3

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
15.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
47.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series27.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
15.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08542083
146421650
250021650

prune393.0ms

Filtered
292 candidates to 111 candidates (62.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2911292
Fresh022
Picked011
Done000
Total2914295

Merged error: 0b

Counts
295 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
18.8b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
18.8b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
18.8b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
30×associate-*r/
26×frac-sub
25×cbrt-prod
23×add-sqr-sqrt
16×frac-times
15×add-cube-cbrt *-un-lft-identity
13×flip3-- flip3-+ flip-- flip-+
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×associate-*l/ add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
27.0ms
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
14.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
11.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
11.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

series114.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
23.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
26.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
23.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

simplify101.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05534431
126104246
250024123

prune1.3s

Filtered
121 candidates to 93 candidates (23.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1210121
Fresh022
Picked011
Done011
Total1214125

Merged error: 0b

Counts
125 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
10.0b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube distribute-lft-out
5×pow1 difference-of-squares sqr-pow
4×cube-mult unpow3 distribute-lft-out--
3×flip3-+ div-exp flip-+ associate-/l*
2×log-div diff-log sum-log frac-sub
1×cbrt-undiv +-commutative pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow flip-- div-inv
Counts
4 → 117
Calls
4 calls:
5.0ms
(+ x (/ 0.5 x))
18.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))
21.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series20.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ x (/ 0.5 x))
4.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
3.0ms
(/ 0.125 (pow x 3))
9.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0478840
12197799
25001799

prune156.0ms

Filtered
129 candidates to 77 candidates (40.3%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1290129
Fresh011
Picked011
Done022
Total1294133

Merged error: 0b

Counts
133 → 4

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.0b

bsearch31.0ms

Steps
ItersRangePoint
9
0.00021166572504141735
1495.4209016812965
0.8925876196495554
10
-249197998.3190651
-3.6532051617239265e-06
-1.018192898139174

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2339×body1280valid
446.0ms1584×body640valid
276.0ms815×body2560valid
128.0ms763×body320valid
89.0ms2110×body80valid
38.0ms389×body160valid

Profiling

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