Details

Time bar (total: 4.4s)

sample76.0ms

Algorithm
intervals
Results
39.0ms85×body1280valid
14.0ms56×body640valid
8.0ms27×body2560valid
3.0ms19×body320valid
2.0ms57×body80valid
1.0ms12×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 54.2b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(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))

series24.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ x (sqrt (+ (* x x) 1.0)))
13.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms
(sqrt (+ (* x x) 1.0))

simplify169.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (163.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune109.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New47451
Fresh000
Picked101
Done000
Total48452

Merged error: 0b

Counts
52 → 4

localize11.0ms

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))))
0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite124.0ms

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:
21.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
65.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series44.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
25.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify150.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
08542083
146421650
250021650

prune370.0ms

Filtered
111 candidates to 292 candidates (-163.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh033
Picked011
Done000
Total2924296

Merged error: 0b

Counts
296 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (neg 0.0625) (pow x 5))
0.4b
(/ 0.125 (pow x 3))
14.3b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
21.3b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
6.0ms
(/ (neg 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
67.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
69.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ (neg 0.0625) (pow x 5))
3.0ms
(/ 0.125 (pow x 3))
10.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
9.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify98.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08371963
137941884
250021876

prune453.0ms

Filtered
152 candidates to 235 candidates (-54.6%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh022
Picked011
Done011
Total2354239

Merged error: 0b

Counts
239 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
10.9b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×add-sqr-sqrt
40×times-frac
29×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
9×add-exp-log
8×add-log-exp
6×log-prod
5×add-cbrt-cube distribute-lft-out difference-of-squares sqr-pow
4×pow1 cube-mult unpow3 distribute-lft-out--
3×div-exp associate-/l*
2×log-div flip3-+ diff-log frac-sub flip-+
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num sum-log log-pow flip-- div-inv
Counts
3 → 105
Calls
3 calls:
18.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))
22.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series16.0ms

Counts
3 → 9
Calls
3 calls:
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)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
0469784
12135746
25003746

prune137.0ms

Filtered
67 candidates to 114 candidates (-70.1%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1140114
Fresh011
Picked011
Done022
Total1144118

Merged error: 0b

Counts
118 → 4

regimes42.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch30.0ms

Steps
ItersRangePoint
10
1.6467731241392944e-08
62869179882.65231
0.8766955773154053
9
-3.3701171682469404
-2.708263725627834e-09
-1.0022743825950324

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2315×body1280valid
425.0ms1551×body640valid
266.0ms819×body2560valid
137.0ms815×body320valid
84.0ms2110×body80valid
38.0ms390×body160valid

Profiling

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