Details

Time bar (total: 4.3s)

sample73.0ms

Algorithm
intervals
Results
34.0ms69×body1280valid
14.0ms51×body640valid
8.0ms24×body2560valid
4.0ms24×body320valid
3.0ms71×body80valid
2.0ms17×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: 53.2b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
4.3b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.4b
(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))

series17.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms
(sqrt (+ (* x x) 1.0))

simplify142.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune117.0ms

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

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
79.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify89.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07251757
138321368
250011368

prune313.0ms

Filtered
95 candidates to 273 candidates (-187.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh033
Picked011
Done000
Total2734277

Merged error: 0b

Counts
277 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.3b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube distribute-lft-out--
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult diff-log unpow3
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×sub-neg log-div associate--l+ frac-sub
1×cbrt-undiv +-commutative pow-to-exp associate-+r- flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 125
Calls
4 calls:
17.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
19.0ms
(+ x (- (+ 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)))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
3.0ms
(/ 0.125 (pow x 3))
11.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0505968
12347911
25002911

prune167.0ms

Filtered
80 candidates to 137 candidates (-71.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1370137
Fresh022
Picked011
Done011
Total1374141

Merged error: 0b

Counts
141 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (neg 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
11.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
18.2b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite153.0ms

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))
66.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
67.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ (neg 0.0625) (pow x 5))
3.0ms
(/ 0.125 (pow x 3))
9.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
5.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify111.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08371963
137941884
250021876

prune434.0ms

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

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh011
Picked011
Done022
Total2354239

Merged error: 0b

Counts
239 → 4

regimes80.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch30.0ms

Steps
ItersRangePoint
8
0.3609580473631881
2872.6372031135757
0.8926364099887224
10
-522.1368722912733
-5.949899967025005e-16
-1.0153454212587587

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2339×body1280valid
432.0ms1551×body640valid
271.0ms799×body2560valid
135.0ms790×body320valid
90.0ms2120×body80valid
40.0ms401×body160valid

Profiling

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