Details

Time bar (total: 5.5s)

sample72.0ms

Algorithm
intervals
Results
37.0ms78×body1280valid
11.0ms39×body640valid
8.0ms22×body2560valid
4.0ms24×body320valid
3.0ms83×body80valid
1.0ms10×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 50.9b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.8b
(+ x (sqrt (+ (* x x) 1.0)))
3.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite16.0ms

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:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series271.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify134.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune134.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0.0b

Counts
52 → 5

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite72.0ms

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:
54.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series143.0ms

Counts
1 → 3
Calls
1 calls:
143.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify99.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07251757
138321368
250021368

prune378.0ms

Filtered
273 candidates to 95 candidates (34.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh044
Picked011
Done000
Total2735278

Merged error: 0.0b

Counts
278 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.2b
(/ 0.125 (pow x 3))
10.9b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
36×times-frac
30×add-sqr-sqrt add-cube-cbrt
15×add-log-exp
12×unpow-prod-down cube-prod associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube
5×pow1 sum-log
4×cube-mult unpow3 distribute-lft-out-- sqr-pow
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×+-commutative log-div diff-log
1×cbrt-undiv pow-to-exp associate-+r- sub-neg frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow div-inv
Counts
4 → 114
Calls
4 calls:
6.0ms
(+ x (/ 0.5 x))
23.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
5.0ms
(/ 0.125 (pow x 3))
20.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ x (/ 0.5 x))
49.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
36.0ms
(/ 0.125 (pow x 3))
156.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0436780
12073718
25001718

prune198.0ms

Filtered
126 candidates to 73 candidates (57.9%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1260126
Fresh033
Picked011
Done011
Total1265131

Merged error: 0.0b

Counts
131 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite169.0ms

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
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
71.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
76.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (- 0.0625) (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
189.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
60.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify105.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371970
138171891
250021883

prune543.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh022
Picked011
Done022
Total2355240

Merged error: 0.0b

Counts
240 → 5

regimes103.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.0b

bsearch103.0ms

Steps
ItersRangePoint
10
0.005370866090842012
4.21737757242384e+15
0.8915668775484289
10
-3.4402871636077537
-5.738045557766166e-18
-1.0185275619862584

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2327×body1280valid
455.0ms1593×body640valid
263.0ms782×body2560valid
138.0ms797×body320valid
89.0ms2083×body80valid
44.0ms418×body160valid