Details

Time bar (total: 9.6s)

sample2.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75.012207%

Results
36.0ms84×body1280valid
14.0ms51×body640valid
6.0ms20×body2560valid
3.0ms20×body320valid
3.0ms66×body80valid
2.0ms15×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
3.4b
(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:
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)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune115.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
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 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))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite84.0ms

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:
12.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
51.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series28.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(- (+ (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)))

simplify114.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08542083
146421650
250021650

prune386.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh044
Picked011
Done000
Total2925297

Merged error: 0.0b

Counts
297 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (neg 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
13.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
19.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite168.0ms

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:
7.0ms
(/ (neg 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
72.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
73.0ms
(- (/ 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))
4.0ms
(/ 0.125 (pow x 3))
10.0ms
(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))))

simplify102.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371963
137941884
250021876

prune439.0ms

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

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh033
Picked011
Done011
Total2355240

Merged error: 0.0b

Counts
240 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 0.125 (pow x 3))
11.7b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
8×add-exp-log
6×log-prod
4×cube-mult unpow3 add-cbrt-cube distribute-lft-out sqr-pow
3×pow1 div-exp associate-/l*
2×log-div distribute-lft-out-- add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg flip3-+ rem-log-exp pow-exp clear-num log-pow flip-+ div-inv
Counts
2 → 82
Calls
2 calls:
5.0ms
(/ 0.125 (pow x 3))
22.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series12.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(/ 0.125 (pow x 3))
9.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0325535
11471499
25001499

prune100.0ms

Filtered
50 candidates to 88 candidates (-76.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New88088
Fresh022
Picked011
Done022
Total88593

Merged error: 0.0b

Counts
93 → 5

regimes142.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch62.0ms

Steps
ItersRangePoint
8
0.008350138005101829
54.54945933405799
0.9031469695271067
11
-9013128802.901398
-6.237372989685382e-14
-1.0027511935495552

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample4.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75.012207%

Results
1.0s2288×body1280valid
427.0ms1535×body640valid
243.0ms747×body2560valid
136.0ms798×body320valid
95.0ms2208×body80valid
41.0ms424×body160valid

Profiling

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