Details

Time bar (total: 4.3s)

sample85.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50%

Results
37.0ms69×body1280valid
17.0ms56×body640valid
8.0ms23×body2560valid
5.0ms27×body320valid
3.0ms73×body80valid
1.0ms8×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 51.5b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.6b
(+ x (sqrt (+ (* x x) 1.0)))
2.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.1b
(sqrt (+ (* x x) 1.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series22.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0333450
11163414
25001398

prune158.0ms

Filtered
53 candidates to 65 candidates (-22.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New61465
Fresh000
Picked101
Done000
Total62466

Merged error: 0.0b

Counts
66 → 4

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite77.0ms

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:
57.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series17.0ms

Counts
1 → 3
Calls
1 calls:
17.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify87.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07251757
138321368
250011368

prune342.0ms

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: 0.0b

Counts
277 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b
(+ x (/ 0.5 x))
0.3b
(/ 0.125 (pow x 3))
12.4b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite60.0ms

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:
24.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
6.0ms
(+ x (/ 0.5 x))
5.0ms
(/ 0.125 (pow x 3))
21.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series21.0ms

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

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0436780
12075717
25002717

prune150.0ms

Filtered
73 candidates to 126 candidates (-72.6%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1260126
Fresh022
Picked011
Done011
Total1264130

Merged error: 0.0b

Counts
130 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (neg 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
15.1b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
18.7b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite176.0ms

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))
7.0ms
(/ 0.125 (pow x 3))
76.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
77.0ms
(- (/ 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))
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))))

simplify95.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08371963
137941884
250021876

prune446.0ms

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: 0.0b

Counts
239 → 4

regimes43.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch40.0ms

Steps
ItersRangePoint
10
0.00031157581617804726
87511408.73844521
0.8849853411469668
9
-871263.1049503816
-0.0065084385888304844
-1.0214182645926628

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50%

Results
1.1s2303×body1280valid
458.0ms1604×body640valid
264.0ms761×body2560valid
140.0ms789×body320valid
95.0ms2151×body80valid
41.0ms392×body160valid

Profiling

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