Details

Time bar (total: 7.5s)

sample76.0ms

Algorithm
intervals
Results
36.0ms77×body1280valid
14.0ms50×body640valid
8.0ms26×body2560valid
4.0ms23×body320valid
3.0ms69×body80valid
1.0ms11×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.5b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.4b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.9b
(sqrt (+ (* x x) 1.0))

rewrite24.0ms

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)
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(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))

simplify33.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0333451
11157414
25001398

prune328.0ms

Filtered
65 candidates to 53 candidates (18.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New59665
Fresh000
Picked101
Done000
Total60666

Merged error: 0.0b

Counts
66 → 6

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)))

rewrite86.0ms

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))))
16.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify115.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542083
146421650
250021650

prune932.0ms

Filtered
292 candidates to 111 candidates (62.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh055
Picked011
Done000
Total2926298

Merged error: 0.0b

Counts
298 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b
(+ x (/ 0.5 x))
0.1b
(/ 0.125 (pow x 3))
10.7b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube distribute-lft-out
5×pow1 difference-of-squares sqr-pow
4×cube-mult unpow3 distribute-lft-out--
3×flip3-+ div-exp flip-+ associate-/l*
2×log-div diff-log sum-log frac-sub
1×cbrt-undiv +-commutative pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow flip-- div-inv
Counts
4 → 117
Calls
4 calls:
20.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms
(+ x (/ 0.5 x))
5.0ms
(/ 0.125 (pow x 3))
19.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series22.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms
(+ x (/ 0.5 x))
4.0ms
(/ 0.125 (pow x 3))
10.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0478840
12197799
25001799

prune703.0ms

Filtered
129 candidates to 77 candidates (40.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh044
Picked011
Done011
Total1296135

Merged error: 0.0b

Counts
135 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (neg 0.0625) (pow x 5))
0.1b
(/ 0.125 (pow x 3))
12.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
20.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite160.0ms

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))
68.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
70.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series24.0ms

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)))))
6.0ms
(- (/ 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 (76.0ms)

IterNodesCost
08371963
137941884
250021876

prune2.4s

Filtered
235 candidates to 152 candidates (35.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh033
Picked011
Done022
Total2356241

Merged error: 0.0b

Counts
241 → 6

regimes57.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.8b

bsearch94.0ms

Steps
ItersRangePoint
10
4.00241138285282e-13
41.84587058567329
0.8923624192356572
7
-27.465585783021098
-0.4867936294477796
-1.0064048142811262

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2382×body1280valid
420.0ms1521×body640valid
257.0ms795×body2560valid
125.0ms770×body320valid
83.0ms2104×body80valid
41.0ms428×body160valid

Profiling

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