Details

Time bar (total: 4.2s)

sample74.0ms

Algorithm
intervals
Results
37.0ms78×body1280valid
14.0ms54×body640valid
6.0ms19×body2560valid
4.0ms25×body320valid
3.0ms69×body80valid
1.0ms11×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

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: 52.2b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.5b
(+ x (sqrt (+ (* x x) 1.0)))
1.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.6b
(sqrt (+ (* x x) 1.0))

rewrite19.0ms

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)))
9.0ms
(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))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify138.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune108.0ms

Filtered
51 candidates to 42 candidates (17.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New48351
Fresh000
Picked101
Done000
Total49352

Merged error: 0b

Counts
52 → 3

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite69.0ms

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:
51.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series15.0ms

Counts
1 → 3
Calls
1 calls:
15.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify96.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07251757
138321368
250011368

prune317.0ms

Filtered
273 candidates to 95 candidates (65.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh022
Picked011
Done000
Total2733276

Merged error: 0b

Counts
276 → 3

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))
0.3b
(/ 0.125 (pow x 3))
9.7b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite55.0ms

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))
20.0ms
(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)))
5.0ms
(+ x (/ 0.5 x))
4.0ms
(/ 0.125 (pow x 3))
9.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0478840
12197799
25001799

prune160.0ms

Filtered
129 candidates to 77 candidates (40.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh011
Picked011
Done011
Total1293132

Merged error: 0b

Counts
132 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (neg 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
11.2b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
21.1b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite161.0ms

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))
69.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
71.0ms
(- (/ 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)))))
6.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify101.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08371963
137941884
250021876

prune428.0ms

Filtered
235 candidates to 152 candidates (35.3%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh000
Picked011
Done022
Total2353238

Merged error: 0b

Counts
238 → 3

regimes39.0ms

Accuracy

100% (0.0b remaining)

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

bsearch32.0ms

Steps
ItersRangePoint
10
1.8861453929162526e-07
127140.91663662092
0.8893153248050113
10
-81569296.22560106
-6.097158829196934e-11
-1.038874668650356

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2295×body1280valid
442.0ms1556×body640valid
271.0ms815×body2560valid
137.0ms814×body320valid
86.0ms2108×body80valid
40.0ms412×body160valid

Profiling

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