Details

Time bar (total: 5.5s)

sample72.0ms

Algorithm
intervals
Results
34.0ms76×body1280valid
14.0ms50×body640valid
7.0ms21×body2560valid
5.0ms32×body320valid
3.0ms62×body80valid
1.0ms15×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: 53.8b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
4.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(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))

series264.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
165.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify141.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune164.0ms

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

localize12.0ms

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)))

rewrite93.0ms

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:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series288.0ms

Counts
2 → 6
Calls
2 calls:
149.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542083
146421650
250021650

prune377.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh044
Picked011
Done000
Total2925297

Merged error: 0.0b

Counts
297 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.3b
(/ (neg 0.0625) (pow x 5))
14.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
18.3b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite166.0ms

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:
5.0ms
(/ 0.125 (pow x 3))
6.0ms
(/ (neg 0.0625) (pow x 5))
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))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 0.125 (pow x 3))
70.0ms
(/ (neg 0.0625) (pow x 5))
183.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
58.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify104.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08371963
137941884
250021876

prune503.0ms

Filtered
235 candidates to 152 candidates (64.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh033
Picked011
Done011
Total2355240

Merged error: 0.0b

Counts
240 → 5

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
12.2b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite29.0ms

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

series197.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(/ 0.125 (pow x 3))
154.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0325535
11469500
25001500

prune137.0ms

Filtered
88 candidates to 50 candidates (56.8%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New88088
Fresh022
Picked011
Done022
Total88593

Merged error: 0.0b

Counts
93 → 5

regimes95.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.5b

bsearch79.0ms

Steps
ItersRangePoint
10
2.2826621327002547e-07
125321.6248081686
0.8968798305846061
7
-11.514549394350572
-0.06461929534003709
-0.9984800716907896

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.0s2262×body1280valid
431.0ms1559×body640valid
279.0ms826×body2560valid
143.0ms820×body320valid
93.0ms2121×body80valid
47.0ms412×body160valid

Profiling

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