Details

Time bar (total: 4.9s)

analyze267.0ms

Algorithm
search

sample75.0ms

Algorithm
intervals
Results
37.0ms78×body1280valid
13.0ms48×body640valid
9.0ms24×body2560valid
3.0ms18×body320valid
3.0ms67×body80valid
2.0ms21×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: 53.6b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.5b
(+ x (sqrt (+ (* x x) 1.0)))
3.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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))

series17.0ms

Counts
3 → 9
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))

simplify144.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune124.0ms

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 1 expressions with local error:

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

rewrite76.0ms

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)))

series16.0ms

Counts
1 → 3
Calls
1 calls:
16.0ms
(* 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

prune343.0ms

Filtered
95 candidates to 273 candidates (-187.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh044
Picked011
Done000
Total2735278

Merged error: 0.0b

Counts
278 → 5

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))
0.2b
(/ 0.125 (pow x 3))
9.7b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite58.0ms

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:
22.0ms
(- (+ 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)))))

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))
9.0ms
(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

prune179.0ms

Filtered
77 candidates to 129 candidates (-67.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh033
Picked011
Done011
Total1295134

Merged error: 0.0b

Counts
134 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (neg 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
11.7b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
20.6b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite180.0ms

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))
77.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
81.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ (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))))

simplify105.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371963
137941884
250021876

prune467.0ms

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

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh022
Picked011
Done022
Total2355240

Merged error: 0.0b

Counts
240 → 5

regimes51.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch47.0ms

Steps
ItersRangePoint
9
0.0036169149220601562
1458112.2672928227
0.8973806971972467
9
-753068416.2682383
-0.41936216679413546
-1.027679404914925

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

analyze274.0ms

Algorithm
search

sample2.2s

Algorithm
intervals
Results
1.1s2369×body1280valid
440.0ms1567×body640valid
269.0ms794×body2560valid
123.0ms732×body320valid
90.0ms2122×body80valid
42.0ms416×body160valid

Profiling

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