Details

Time bar (total: 4.6s)

sample87.0ms

Algorithm
intervals
Results
42.0ms81×body1280valid
19.0ms59×body640valid
9.0ms23×body2560valid
4.0ms21×body320valid
2.0ms58×body80valid
2.0ms14×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

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: 54.7b

Counts
2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b
(sqrt (+ (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×flip3-+ flip-+
2×+-commutative log-div fma-def sqrt-div
1×pow1/2 *-commutative
Counts
4 → 13
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
3.0ms
(+ x (sqrt (+ (* x x) 1.0)))
3.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series290.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x x) 1.0)
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
160.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0272195
1942183
24415167
35001165

prune85.0ms

Filtered
25 candidates to 21 candidates (84.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New21425
Fresh000
Picked101
Done000
Total22426

Merged error: 0.0b

Counts
26 → 4

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)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
21×associate-*r/
16×frac-sub
10×unpow3 sqr-pow
8×flip3-+ flip-+
6×clear-num associate-/r* associate-/l*
5×associate-*r*
4×times-frac
3×frac-2neg un-div-inv
2×associate--l+
1×+-commutative sub-neg flip3-- *-commutative flip-- div-inv
Counts
2 → 36
Calls
2 calls:
8.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
5.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series276.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
132.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify57.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0366855
11714791
25002765

prune133.0ms

Filtered
42 candidates to 34 candidates (81.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New42042
Fresh033
Picked011
Done000
Total42446

Merged error: 0.0b

Counts
46 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.1b
(/ 0.125 (pow x 3))
12.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
320×frac-sub
116×frac-2neg clear-num
101×associate-/r*
87×log-div
68×sqr-pow
35×unpow3
33×neg-mul-1
31×associate-/l*
12×flip3-- flip--
6×div-inv
5×associate--r+
2×neg-sub0 sub-neg times-frac div-sub prod-diff associate--r-
1×fma-neg distribute-frac-neg
Counts
4 → 196
Calls
4 calls:
3.0ms
(/ (- 0.0625) (pow x 5))
2.0ms
(/ 0.125 (pow x 3))
17.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
13.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- 0.0625) (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
50.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify80.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
020584396
150014168

prune647.0ms

Filtered
208 candidates to 166 candidates (79.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2080208
Fresh022
Picked011
Done011
Total2084212

Merged error: 0.0b

Counts
212 → 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)) (/ 0.125 (pow x 3)))
0.1b
(/ 0.125 (pow x 3))
10.9b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×frac-sub
7×flip3-+ flip-+
6×associate-/r*
4×associate-+r+ associate--l+
3×+-commutative frac-2neg unpow3 clear-num sqr-pow
2×sub-neg log-div
1×associate-+r- flip3-- flip-- div-inv
Counts
4 → 31
Calls
4 calls:
4.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
5.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
2.0ms
(/ 0.125 (pow x 3))
4.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
35.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
40.0ms
(/ 0.125 (pow x 3))
147.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0387461
11606422
25001414

prune107.0ms

Filtered
43 candidates to 32 candidates (74.4%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New43043
Fresh011
Picked011
Done022
Total43447

Merged error: 0.0b

Counts
47 → 4

regimes26.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch77.0ms

Steps
ItersRangePoint
9
2.5653698016906928e-06
357.20278190505735
0.8785903162684238
9
-119005586.03332348
-0.6319501064166059
-0.9946231399154715

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
961.0ms2315×body1280valid
373.0ms1580×body640valid
220.0ms815×body2560valid
106.0ms775×body320valid
64.0ms2104×body80valid
32.0ms411×body160valid