Details

Time bar (total: 4.7s)

sample67.0ms

Algorithm
intervals
Results
34.0ms76×body1280valid
13.0ms56×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms68×body80valid
1.0ms9×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: 53.8b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(sqrt (+ (* x x) 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×flip3-+ flip-+
2×log-div sqrt-div
1×+-commutative pow1/2
Counts
3 → 8
Calls
3 calls:
3.0ms
(+ x (sqrt (+ (* x x) 1.0)))
4.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series263.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
165.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify127.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0270175
1942166
24415151
35001150

prune77.0ms

Filtered
17 candidates to 17 candidates (100.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New13417
Fresh000
Picked101
Done000
Total14418

Merged error: 0.0b

Counts
18 → 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)))

rewrite14.0ms

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)))

series326.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
148.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify55.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0366855
11714791
25002765

prune167.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×frac-sub
7×flip3-+ flip-+
6×associate-/r*
3×frac-2neg unpow3 clear-num sqr-pow
2×+-commutative log-div associate--l+
1×sub-neg flip3-- flip-- div-inv
Counts
4 → 26
Calls
4 calls:
3.0ms
(+ x (/ 0.5 x))
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)))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ x (/ 0.5 x))
36.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
40.0ms
(/ 0.125 (pow x 3))
148.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0375410
11567381
25001373

prune96.0ms

Filtered
38 candidates to 29 candidates (76.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New38038
Fresh022
Picked011
Done011
Total38442

Merged error: 0.0b

Counts
42 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.4b
(/ (- 0.0625) (pow x 5))
13.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite50.0ms

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:
2.0ms
(/ 0.125 (pow x 3))
3.0ms
(/ (- 0.0625) (pow x 5))
17.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
14.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 0.125 (pow x 3))
51.0ms
(/ (- 0.0625) (pow x 5))
177.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
57.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify91.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
020584396
150014168

prune633.0ms

Filtered
208 candidates to 166 candidates (79.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2080208
Fresh011
Picked011
Done022
Total2084212

Merged error: 0.0b

Counts
212 → 4

regimes31.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch85.0ms

Steps
ItersRangePoint
9
0.09117784756913819
2697524.489058797
0.8902423635659321
10
-1421.6155834850151
-1.485944467815708e-07
-1.0153027309600835

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
992.0ms2342×body1280valid
372.0ms1525×body640valid
232.0ms839×body2560valid
102.0ms731×body320valid
67.0ms2144×body80valid
33.0ms419×body160valid