Details

Time bar (total: 5.4s)

sample67.0ms

Algorithm
intervals
Results
34.0ms76×body1280valid
12.0ms56×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 (2.0ms)

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

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))

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))

series274.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
168.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify148.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (142.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune145.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New47451
Fresh000
Picked101
Done000
Total48452

Merged error: 0.0b

Counts
52 → 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)))

rewrite94.0ms

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:
14.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
56.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series296.0ms

Counts
2 → 6
Calls
2 calls:
158.0ms
(- (+ (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)))

simplify125.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08542089
146421654
250011654

prune433.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh033
Picked011
Done000
Total2924296

Merged error: 0.0b

Counts
296 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.1b
(/ 0.125 (pow x 3))
10.7b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
33×*-un-lft-identity
29×add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
8×add-log-exp
6×log-prod
5×add-cbrt-cube
4×pow1 cube-mult log-div flip3-- unpow3 frac-sub flip-- difference-of-squares sqr-pow
3×diff-log div-exp associate-/l*
2×sub-neg associate--r+ distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv associate--r-
Counts
3 → 105
Calls
3 calls:
20.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
5.0ms
(/ 0.125 (pow x 3))
17.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series234.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
37.0ms
(/ 0.125 (pow x 3))
150.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify70.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0475884
12181836
25002836

prune231.0ms

Filtered
114 candidates to 70 candidates (61.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh022
Picked011
Done011
Total1144118

Merged error: 0.0b

Counts
118 → 4

localize16.0ms

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))))

rewrite183.0ms

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))
7.0ms
(/ (- 0.0625) (pow x 5))
79.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
81.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 0.125 (pow x 3))
52.0ms
(/ (- 0.0625) (pow x 5))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
58.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify110.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08402002
138201923
250011915

prune580.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh011
Picked011
Done022
Total2354239

Merged error: 0.0b

Counts
239 → 4

regimes30.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch78.0ms

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

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
952.0ms2342×body1280valid
365.0ms1525×body640valid
221.0ms839×body2560valid
97.0ms731×body320valid
69.0ms2144×body80valid
32.0ms419×body160valid