Details

Time bar (total: 23.8s)

sample63.0ms

Algorithm
intervals
Results
29.0ms72×body1280valid
13.0ms52×body640valid
5.0ms19×body2560valid
5.0ms31×body320valid
2.0ms63×body80valid
2.0ms19×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
095
195

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
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 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
4.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.9b
(sqrt (+ (* x x) 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt sqrt-prod add-log-exp
4×add-exp-log log-prod distribute-lft-out
3×flip3-+ add-cbrt-cube flip-+
2×log-div sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp associate-*l* sum-log log-pow
Counts
3 → 44
Calls
3 calls:
10.0ms
(+ x (sqrt (+ (* x x) 1.0)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
12.0ms
(sqrt (+ (* x x) 1.0))

series304.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ x (sqrt (+ (* x x) 1.0)))
189.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify143.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
0304401
1987372
24427356
35003353

prune123.0ms

Filtered
53 candidates to 42 candidates (20.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New47653
Fresh000
Picked101
Done000
Total48654

Merged error: 0.0b

Counts
54 → 6

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)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
144×add-sqr-sqrt
128×unpow-prod-down
112×times-frac
92×associate-*r*
84×*-un-lft-identity
67×add-cube-cbrt
66×associate-*r/
48×frac-sub
42×sqrt-prod
39×sqr-pow
33×associate-/r*
27×associate-/l*
26×unswap-sqr
25×add-exp-log unpow3
24×flip3-+ flip-+
14×difference-of-squares
10×prod-exp
9×div-exp add-log-exp
8×associate--l+
7×add-cbrt-cube
6×pow1 pow-to-exp associate-+l+ log-prod associate-*l* pow-exp clear-num un-div-inv distribute-lft-out--
4×distribute-lft-out
3×frac-2neg diff-log
2×sum-log log-pow cbrt-unprod
1×cbrt-undiv +-commutative sub-neg flip3-- pow-prod-down *-commutative flip-- div-inv
Counts
2 → 243
Calls
2 calls:
71.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
34.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series318.0ms

Counts
2 → 6
Calls
2 calls:
170.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
147.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify67.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012993804
150013592

prune718.0ms

Filtered
249 candidates to 146 candidates (41.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2481249
Fresh055
Picked011
Done000
Total2487255

Merged error: 0.0b

Counts
255 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.125 (pow x 3)) (* 2 x))
0.1b
(/ 0.125 (pow x 3))
9.7b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
25×add-cube-cbrt
20×log-div
18×frac-sub
14×unpow-prod-down associate-/r*
11×flip3-- flip--
10×difference-of-squares
9×add-exp-log associate-/l*
8×log-prod
7×distribute-lft-out--
6×sqr-pow
5×add-cbrt-cube add-log-exp
4×pow1 unpow3 unswap-sqr
3×frac-2neg div-exp clear-num
2×associate-*l*
1×cbrt-undiv pow-to-exp sub-neg diff-log rem-log-exp pow-exp log-pow div-inv
Counts
3 → 108
Calls
3 calls:
25.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
5.0ms
(/ 0.125 (pow x 3))
36.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series316.0ms

Counts
3 → 9
Calls
3 calls:
109.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
43.0ms
(/ 0.125 (pow x 3))
163.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify105.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08341349
139831295
250021295

prune246.0ms

Filtered
117 candidates to 80 candidates (31.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1170117
Fresh055
Picked011
Done011
Total1177124

Merged error: 0.0b

Counts
124 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.1b
(/ 0.125 (pow x 3))
11.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
10136×frac-sub
6371×associate-/r*
5305×associate-/l*
3574×*-un-lft-identity
3560×add-sqr-sqrt
3540×add-cube-cbrt
2550×log-div
1895×unpow-prod-down
1178×frac-2neg clear-num
782×distribute-rgt-neg-in
780×distribute-lft-neg-in
633×sqr-pow
368×unpow3
260×neg-mul-1
112×times-frac
30×flip3-- flip--
15×add-exp-log
14×distribute-lft-out--
11×log-prod
9×add-log-exp
8×add-cbrt-cube difference-of-squares
6×div-exp
5×pow1
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg div-sub pow-exp div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 5295
Calls
4 calls:
8.0ms
(/ (- 0.0625) (pow x 5))
6.0ms
(/ 0.125 (pow x 3))
348.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
202.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (- 0.0625) (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
213.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
69.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify1.6s

Algorithm
egg-herbie
Counts
5307 → 5307
Iterations

Useful iterations: 0 (127.0ms)

IterNodesCost
010029153087

prune15.8s

Filtered
5307 candidates to 3477 candidates (34.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New530705307
Fresh044
Picked011
Done022
Total530775314

Merged error: 0.0b

Counts
5314 → 7

regimes96.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch76.0ms

Steps
ItersRangePoint
9
0.0004381094517774334
96283.49646244562
0.8970489443660148
8
-69.11608992374592
-0.04448272872103196
-1.0232220075550487

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
965.0ms2298×body1280valid
370.0ms1549×body640valid
218.0ms801×body2560valid
112.0ms816×body320valid
65.0ms2129×body80valid
32.0ms407×body160valid