Details

Time bar (total: 5.8s)

sample39.0ms

Algorithm
intervals
Results
9.0ms263×body80nan
7.0ms52×body640valid
6.0ms34×body1280valid
5.0ms144×body80valid
2.0ms18×body320valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

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: 18.3b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.0b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
34.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
133.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04431097
114341038
25001992

prune284.0ms

Filtered
145 candidates to 98 candidates (67.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New13312145
Fresh000
Picked101
Done000
Total13412146

Merged error: 17.8b

Counts
146 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.0b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
240×*-un-lft-identity
167×add-sqr-sqrt
125×add-cube-cbrt
120×sqrt-prod
70×distribute-lft-out
28×swap-sqr
22×associate-*r* associate-*l*
20×add-exp-log associate-/r* add-cbrt-cube
18×frac-sub
16×div-inv difference-of-squares
13×frac-times associate-*r/ associate-*l/
11×pow1 associate-/l/
9×unswap-sqr
7×associate-/l*
6×cbrt-undiv div-exp add-log-exp
4×prod-exp cbrt-unprod
3×associate-/r/
2×flip3-- frac-2neg clear-num flip--
1×pow2 sub-neg flip3-+ pow-plus diff-log div-sub pow-prod-down frac-add pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 267
Calls
4 calls:
4.0ms
(/ 1.0 (sqrt x))
43.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
21.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
9.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (sqrt x))
356.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
31.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
60.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
279 → 279
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011934628
150014304

prune524.0ms

Filtered
279 candidates to 165 candidates (59.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2745279
Fresh10111
Picked101
Done000
Total2856291

Merged error: 6.4b

Counts
291 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.5b
(- (+ x 1.0) x)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
52.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
6.0ms
(- (+ x 1.0) x)

series612.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
43.0ms
(/ 1.0 (sqrt x))
490.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify66.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012493999
150013639

prune419.0ms

Filtered
260 candidates to 140 candidates (53.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2600260
Fresh055
Picked011
Done000
Total2606266

Merged error: 6.4b

Counts
266 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
1.9b
(/ (/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.1b
(/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x)))
16.2b
(+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
372×times-frac
351×*-un-lft-identity
140×distribute-lft-out
132×sqrt-prod
121×add-sqr-sqrt add-cube-cbrt
38×div-inv
35×associate-/r/
32×associate-*l/
21×associate-/r*
20×add-exp-log add-cbrt-cube
19×flip3-+ flip-+
15×associate-/l*
9×div-sub
8×cbrt-undiv div-exp add-log-exp
4×pow1 distribute-rgt-in associate-+l+ distribute-lft-in
3×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
2×prod-exp sum-log cbrt-unprod
1×+-commutative neg-log frac-add
Counts
4 → 258
Calls
4 calls:
4.0ms
(/ 1.0 (sqrt x))
52.0ms
(/ (/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
19.0ms
(/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x)))
13.0ms
(+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1.0 (sqrt x))
583.0ms
(/ (/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
112.0ms
(/ (+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0)))) (* (+ x 1.0) (sqrt x)))
83.0ms
(+ (* 1.0 (* (/ 1.0 (sqrt x)) (+ x 1.0))) (- (* (sqrt x) (* 1.0 1.0))))

simplify89.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012456882
150026299

prune502.0ms

Filtered
270 candidates to 155 candidates (57.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2700270
Fresh044
Picked011
Done011
Total2706276

Merged error: 6.4b

Counts
276 → 6

regimes34.0ms

Accuracy

98.5% (0.2b remaining)

Error of 5.9b against oracle of 5.7b and baseline of 19.1b

bsearch42.0ms

Steps
ItersRangePoint
8
8.601567399579238
18724.121991280714
7117.860928874251

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03633
13633

end0.0ms

sample1.1s

Algorithm
intervals
Results
269.0ms8059×body80nan
245.0ms1797×body640valid
206.0ms1152×body1280valid
146.0ms4100×body80valid
61.0ms608×body320valid
24.0ms343×body160valid