Details

Time bar (total: 3.6s)

sample31.0ms

Algorithm
intervals
Results
6.0ms43×body1280valid
5.0ms229×body80nan
5.0ms52×body640valid
4.0ms127×body80valid
2.0ms21×body320valid
1.0ms13×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: 21.2b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
4.8b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×frac-sub
8×frac-2neg clear-num
4×div-inv
2×sqrt-div associate-/r/
1×sub-neg flip3-- flip3-+ flip-- flip-+ distribute-lft-out--
Counts
3 → 22
Calls
3 calls:
3.0ms
(/ 1.0 (sqrt (+ x 1.0)))
2.0ms
(/ 1.0 (sqrt x))
7.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series254.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
39.0ms
(/ 1.0 (sqrt x))
138.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0313324
11058282
25001260

prune82.0ms

Filtered
31 candidates to 25 candidates (80.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New26531
Fresh000
Picked101
Done000
Total27532

Merged error: 21.0b

Counts
32 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
4.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
7×*-commutative
6×associate-*r/
4×times-frac sqrt-div
2×flip3-- flip3-+ pow1/2 associate-/r* associate-/r/ flip-- flip-+ associate-/l/ associate-/l*
1×sub-neg frac-2neg sqrt-unprod pow-prod-down clear-num div-inv
Counts
3 → 24
Calls
3 calls:
9.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
4.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
4.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series394.0ms

Counts
3 → 9
Calls
3 calls:
262.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify34.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0335301
11115267
25001237

prune96.0ms

Filtered
33 candidates to 30 candidates (90.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New31233
Fresh224
Picked011
Done000
Total33538

Merged error: 0.3b

Counts
38 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×times-frac associate-/r/ *-commutative associate-/l/
9×flip3-+ associate-*r/ associate-*r* flip-+
5×div-inv associate-/l*
4×sqrt-div clear-num
3×frac-2neg
2×pow1/2 associate-/r*
1×+-commutative sqrt-unprod pow-prod-down un-div-inv
Counts
4 → 43
Calls
4 calls:
3.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
6.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
4.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series785.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
151.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
509.0ms
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0508637
12015541
25001527

prune197.0ms

Filtered
55 candidates to 50 candidates (90.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New51455
Fresh033
Picked101
Done101
Total53760

Merged error: 0.1b

Counts
60 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b
(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ x 1.0)))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.3b
(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-/l*
6×associate-/r/
5×flip3-+ flip-+ associate-/l/
4×sqrt-div
3×frac-2neg clear-num *-commutative div-inv
2×pow1/2 associate-*r/
1×+-commutative sqrt-unprod pow-prod-down
Counts
4 → 28
Calls
4 calls:
3.0ms
(+ x (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms
(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ x 1.0)))
4.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms
(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ x (* (sqrt x) (sqrt (+ x 1.0))))
232.0ms
(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ x 1.0)))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
83.0ms
(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0356366
11063329
25002294

prune108.0ms

Filtered
40 candidates to 35 candidates (87.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New35540
Fresh246
Picked011
Done000
Total371047

Merged error: 0.0b

Counts
47 → 10

regimes42.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01310
11310

end0.0ms

sample879.0ms

Algorithm
intervals
Results
198.0ms1936×body640valid
182.0ms7833×body80nan
149.0ms1128×body1280valid
106.0ms4028×body80valid
46.0ms589×body320valid
16.0ms319×body160valid