Details

Time bar (total: 4.7s)

sample31.0ms

Algorithm
intervals
Results
5.0ms43×body1280valid
5.0ms229×body80nan
5.0ms52×body640valid
3.0ms127×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

localize7.0ms

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))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×frac-sub div-inv
8×frac-2neg clear-num
4×sqrt-div associate-/r/
3×prod-diff
2×flip3-+ flip-+
1×sub-neg flip3-- fma-neg flip-- distribute-lft-out--
Counts
3 → 26
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))))

series270.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(/ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ 1.0 (sqrt x))
147.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify41.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0392413
11308349
25002327

prune114.0ms

Filtered
35 candidates to 29 candidates (82.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New29635
Fresh000
Picked101
Done000
Total30636

Merged error: 20.7b

Counts
36 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r/
6×associate-/r/ associate-/l/
5×clear-num
4×sqrt-div
3×frac-2neg associate-/r* div-inv
2×flip3-- flip3-+ associate-*r* un-div-inv *-commutative flip-- flip-+
1×sub-neg div-sub
Counts
3 → 27
Calls
3 calls:
8.0ms
(/ (- (sqrt (+ x 1.0)) (sqrt x)) (* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0)))
5.0ms
(* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0))
4.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series442.0ms

Counts
3 → 9
Calls
3 calls:
286.0ms
(/ (- (sqrt (+ x 1.0)) (sqrt x)) (* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0)))
78.0ms
(* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0))
77.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify45.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0358319
11442277
25002266

prune117.0ms

Filtered
36 candidates to 31 candidates (86.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New34236
Fresh325
Picked011
Done000
Total37542

Merged error: 0.3b

Counts
42 → 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 0) (+ (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0)))
0.3b
(* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-/r/
13×associate-/l/
11×div-inv
10×flip3-+ associate-*r/ flip-+
9×times-frac
7×clear-num
5×frac-2neg associate-*r* *-commutative
4×sqrt-div
3×associate-/r* associate-/l*
2×un-div-inv
1×+-commutative
Counts
4 → 47
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 0) (+ (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0)))
5.0ms
(* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0))

series826.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
151.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
523.0ms
(/ (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0)))
81.0ms
(* (sqrt x) (/ (sqrt (+ x 1.0)) 1.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0555674
12599577
25002560

prune205.0ms

Filtered
59 candidates to 52 candidates (88.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New53659
Fresh123
Picked101
Done101
Total56864

Merged error: 0.1b

Counts
64 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sqrt (+ x 1.0)) (sqrt x) x)
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.1b
(* (* (/ 1.0 (sqrt (+ x 1.0))) 1.0) (* (/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x)) 1/2))
0.3b
(/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-*l/
10×frac-2neg clear-num
9×frac-times associate-*l*
4×sqrt-div associate-/r/ div-inv
3×associate-*r/ associate-*r* *-commutative
2×flip3-+ flip-+
1×fma-udef
Counts
4 → 33
Calls
4 calls:
1.0ms
(fma (sqrt (+ x 1.0)) (sqrt x) x)
3.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(* (* (/ 1.0 (sqrt (+ x 1.0))) 1.0) (* (/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x)) 1/2))
2.0ms
(/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
132.0ms
(fma (sqrt (+ x 1.0)) (sqrt x) x)
81.0ms
(/ 1.0 (sqrt (+ x 1.0)))
682.0ms
(* (* (/ 1.0 (sqrt (+ x 1.0))) 1.0) (* (/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x)) 1/2))
332.0ms
(/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0714573
13434509
25002503

prune146.0ms

Filtered
45 candidates to 38 candidates (84.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New43245
Fresh167
Picked101
Done000
Total45853

Merged error: 0.1b

Counts
53 → 8

regimes39.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01511
12111
22311
32311

end0.0ms

sample873.0ms

Algorithm
intervals
Results
194.0ms1936×body640valid
186.0ms7833×body80nan
145.0ms1128×body1280valid
105.0ms4028×body80valid
43.0ms589×body320valid
16.0ms319×body160valid