Details

Time bar (total: 3.6s)

sample32.0ms

Algorithm
intervals
Results
6.0ms274×body80nan
5.0ms50×body640valid
5.0ms39×body1280valid
4.0ms135×body80valid
2.0ms24×body320valid
0.0ms8×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: 18.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite15.0ms

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))
9.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series243.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ 1.0 (sqrt (+ x 1.0)))
40.0ms
(/ 1.0 (sqrt x))
129.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0392413
11308349
25002327

prune97.0ms

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: 18.5b

Counts
36 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
0.2b
(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
3.2b
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r/
6×associate-/r/
5×clear-num
4×sqrt-div associate-/r* associate-/l/
3×frac-2neg div-inv
2×neg-mul-1 flip3-+ associate-*r* associate-*l* un-div-inv *-commutative flip-+
1×distribute-lft-neg-out fma-udef
Counts
3 → 24
Calls
3 calls:
6.0ms
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
4.0ms
(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
1.0ms
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

series477.0ms

Counts
3 → 9
Calls
3 calls:
307.0ms
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0)))
72.0ms
(* (- (sqrt x)) (/ (sqrt (+ x 1.0)) 1.0))
97.0ms
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

simplify31.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0306301
11029267
25001254

prune110.0ms

Filtered
33 candidates to 29 candidates (87.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New31233
Fresh055
Picked101
Done000
Total32739

Merged error: 18.5b

Counts
39 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x)))
3.2b
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×frac-times clear-num
11×frac-2neg
5×neg-mul-1 associate-/r*
4×sqrt-div associate-*l/ associate-/r/ div-inv
3×associate-*r/ associate-*r*
2×flip3-+ flip-+
1×associate-*l* un-div-inv *-commutative fma-udef
Counts
4 → 35
Calls
4 calls:
6.0ms
(* (/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))
3.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x)))
1.0ms
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

series748.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(* (/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))
70.0ms
(/ 1.0 (sqrt (+ x 1.0)))
260.0ms
(/ (fma 1 (- (sqrt (+ x 1.0))) (sqrt x)) (- (sqrt x)))
96.0ms
(fma 1 (- (sqrt (+ x 1.0))) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0364492
11377442
25002416

prune149.0ms

Filtered
47 candidates to 41 candidates (87.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New47047
Fresh066
Picked011
Done000
Total47754

Merged error: 18.5b

Counts
54 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (/ 1.0 (sqrt x)) (sqrt x))
3.1b
(- (/ (/ 1.0 (sqrt x)) (sqrt x)) (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
63×frac-sub
51×associate-/l/
36×frac-2neg clear-num
31×associate-/l*
25×div-inv
16×sqrt-div associate-/r/
8×flip3-+ flip-+
3×prod-diff
1×sub-neg flip3-- fma-neg flip--
Counts
4 → 84
Calls
4 calls:
2.0ms
(/ 1.0 (sqrt x))
2.0ms
(/ 1.0 (sqrt x))
3.0ms
(/ (/ 1.0 (sqrt x)) (sqrt x))
16.0ms
(- (/ (/ 1.0 (sqrt x)) (sqrt x)) (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1.0 (sqrt x))
37.0ms
(/ 1.0 (sqrt x))
32.0ms
(/ (/ 1.0 (sqrt x)) (sqrt x))
59.0ms
(- (/ (/ 1.0 (sqrt x)) (sqrt x)) (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))))

simplify119.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
010931592
147491091
250011073

prune199.0ms

Filtered
96 candidates to 55 candidates (57.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh415
Picked101
Done101
Total994103

Merged error: 5.8b

Counts
103 → 4

regimes31.0ms

Accuracy

98.8% (0.2b remaining)

Error of 5.7b against oracle of 5.5b and baseline of 19.2b

bsearch65.0ms

Steps
ItersRangePoint
9
357.20278190505735
4524963932.878733
10784.107655470898

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06150
16150

end0.0ms

sample883.0ms

Algorithm
intervals
Results
194.0ms1867×body640valid
185.0ms7959×body80nan
155.0ms1126×body1280valid
108.0ms4097×body80valid
44.0ms595×body320valid
16.0ms315×body160valid