Details

Time bar (total: 5.1s)

sample23.0ms

Algorithm
intervals
Results
5.0ms59×body1280valid
4.0ms229×body80nan
2.0ms127×body80valid
2.0ms36×body640valid
1.0ms21×body320valid
0.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

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: 30.9b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

4.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg flip3-- flip--
Counts
1 → 4
Calls
1 calls:
4.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series75.0ms

Counts
1 → 3
Calls
1 calls:
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify52.0ms

Algorithm
egg-herbie
Counts
7 → 7
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
011060
134253
2138747
3500243

prune15.0ms

Filtered
7 candidates to 5 candidates (71.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New617
Fresh000
Picked011
Done000
Total628

Merged error: 0.1b

Counts
8 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-+ associate-/r/ flip-+
1×+-commutative frac-2neg clear-num div-inv
Counts
2 → 8
Calls
2 calls:
3.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series387.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
322.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify137.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0197148
1706131
23668107
35001107

prune60.0ms

Filtered
14 candidates to 12 candidates (85.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New13114
Fresh000
Picked011
Done011
Total13316

Merged error: 0.1b

Counts
16 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt x) (sqrt x))
0.5b
(/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
4.5b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
9.3b
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-div
112×frac-times
80×frac-add
67×flip3-+ flip-+
41×flip3-- flip--
38×associate-*r/
24×associate-*l/
20×frac-2neg clear-num associate-/r* sum-cubes
6×pow1/2 *-commutative
4×distribute-rgt-in associate-+r+ distribute-lft-in associate-/r/
3×sub-neg associate-*l*
2×+-commutative distribute-rgt-out-- div-inv distribute-lft-out--
1×pow2 sqrt-unprod pow-prod-down rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 127
Calls
4 calls:
3.0ms
(* (sqrt x) (sqrt x))
5.0ms
(/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
6.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sqrt x) (sqrt x))
162.0ms
(/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
83.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
263.0ms
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017496299
150025664

prune609.0ms

Filtered
139 candidates to 96 candidates (69.1%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1363139
Fresh000
Picked011
Done022
Total1366142

Merged error: 0.1b

Counts
142 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt x) (sqrt x))
4.5b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
4.9b
(- (sqrt x) (sqrt (+ x 1.0)))
9.3b
(* (/ (/ 1.0 (+ (* (sqrt x) (- (sqrt x) (sqrt (+ x 1.0)))) (+ x 1.0))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
346×frac-times
336×sqrt-div
300×frac-add
240×flip3-+ flip-+
152×flip3-- flip--
150×associate-*r/
133×associate-/l*
116×associate-/r/
69×associate-*l/
57×associate-/l/
38×frac-2neg clear-num
20×div-inv
6×pow1/2 *-commutative
4×distribute-rgt-in sub-neg associate-+r+ distribute-lft-in
3×associate-*l*
2×+-commutative distribute-rgt-out-- distribute-lft-out--
1×pow2 sqrt-unprod pow-prod-down rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 296
Calls
4 calls:
4.0ms
(* (sqrt x) (sqrt x))
6.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
2.0ms
(- (sqrt x) (sqrt (+ x 1.0)))
35.0ms
(* (/ (/ 1.0 (+ (* (sqrt x) (- (sqrt x) (sqrt (+ x 1.0)))) (+ x 1.0))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (sqrt x) (sqrt x))
87.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
77.0ms
(- (sqrt x) (sqrt (+ x 1.0)))
209.0ms
(* (/ (/ 1.0 (+ (* (sqrt x) (- (sqrt x) (sqrt (+ x 1.0)))) (+ x 1.0))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

simplify229.0ms

Algorithm
egg-herbie
Counts
308 → 308
Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
0364721412
1500121250

prune1.6s

Filtered
308 candidates to 198 candidates (64.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3035308
Fresh202
Picked011
Done123
Total3068314

Merged error: 0.0b

Counts
314 → 8

regimes65.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample627.0ms

Algorithm
intervals
Results
138.0ms1742×body1280valid
123.0ms7833×body80nan
81.0ms1315×body640valid
74.0ms4034×body80valid
27.0ms591×body320valid
10.0ms318×body160valid