Details

Time bar (total: 8.6s)

sample22.0ms

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:
3.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series68.0ms

Counts
1 → 3
Calls
1 calls:
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm
egg-herbie
Counts
7 → 7
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
011762
136650
2154745
3500142

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)))

series200.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify126.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
0209148
1752127
23995104
35001103

prune40.0ms

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

localize17.0ms

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)))))

rewrite53.0ms

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
19×*-commutative
12×associate-+r+ prod-diff
8×distribute-rgt-in distribute-lft-in
6×pow1/2
4×associate-/r/
3×sub-neg associate-*l*
2×+-commutative distribute-rgt-out-- fma-neg div-inv distribute-lft-out--
1×pow2 sqrt-unprod pow-prod-down rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 141
Calls
4 calls:
3.0ms
(* (sqrt x) (sqrt x))
5.0ms
(/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
7.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(* (/ 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)))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (sqrt x) (sqrt x))
142.0ms
(/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
89.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
270.0ms
(* (/ 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)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018446673
150015725

prune687.0ms

Filtered
153 candidates to 99 candidates (64.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1485153
Fresh000
Picked011
Done112
Total1497156

Merged error: 0.0b

Counts
156 → 7

localize14.0ms

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
1080×sqrt-div
810×frac-times
720×frac-add
586×flip3-+ flip-+
362×flip3-- flip--
361×associate-/l*
344×associate-/r/
205×associate-*l/
198×associate-*r/
57×associate-/l/
38×frac-2neg clear-num
28×*-commutative
20×div-inv
16×prod-diff
12×associate-+r+
8×distribute-rgt-in distribute-lft-in
6×pow1/2
4×sub-neg distribute-rgt-out-- fma-neg distribute-lft-out--
3×associate-*l*
2×+-commutative
1×pow2 sqrt-unprod pow-prod-down rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 548
Calls
4 calls:
3.0ms
(* (sqrt x) (sqrt x))
7.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
48.0ms
(* (/ (/ 1.0 (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (sqrt x) (sqrt x))
90.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
90.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
152.0ms
(* (/ (/ 1.0 (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))

simplify459.0ms

Algorithm
egg-herbie
Counts
560 → 560
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500159522

prune5.0s

Filtered
560 candidates to 535 candidates (95.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New5555560
Fresh314
Picked101
Done022
Total5598567

Merged error: 0.0b

Counts
567 → 8

regimes44.0ms

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

sample629.0ms

Algorithm
intervals
Results
150.0ms1742×body1280valid
118.0ms7833×body80nan
88.0ms1315×body640valid
70.0ms4034×body80valid
28.0ms591×body320valid
10.0ms318×body160valid