Details

Time bar (total: 4.6s)

sample26.0ms

Algorithm
intervals
Results
4.0ms53×body1280valid
4.0ms274×body80nan
2.0ms135×body80valid
2.0ms36×body640valid
1.0ms24×body320valid
0.0ms8×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: 28.7b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (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))

series71.0ms

Counts
1 → 3
Calls
1 calls:
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify44.0ms

Algorithm
egg-herbie
Counts
7 → 7
Iterations

Useful iterations: 3 (41.0ms)

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))
0.2b
(/ 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)))

series205.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify121.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0197148
1706131
23668107
35001107

prune34.0ms

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
(pow (sqrt x) 3)
0.5b
(* (sqrt x) (sqrt x))
2.9b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
9.7b
(* (/ 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)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
120×sqrt-div
112×frac-times
80×frac-add
66×flip3-+ flip-+
41×flip3-- flip--
38×associate-*r/
24×associate-*l/
19×frac-2neg clear-num associate-/r* sum-cubes
7×pow1/2
6×*-commutative
4×distribute-rgt-in associate-+r+ distribute-lft-in
3×sub-neg associate-*l*
2×+-commutative distribute-rgt-out-- associate-/r/ distribute-lft-out--
1×pow2 pow-to-exp pow-pow sqrt-unprod unpow3 pow-prod-down rem-square-sqrt pow-sqr pow-prod-up sqrt-pow2 div-inv sqr-pow
Counts
4 → 126
Calls
4 calls:
2.0ms
(pow (sqrt x) 3)
3.0ms
(* (sqrt x) (sqrt x))
6.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(* (/ 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)))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(pow (sqrt x) 3)
16.0ms
(* (sqrt x) (sqrt x))
87.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
268.0ms
(* (/ 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)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
017326225
150035594

prune600.0ms

Filtered
138 candidates to 94 candidates (68.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1344138
Fresh000
Picked011
Done112
Total1356141

Merged error: 0.1b

Counts
141 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sqrt x) 3)
9.3b
(/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))
9.7b
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))))
27.2b
(+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
300×sqrt-div
268×frac-times
200×frac-add
199×flip3-+ flip-+
92×associate-*r/
84×frac-2neg clear-num
82×associate-/l/
54×associate-*l/
43×associate-/r* sum-cubes
4×associate-/r/
3×+-commutative div-sub associate-*l*
2×neg-sub0 distribute-rgt-in associate-+r- distribute-lft-in unsub-neg div-inv
1×pow-to-exp pow-pow pow1/2 unpow3 *-commutative sqrt-pow2 sqr-pow
Counts
4 → 243
Calls
4 calls:
2.0ms
(pow (sqrt x) 3)
17.0ms
(/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))
39.0ms
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))))
9.0ms
(+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x)))

series669.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(pow (sqrt x) 3)
112.0ms
(/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))
474.0ms
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (/ (+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x))) (+ (* (sqrt (+ x 1.0)) (sqrt x)) x))))
39.0ms
(+ (* (pow (sqrt x) 3) (sqrt x)) (- (* (+ x 1.0) x)))

simplify165.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0332713697
1500113556

prune1.3s

Filtered
255 candidates to 172 candidates (67.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2541255
Fresh123
Picked011
Done022
Total2556261

Merged error: 0.1b

Counts
261 → 6

regimes37.0ms

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

sample635.0ms

Algorithm
intervals
Results
143.0ms1708×body1280valid
122.0ms7959×body80nan
81.0ms1279×body640valid
78.0ms4106×body80valid
31.0ms591×body320valid
10.0ms316×body160valid