Details

Time bar (total: 3.7s)

sample23.0ms

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

series72.0ms

Counts
1 → 3
Calls
1 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm
egg-herbie
Counts
7 → 7
Iterations

Useful iterations: 3 (44.0ms)

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

localize7.0ms

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)))

rewrite9.0ms

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))
5.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series216.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify122.0ms

Algorithm
egg-herbie
Counts
14 → 14
Iterations

Useful iterations: 3 (119.0ms)

IterNodesCost
0209148
1752127
23995104
35001103

prune33.0ms

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

localize21.0ms

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)))))

rewrite47.0ms

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 *-commutative
12×associate-+r+ prod-diff
8×distribute-rgt-in distribute-lft-in
7×pow1/2
3×sub-neg associate-*l*
2×+-commutative distribute-rgt-out-- fma-neg 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 → 140
Calls
4 calls:
2.0ms
(pow (sqrt x) 3)
3.0ms
(* (sqrt x) (sqrt x))
7.0ms
(- (* (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)))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(pow (sqrt x) 3)
22.0ms
(* (sqrt x) (sqrt x))
88.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))
269.0ms
(* (/ 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)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
018236600
150035651

prune782.0ms

Filtered
152 candidates to 97 candidates (63.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1484152
Fresh000
Picked101
Done112
Total1505155

Merged error: 0.1b

Counts
155 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sqrt x) 3)
10.2b
(/ (* 1.0 (fma (sqrt (+ x 1.0)) (sqrt (+ x 1.0)) (fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x)))))) (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
29.1b
(fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x))))
31.1b
(fma (- (sqrt (+ x 1.0))) (sqrt x) (* (sqrt (+ x 1.0)) (sqrt x)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×sum-cubes
2×times-frac associate-/r/ *-commutative fma-udef associate-/l*
1×pow-to-exp pow-pow frac-2neg flip3-+ pow1/2 unpow3 clear-num associate-/r* sqrt-pow2 flip-+ div-inv sqr-pow
Counts
4 → 17
Calls
4 calls:
2.0ms
(pow (sqrt x) 3)
7.0ms
(/ (* 1.0 (fma (sqrt (+ x 1.0)) (sqrt (+ x 1.0)) (fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x)))))) (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
1.0ms
(fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x))))
1.0ms
(fma (- (sqrt (+ x 1.0))) (sqrt x) (* (sqrt (+ x 1.0)) (sqrt x)))

series848.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(pow (sqrt x) 3)
425.0ms
(/ (* 1.0 (fma (sqrt (+ x 1.0)) (sqrt (+ x 1.0)) (fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x)))))) (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3)))
144.0ms
(fma (sqrt x) (sqrt x) (- (* (sqrt (+ x 1.0)) (sqrt x))))
236.0ms
(fma (- (sqrt (+ x 1.0))) (sqrt x) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0375383
11281283
25002246

prune147.0ms

Filtered
29 candidates to 27 candidates (93.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New28129
Fresh033
Picked011
Done011
Total28634

Merged error: 0.1b

Counts
34 → 6

regimes38.0ms

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

sample650.0ms

Algorithm
intervals
Results
144.0ms1708×body1280valid
131.0ms7959×body80nan
82.0ms1279×body640valid
74.0ms4106×body80valid
29.0ms591×body320valid
13.0ms316×body160valid