Details

Time bar (total: 4.0s)

sample27.0ms

Algorithm
intervals
Results
8.0ms255×body80nan
4.0ms51×body1280valid
3.0ms42×body640valid
2.0ms133×body80valid
1.0ms23×body320valid
0.0ms7×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: 29.4b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series97.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(sqrt (+ x 1.0))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune66.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New39241
Fresh000
Picked011
Done000
Total39342

Merged error: 0.1b

Counts
42 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 71
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(sqrt (+ x 1.0))
64.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
131.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0341624
11239566
25001533

prune147.0ms

Filtered
80 candidates to 53 candidates (66.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New71980
Fresh011
Picked101
Done101
Total731083

Merged error: 0.0b

Counts
83 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
10.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series447.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
101.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
85.0ms
(cbrt (+ x 1.0))
86.0ms
(cbrt (+ x 1.0))

simplify95.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08501475
139671385
250021364

prune380.0ms

Filtered
98 candidates to 79 candidates (80.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New95398
Fresh189
Picked101
Done000
Total9711108

Merged error: 0.0b

Counts
108 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
155.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
313.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
165.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify137.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
010338862
141207704
250017681

prune638.0ms

Filtered
457 candidates to 147 candidates (32.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4534457
Fresh6410
Picked101
Done000
Total4608468

Merged error: 0.0b

Counts
468 → 8

regimes32.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11113

end0.0ms

sample650.0ms

Algorithm
intervals
Results
142.0ms1670×body1280valid
129.0ms7950×body80nan
85.0ms1252×body640valid
75.0ms4160×body80valid
30.0ms613×body320valid
12.0ms305×body160valid