Details

Time bar (total: 2.5s)

sample27.0ms

Algorithm
intervals
Results
10.0ms53×body1280valid
4.0ms134×body80valid
4.0ms35×body640valid
2.0ms21×body320valid
1.0ms13×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.3b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
4.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

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))

series13.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify30.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0282318
11037308
25001297

prune72.0ms

Filtered
31 candidates to 41 candidates (-32.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New38341
Fresh000
Picked101
Done000
Total39342

Merged error: 0.1b

Counts
42 → 3

localize7.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
17×add-sqr-sqrt
16×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 80
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0514800
12206753
25001721

prune149.0ms

Filtered
59 candidates to 89 candidates (-50.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New84589
Fresh022
Picked011
Done000
Total84892

Merged error: 0.0b

Counts
92 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
25×add-sqr-sqrt
19×add-cube-cbrt
13×cbrt-prod
12×times-frac
10×associate-*r*
9×sqrt-prod
8×add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1 cbrt-div
5×flip3-+ flip-+
4×associate-/l* add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 92
Calls
4 calls:
8.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
15.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series71.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
43.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
6.0ms
(cbrt (+ x 1.0))
8.0ms
(cbrt (+ x 1.0))

simplify128.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09311718
149451624
250011624

prune360.0ms

Filtered
86 candidates to 104 candidates (-20.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1022104
Fresh066
Picked101
Done011
Total1039112

Merged error: 0.0b

Counts
112 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (+ x 1.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
66×cbrt-prod
43×add-sqr-sqrt
41×*-un-lft-identity
36×sqrt-prod
21×add-cube-cbrt
18×cbrt-div
16×sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
13.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
4.0ms
(cbrt (sqrt (+ x 1.0)))
4.0ms
(cbrt (sqrt (+ x 1.0)))
3.0ms
(cbrt (+ x 1.0))

series24.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
6.0ms
(cbrt (sqrt (+ x 1.0)))
6.0ms
(cbrt (sqrt (+ x 1.0)))
6.0ms
(cbrt (+ x 1.0))

simplify164.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03601295
111671224
249921069
350011069

prune275.0ms

Filtered
77 candidates to 129 candidates (-67.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh077
Picked011
Done011
Total1299138

Merged error: 0.0b

Counts
138 → 9

regimes137.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample843.0ms

Algorithm
intervals
Results
408.0ms1679×body1280valid
124.0ms1235×body640valid
111.0ms4101×body80valid
50.0ms646×body320valid
23.0ms339×body160valid

Profiling

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