Details

Time bar (total: 2.8s)

sample26.0ms

Algorithm
intervals
Results
9.0ms66×body1280valid
4.0ms39×body640valid
4.0ms125×body80valid
1.0ms18×body320valid
0.0ms8×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.9b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.7b
(- (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))

series14.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
11.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify32.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0282318
11037308
25001297

prune72.0ms

Filtered
41 candidates to 31 candidates (24.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New38341
Fresh000
Picked011
Done000
Total38442

Merged error: 0.1b

Counts
42 → 4

localize8.0ms

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)))

rewrite26.0ms

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))
9.0ms
(+ (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))
6.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify68.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0514800
12206753
25001721

prune156.0ms

Filtered
89 candidates to 59 candidates (33.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New81889
Fresh112
Picked011
Done101
Total831093

Merged error: 0.0b

Counts
93 → 10

localize11.0ms

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)))
0.2b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
900×sqrt-prod
774×times-frac
460×distribute-lft-out
294×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 547
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
19.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify123.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0130411537
150019913

prune684.0ms

Filtered
559 candidates to 154 candidates (72.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5545559
Fresh538
Picked011
Done011
Total55910569

Merged error: 0b

Counts
569 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 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))

rewrite28.0ms

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:
12.0ms
(/ (+ 1.0 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))

series69.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
11.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
6.0ms
(cbrt (+ x 1.0))
6.0ms
(cbrt (+ x 1.0))

simplify129.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09311718
149451624
250011624

prune336.0ms

Filtered
104 candidates to 86 candidates (17.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1022104
Fresh257
Picked011
Done022
Total10410114

Merged error: 0b

Counts
114 → 10

regimes116.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample686.0ms

Algorithm
intervals
Results
237.0ms1717×body1280valid
129.0ms1264×body640valid
115.0ms4069×body80valid
48.0ms636×body320valid
16.0ms314×body160valid

Profiling

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