Details

Time bar (total: 3.2s)

sample25.0ms

Algorithm
intervals
Results
4.0ms259×body80nan
4.0ms47×body1280valid
3.0ms41×body640valid
3.0ms130×body80valid
1.0ms24×body320valid
0.0ms14×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: 29.9b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.4b
(- (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))
7.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series110.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(sqrt (+ x 1.0))
76.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify59.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0178265
1527243
21971233
35002230

prune72.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New38341
Fresh000
Picked101
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))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite22.0ms

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)))

series247.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
70.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0338624
11209566
25002533

prune139.0ms

Filtered
80 candidates to 53 candidates (66.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh112
Picked011
Done000
Total75883

Merged error: 0.0b

Counts
83 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
26×add-sqr-sqrt
20×add-cube-cbrt
15×times-frac
13×cbrt-prod
11×distribute-lft-out
10×associate-*r*
9×sqrt-prod
8×add-exp-log add-cbrt-cube
7×associate-*l*
6×pow1 cbrt-div
5×associate-/r*
4×flip3-+ flip-+ add-log-exp
3×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 → 94
Calls
4 calls:
20.0ms
(/ 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))

series492.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
105.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
92.0ms
(cbrt (+ x 1.0))
94.0ms
(cbrt (+ x 1.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08421547
139091453
250021442

prune310.0ms

Filtered
106 candidates to 80 candidates (75.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1024106
Fresh246
Picked101
Done011
Total1059114

Merged error: 0.0b

Counts
114 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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
8×add-cbrt-cube
6×add-exp-log
4×frac-times cbrt-unprod add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Counts
4 → 120
Calls
4 calls:
12.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (sqrt (+ x 1.0)))
4.0ms
(cbrt (sqrt (+ x 1.0)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
93.0ms
(cbrt (+ x 1.0))
94.0ms
(cbrt (sqrt (+ x 1.0)))
94.0ms
(cbrt (sqrt (+ x 1.0)))

simplify51.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03711294
112171208
250011094

prune343.0ms

Filtered
132 candidates to 81 candidates (61.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh077
Picked011
Done011
Total1329141

Merged error: 0.0b

Counts
141 → 9

regimes40.0ms

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
095
195

end0.0ms

sample687.0ms

Algorithm
intervals
Results
154.0ms1688×body1280valid
133.0ms7818×body80nan
88.0ms1267×body640valid
86.0ms4113×body80valid
32.0ms602×body320valid
12.0ms330×body160valid