Details

Time bar (total: 3.4s)

sample28.0ms

Algorithm
intervals
Results
7.0ms254×body80nan
5.0ms56×body1280valid
3.0ms44×body640valid
2.0ms123×body80valid
1.0ms19×body320valid
1.0ms14×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
4.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite14.0ms

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:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series148.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(sqrt (+ x 1.0))
108.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify54.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune83.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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 (+ (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)))

series236.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0341624
11239566
25001533

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
7.0ms
(sqrt (sqrt (+ x 1.0)))
15.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
14.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(sqrt (sqrt (+ x 1.0)))
83.0ms
(sqrt (sqrt (+ x 1.0)))
319.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
30.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05251350
123291176
250011152

prune330.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×sqrt-prod
32×sqrt-div
24×*-un-lft-identity
23×associate-*r*
22×add-sqr-sqrt
21×cbrt-prod
16×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
10×cbrt-div associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod distribute-lft-out add-log-exp
3×unswap-sqr
2×pow1/3 associate-*l/ *-commutative
Counts
4 → 99
Calls
4 calls:
15.0ms
(* (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
8.0ms
(* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0))))
6.0ms
(cbrt (sqrt (+ x 1.0)))
4.0ms
(cbrt (sqrt (+ x 1.0)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
94.0ms
(* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0))))
84.0ms
(cbrt (sqrt (+ x 1.0)))
86.0ms
(cbrt (sqrt (+ x 1.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06361440
123681336
250021291

prune391.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes37.0ms

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

sample711.0ms

Algorithm
intervals
Results
162.0ms1698×body1280valid
147.0ms7827×body80nan
93.0ms1249×body640valid
83.0ms4106×body80valid
35.0ms619×body320valid
15.0ms328×body160valid