Details

Time bar (total: 3.6s)

sample36.0ms

Algorithm
intervals
Results
8.0ms273×body80nan
8.0ms51×body1280valid
5.0ms47×body640valid
4.0ms132×body80valid
2.0ms18×body320valid
0.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite26.0ms

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))
21.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series102.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(sqrt (+ x 1.0))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify61.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune80.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite48.0ms

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:
4.0ms
(sqrt (+ x 1.0))
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0341625
11233566
25001533

prune157.0ms

Pruning

6 alts after pruning (5 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)))
0.1b
(/ 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))))

rewrite69.0ms

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)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
27.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
26.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(sqrt (sqrt (+ x 1.0)))
88.0ms
(sqrt (sqrt (+ x 1.0)))
140.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
31.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify78.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05251350
123291176
250011152

prune332.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
37×sqrt-prod
32×sqrt-div
24×add-sqr-sqrt *-un-lft-identity
23×cbrt-prod associate-*r*
16×add-cube-cbrt
12×cbrt-div
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod distribute-lft-out add-log-exp unswap-sqr
2×pow1/3 associate-*l/ *-commutative
Counts
4 → 100
Calls
4 calls:
15.0ms
(* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
3.0ms
(cbrt (sqrt (+ x 1.0)))
3.0ms
(cbrt (sqrt (+ x 1.0)))
32.0ms
(* (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (sqrt (+ x 1.0))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
92.0ms
(cbrt (sqrt (+ x 1.0)))
90.0ms
(cbrt (sqrt (+ x 1.0)))
100.0ms
(* (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (sqrt (+ x 1.0))))

simplify69.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06311484
123181378
250011332

prune392.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

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

sample1.0s

Algorithm
intervals
Results
269.0ms1783×body1280valid
230.0ms8186×body80nan
148.0ms1240×body640valid
134.0ms4082×body80valid
53.0ms599×body320valid
17.0ms296×body160valid