Details

Time bar (total: 4.4s)

sample28.0ms

Algorithm
intervals
Results
5.0ms321×body80nan
5.0ms62×body1280valid
2.0ms124×body80valid
2.0ms35×body640valid
1.0ms24×body320valid
0.0ms11×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: 31.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.8b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite51.0ms

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:
7.0ms
(sqrt (+ x 1.0))
42.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series94.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(sqrt (+ x 1.0))
66.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify63.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune82.0ms

Pruning

3 alts after pruning (3 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)))

rewrite88.0ms

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:
7.0ms
(sqrt (+ x 1.0))
31.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
46.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series224.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
134.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0341624
11239566
25001533

prune175.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

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))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out 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 → 86
Calls
4 calls:
28.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
30.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms
(cbrt (+ x 1.0))
5.0ms
(cbrt (+ x 1.0))

series447.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
95.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
84.0ms
(cbrt (+ x 1.0))
86.0ms
(cbrt (+ x 1.0))

simplify101.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
08501475
139671385
250021364

prune362.0ms

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

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
47.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
210.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
129.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
135.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06472845
131522529
250022489

prune509.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample734.0ms

Algorithm
intervals
Results
150.0ms1837×body1280valid
142.0ms8004×body80nan
81.0ms1240×body640valid
75.0ms3977×body80valid
33.0ms619×body320valid
11.0ms327×body160valid