Details

Time bar (total: 3.4s)

sample28.0ms

Algorithm
intervals
Results
6.0ms45×body640valid
5.0ms275×body80nan
4.0ms44×body1280valid
3.0ms140×body80valid
1.0ms14×body320valid
0.0ms13×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: 27.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite28.0ms

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))
23.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series102.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify60.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune78.0ms

Pruning

3 alts after pruning (2 fresh and 1 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)))

rewrite49.0ms

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))
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series236.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0341624
11239566
25001533

prune162.0ms

Pruning

9 alts after pruning (8 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))))

rewrite72.0ms

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)))
5.0ms
(sqrt (sqrt (+ x 1.0)))
29.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
27.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(sqrt (sqrt (+ x 1.0)))
88.0ms
(sqrt (sqrt (+ x 1.0)))
137.0ms
(/ 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))))

simplify74.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05251350
123081176
250011153

prune333.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
20.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ x 1.0))
95.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
103.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify153.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 3 (144.0ms)

IterNodesCost
0306792
11002747
24420669
35003665

prune421.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

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

sample695.0ms

Algorithm
intervals
Results
152.0ms1723×body1280valid
150.0ms7968×body80nan
85.0ms1228×body640valid
83.0ms4137×body80valid
34.0ms606×body320valid
11.0ms306×body160valid