Details

Time bar (total: 4.9s)

sample27.0ms

Algorithm
intervals
Results
7.0ms268×body80nan
4.0ms54×body1280valid
3.0ms41×body640valid
2.0ms134×body80valid
1.0ms17×body320valid
0.0ms10×body160valid

simplify6.0ms

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: 29.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.0b
(- (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))
22.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify61.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0182265
1544243
22020233
35002232

prune93.0ms

Pruning

4 alts after pruning (4 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)))

rewrite50.0ms

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))
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series435.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
337.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0341624
11239566
25001533

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
22.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
77.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series816.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
335.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
148.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify128.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
010338862
141207704
250017681

prune574.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(/ (/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
132×*-un-lft-identity
120×sqrt-prod
114×times-frac
50×add-sqr-sqrt
48×add-cube-cbrt distribute-lft-out
28×sqrt-div
24×associate-/r/
23×add-exp-log
22×associate-*r/
18×add-cbrt-cube
14×flip3-+ flip-+
12×div-inv associate-/l*
10×div-exp associate-/r*
7×cbrt-undiv
6×pow1
4×prod-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 179
Calls
4 calls:
22.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
15.0ms
(/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
46.0ms
(/ (/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
332.0ms
(/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
144.0ms
(/ (/ 1.0 (* 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify86.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07593252
129272828
250012822

prune400.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes42.0ms

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

sample658.0ms

Algorithm
intervals
Results
145.0ms1712×body1280valid
141.0ms7994×body80nan
77.0ms1209×body640valid
76.0ms4129×body80valid
31.0ms651×body320valid
10.0ms299×body160valid