Details

Time bar (total: 5.2s)

sample26.0ms

Algorithm
intervals
Results
5.0ms63×body1280valid
5.0ms264×body80nan
2.0ms39×body640valid
2.0ms131×body80valid
1.0ms14×body320valid
0.0ms9×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: 30.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite50.0ms

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))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify59.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune87.0ms

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

rewrite82.0ms

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))
32.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series237.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
60.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0341624
11239566
25001533

prune164.0ms

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)) (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))))

rewrite277.0ms

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:
37.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
36.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
118.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series785.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
162.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
331.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
137.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify132.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
010338862
141207704
250017681

prune553.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

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)))) (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
924×*-un-lft-identity
834×times-frac
820×sqrt-prod
352×add-sqr-sqrt
350×add-cube-cbrt
328×distribute-lft-out
306×unpow-prod-down
36×associate-/l*
34×sqrt-div sqr-pow
30×associate-/r/
22×associate-/r*
19×add-exp-log
17×flip3-+ flip-+
16×div-inv
11×add-cbrt-cube
10×div-exp
6×pow1
4×cbrt-undiv add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num
1×associate-/l/
Counts
4 → 583
Calls
4 calls:
37.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
160.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))

series787.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
322.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 1))

simplify121.0ms

Algorithm
egg-herbie
Counts
595 → 595
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0142012788
1500110626

prune643.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes36.0ms

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

sample692.0ms

Algorithm
intervals
Results
148.0ms1766×body1280valid
133.0ms7948×body80nan
76.0ms4094×body80valid
76.0ms1215×body640valid
28.0ms596×body320valid
11.0ms329×body160valid