Details

Time bar (total: 5.8s)

sample41.0ms

Algorithm
intervals
Results
11.0ms268×body80nan
8.0ms54×body1280valid
6.0ms134×body80valid
5.0ms41×body640valid
2.0ms17×body320valid
1.0ms10×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: 29.1b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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))

series100.0ms

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

simplify56.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

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)))

rewrite45.0ms

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

series235.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0341624
11239566
25001533

prune182.0ms

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))))

rewrite177.0ms

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:
23.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
72.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
323.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
145.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify133.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
010338862
141207704
250017681

prune609.0ms

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
(pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2)
0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
780×*-un-lft-identity
654×times-frac
520×sqrt-prod
292×distribute-lft-out
270×add-sqr-sqrt
269×add-cube-cbrt
210×unpow-prod-down
36×associate-/l*
35×sqr-pow
26×sqrt-div
24×associate-/r/
20×add-exp-log
19×associate-/r*
13×flip3-+ flip-+ div-inv
11×add-cbrt-cube
10×div-exp
6×pow1
4×cbrt-undiv add-log-exp
3×pow-to-exp pow-unpow pow-exp
2×frac-2neg clear-num
1×rem-sqrt-square pow-pow sqrt-pow1 pow1/2 associate-/l/ unpow1/2
Counts
4 → 484
Calls
4 calls:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms
(pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2)
25.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
97.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2))

series952.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
304.0ms
(pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2)
334.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
150.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (pow (+ (sqrt (+ x 1.0)) (sqrt x)) 1/2))

simplify108.0ms

Algorithm
egg-herbie
Counts
496 → 496
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013189657
150018235

prune707.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes43.0ms

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

sample1.2s

Algorithm
intervals
Results
323.0ms7994×body80nan
276.0ms1712×body1280valid
182.0ms4129×body80valid
157.0ms1209×body640valid
64.0ms651×body320valid
21.0ms299×body160valid