Details

Time bar (total: 4.1s)

sample24.0ms

Algorithm
intervals
Results
5.0ms56×body1280valid
4.0ms245×body80nan
3.0ms44×body640valid
2.0ms121×body80valid
1.0ms25×body320valid
0.0ms10×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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))
21.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
73.0ms
(- (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

prune88.0ms

Filtered
41 candidates to 28 candidates (68.3%)
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))
0.2b
(/ 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)))

series232.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0341625
11233566
25001533

prune162.0ms

Filtered
80 candidates to 53 candidates (66.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 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))

rewrite35.0ms

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:
13.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
13.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms
(cbrt (+ x 1.0))
5.0ms
(cbrt (+ x 1.0))

series449.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
96.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
87.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))

simplify101.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
08501475
139671385
250021364

prune343.0ms

Filtered
98 candidates to 79 candidates (80.6%)
Pruning

7 alts after pruning (5 fresh and 2 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)))
0.2b
(/ 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))))
73.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series781.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
156.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
323.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify139.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
010338862
141207704
250017681

prune542.0ms

Filtered
457 candidates to 146 candidates (31.9%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

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

sample659.0ms

Algorithm
intervals
Results
143.0ms1724×body1280valid
138.0ms8037×body80nan
88.0ms1246×body640valid
73.0ms4095×body80valid
30.0ms622×body320valid
10.0ms313×body160valid