Details

Time bar (total: 4.6s)

sample24.0ms

Algorithm
intervals
Results
5.0ms55×body1280valid
5.0ms266×body80nan
3.0ms139×body80valid
2.0ms33×body640valid
1.0ms24×body320valid
0.0ms5×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 28.3b

localize5.0ms

Local error

Found 1 expressions with local error:

2.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
24.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series67.0ms

Counts
1 → 3
Calls
1 calls:
67.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify49.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune43.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
16.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series203.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0295535
11077482
25001453

prune117.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
26.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
125.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series791.0ms

Counts
4 → 12
Calls
4 calls:
343.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06472845
131522529
250022489

prune510.0ms

Filtered
262 candidates to 136 candidates (51.9%)
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)))
0.2b
(/ 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))))

rewrite180.0ms

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:
25.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
74.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series788.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
160.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
321.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify138.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
010338862
141207704
250017681

prune521.0ms

Filtered
457 candidates to 146 candidates (31.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes35.0ms

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

sample665.0ms

Algorithm
intervals
Results
154.0ms1728×body1280valid
138.0ms8063×body80nan
84.0ms1199×body640valid
77.0ms4203×body80valid
30.0ms593×body320valid
10.0ms277×body160valid