Details

Time bar (total: 5.0s)

sample37.0ms

Algorithm
intervals
Results
8.0ms263×body80nan
7.0ms62×body1280valid
4.0ms128×body80valid
4.0ms19×body320valid
4.0ms40×body640valid
0.0ms7×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: 30.9b

localize5.0ms

Local error

Found 1 expressions with local error:

2.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite23.0ms

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:
23.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series72.0ms

Counts
1 → 3
Calls
1 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune43.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite41.0ms

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

series211.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0295535
11077482
25001453

prune123.0ms

Pruning

8 alts after pruning (6 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))))

rewrite181.0ms

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))))
74.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
338.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
153.0ms
(/ (/ 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

prune565.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

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:
25.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
121.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
351.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify103.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06472845
131522529
250022494

prune512.0ms

Pruning

8 alts after pruning (6 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

sample958.0ms

Algorithm
intervals
Results
261.0ms7979×body80nan
195.0ms1766×body1280valid
147.0ms4115×body80valid
110.0ms1246×body640valid
42.0ms596×body320valid
14.0ms277×body160valid