Details

Time bar (total: 5.1s)

sample26.0ms

Algorithm
intervals
Results
5.0ms64×body1280valid
4.0ms267×body80nan
3.0ms42×body640valid
2.0ms122×body80valid
1.0ms22×body320valid
0.0ms6×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

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))
45.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series98.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0182266
1538243
22004233
35002230
done5002230

prune81.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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)))

rewrite89.0ms

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))
33.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
47.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series222.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(sqrt (+ x 1.0))
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
128.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify45.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0341624
11239566
25001533
done5001533

prune163.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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

rewrite366.0ms

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:
47.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
44.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
211.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series774.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
134.0ms
(/ 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)))))

simplify114.0ms

Counts
262 → 262
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06472845
131522529
250022489
done50022489

prune525.0ms

Pruning

9 alts after pruning (8 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)))
0.2b
(/ 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))))

rewrite300.0ms

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:
39.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
129.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
313.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify122.0ms

Counts
457 → 457
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
010338864
141207704
250017681
done50017681

prune549.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195
done95

end0.0ms

sample711.0ms

Algorithm
intervals
Results
146.0ms1762×body1280valid
135.0ms7829×body80nan
87.0ms1260×body640valid
72.0ms4053×body80valid
32.0ms624×body320valid
10.0ms301×body160valid