Details

Time bar (total: 12.9s)

sample46.0ms

Algorithm
intervals
Results
8.0ms250×body80nan
8.0ms47×body1280valid
5.0ms142×body80valid
5.0ms38×body640valid
2.0ms17×body320valid
1.0ms12×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
14.0ms
(sqrt (+ x 1.0))
83.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series161.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(sqrt (+ x 1.0))
110.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify823.0ms

Counts
95 → 95
Iterations

Useful iterations: done (818.0ms)

IterNodesCost
01371993
13161446
210401125
done5000951

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
28×distribute-lft-out
24×times-frac sqrt-prod
18×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l*
3×pow1 flip3-+ flip-+
2×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 71
Calls
2 calls:
10.0ms
(sqrt (+ x 1.0))
60.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series257.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(sqrt (+ x 1.0))
195.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.1s

Counts
77 → 77
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01551205
1389956
21839895
done5002890

prune173.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite320.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 258
Calls
4 calls:
39.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
38.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
41.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
185.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
480.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
185.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
192.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
186.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify2.2s

Counts
270 → 270
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03176276
17344476
233354198
done50024140

prune764.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
100×*-un-lft-identity
86×sqrt-prod
46×times-frac
42×add-sqr-sqrt
40×distribute-lft-out
30×add-cube-cbrt
15×associate-/r*
11×add-exp-log add-cbrt-cube
6×pow1 sqrt-div associate-/r/
4×expm1-log1p-u flip3-+ flip-+ hypot-def log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv rem-sqrt-square div-exp div-inv
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv sqrt-unprod associate-*l/ prod-exp cbrt-unprod associate-/l/
Counts
4 → 144
Calls
4 calls:
51.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
58.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
65.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
101.0ms
(/ (* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
477.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
230.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
191.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
211.0ms
(/ (* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify1.9s

Counts
156 → 156
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03063169
17722823
239012609
done50012605

prune605.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11522
done1522

end0.0ms

sample1.6s

Algorithm
intervals
Results
445.0ms7835×body80nan
308.0ms1754×body1280valid
217.0ms4105×body80valid
169.0ms1236×body640valid
57.0ms627×body320valid
18.0ms278×body160valid