Details

Time bar (total: 1.1m)

sample61.0ms

Algorithm
intervals
Results
20.0ms56×body1280valid
10.0ms275×body80nan
6.0ms40×body640valid
5.0ms136×body80valid
2.0ms17×body320valid
1.0ms7×body160valid

simplify4.0ms

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: 28.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite93.0ms

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:
13.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series149.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(sqrt (+ x 1.0))
112.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify896.0ms

Counts
95 → 95
Iterations

Useful iterations: done (891.0ms)

IterNodesCost
01371993
13161446
210401125
done5000951

prune197.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
32×distribute-lft-out
31×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
6×fma-def associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 93
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
21.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
84.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series352.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(sqrt (+ x 1.0))
113.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
201.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01691453
14281178
219951093
done50011085

prune363.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
708×sqrt-prod
594×times-frac
280×distribute-lft-out
270×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
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 461
Calls
4 calls:
54.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
65.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
56.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
183.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
222.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
236.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
456.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
218.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify2.4s

Counts
473 → 473
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
044615335
1109712320
2420011831
done500011831

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.1s

Algorithm
rewrite-expression-head
Rules
56169×sqrt-prod
42381×times-frac
38028×*-un-lft-identity
14256×add-sqr-sqrt add-cube-cbrt
13584×distribute-lft-out
1391×sqrt-div
1389×associate-/r/
714×div-inv
676×flip3-+ flip-+
383×associate-/r*
51×associate-/l*
15×add-exp-log add-cbrt-cube
6×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×sqrt-undiv associate-/l/
Counts
4 → 12725
Calls
4 calls:
77.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
53.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
700.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (/ (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
190.0ms
(/ (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
460.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
469.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
250.0ms
(/ (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (/ (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
737.0ms
(/ (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) (sqrt (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))))

simplify5.7s

Counts
12737 → 12737
Iterations

Useful iterations: 0 (1.6s)

IterNodesCost
06274840710
done6274840710

prune40.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
0911
1129
2139
done139

end0.0ms

sample2.1s

Algorithm
intervals
Results
858.0ms8189×body80nan
339.0ms1741×body1280valid
231.0ms4120×body80valid
174.0ms1234×body640valid
95.0ms602×body320valid
20.0ms303×body160valid