Details

Time bar (total: 16.3s)

sample60.0ms

Algorithm
intervals
Results
12.0ms54×body1280valid
11.0ms251×body80nan
7.0ms135×body80valid
6.0ms37×body640valid
3.0ms21×body320valid
1.0ms9×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite124.0ms

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:
16.0ms
(sqrt (+ x 1.0))
98.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series155.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
101.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.5s

Counts
95 → 95
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01371993
13011432
26771124
31959950
done5000846

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
27×sqrt-prod
21×distribute-lft-out
20×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
6×fma-def associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u 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 hypot-def div-inv
Counts
3 → 84
Calls
3 calls:
19.0ms
(sqrt (+ x 1.0))
23.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
49.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series287.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(sqrt (+ x 1.0))
76.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
172.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.3s

Counts
93 → 93
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01581171
13641060
2967972
32933955
done5000954

prune287.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))))

rewrite375.0ms

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:
55.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
50.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
56.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
148.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
200.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
241.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
420.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
181.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify1.8s

Counts
473 → 473
Iterations

Useful iterations: done (1.8s)

IterNodesCost
044615335
1106012320
2232911633
done500011008

prune925.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

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))))))

rewrite497.0ms

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:
71.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
73.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
51.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
284.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
492.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
214.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
220.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
254.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.7s

Counts
270 → 270
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03176276
16744462
221054194
done50004091

prune775.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes36.0ms

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
079
199
done99

end0.0ms

sample2.0s

Algorithm
intervals
Results
709.0ms8028×body80nan
452.0ms1737×body1280valid
200.0ms1307×body640valid
142.0ms4108×body80valid
59.0ms574×body320valid
17.0ms274×body160valid