Details

Time bar (total: 16.0s)

sample69.0ms

Algorithm
intervals
Results
42.0ms245×body80nan
6.0ms38×body1280valid
4.0ms151×body80valid
3.0ms39×body640valid
1.0ms17×body320valid
0.0ms11×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: 25.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite109.0ms

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:
8.0ms
(sqrt (+ x 1.0))
97.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series128.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(sqrt (+ x 1.0))
92.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.3s

Counts
95 → 95
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01371993
13011432
26771124
31959950
done5000846

prune198.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite118.0ms

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:
17.0ms
(sqrt (+ x 1.0))
32.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
62.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series398.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(sqrt (+ x 1.0))
115.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
230.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.0s

Counts
93 → 93
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01581171
13641060
2967972
32933955
done5000954

prune325.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.0b
(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b
(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
0.2b
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
23×sqrt-prod
20×distribute-lft-out
18×times-frac
17×add-sqr-sqrt add-cube-cbrt
6×add-exp-log fma-def associate-/r* add-cbrt-cube add-log-exp
5×expm1-log1p-u
4×pow1 log1p-expm1-u
3×associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num sum-log div-inv expm1-udef
Counts
4 → 87
Calls
4 calls:
0.0ms
(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
32.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
47.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series2.7s

Counts
4 → 12
Calls
4 calls:
740.0ms
(log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
78.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
1.6s
(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
194.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02271784
15781630
218411446
done50011363

prune396.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.2b
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

rewrite479.0ms

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:
44.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
51.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
49.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
311.0ms
(* (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:
490.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
206.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
249.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
237.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.6s

Counts
270 → 270
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03176276
16744462
221054194
done50004091

prune755.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.1b 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
0911
11111
done1111

end0.0ms

sample1.6s

Algorithm
intervals
Results
441.0ms1691×body1280valid
369.0ms7863×body80nan
184.0ms4098×body80valid
181.0ms1245×body640valid
57.0ms611×body320valid
27.0ms355×body160valid