Details

Time bar (total: 10.5s)

sample26.0ms

Algorithm
intervals
Results
5.0ms276×body80nan
5.0ms54×body1280valid
4.0ms52×body640valid
2.0ms128×body80valid
1.0ms12×body320valid
0.0ms10×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite39.0ms

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:
4.0ms
(sqrt (+ x 1.0))
28.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series114.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(sqrt (+ x 1.0))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
95 → 95
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01371993
13011467
27251124
32365950
done5000943

prune152.0ms

Pruning

5 alts after pruning (5 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 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite48.0ms

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:
4.0ms
(sqrt (+ x 1.0))
11.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
29.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series258.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
72.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
154.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: 3 (860.0ms)

IterNodesCost
01691453
14111200
211051098
337071079
done50011079

prune235.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt x) (fabs (sqrt (+ x 1.0))))
0.2b
(/ (+ 1.0 0) (+ (sqrt x) (fabs (sqrt (+ x 1.0)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
19×add-sqr-sqrt
16×add-cube-cbrt times-frac
12×distribute-lft-out
7×sqrt-prod
6×fma-def
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ associate-/r* 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 → 81
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt x) (fabs (sqrt (+ x 1.0))))
16.0ms
(/ (+ 1.0 0) (+ (sqrt x) (fabs (sqrt (+ x 1.0)))))

series106.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(sqrt (+ x 1.0))
30.0ms
(+ (sqrt x) (fabs (sqrt (+ x 1.0))))
39.0ms
(/ (+ 1.0 0) (+ (sqrt x) (fabs (sqrt (+ x 1.0)))))

simplify2.3s

Counts
90 → 90
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01741432
14301229
211911030
341781009
done50001009

prune243.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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))))))

rewrite193.0ms

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:
25.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
20.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
21.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
112.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series877.0ms

Counts
4 → 12
Calls
4 calls:
387.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
153.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
155.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
181.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify986.0ms

Counts
270 → 270
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
03176276
16764534
222024202
done50004195

prune577.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes43.0ms

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: 1 (1.0ms)

IterNodesCost
01012
11310
done1310

end0.0ms

sample686.0ms

Algorithm
intervals
Results
151.0ms1723×body1280valid
148.0ms8134×body80nan
86.0ms1260×body640valid
79.0ms4068×body80valid
31.0ms621×body320valid
15.0ms328×body160valid