Details

Time bar (total: 9.5s)

sample25.0ms

Algorithm
intervals
Results
5.0ms276×body80nan
4.0ms54×body1280valid
3.0ms52×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))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
26.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(sqrt (+ x 1.0))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts
41 → 41
Iterations

Useful iterations: 4 (1.0s)

IterNodesCost
084488
1183440
2452410
31180402
43522389
done5000389

prune85.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×flip3-+ flip-+ 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 div-inv
Counts
3 → 71
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
17.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series238.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.6s

Counts
80 → 80
Iterations

Useful iterations: 3 (575.0ms)

IterNodesCost
01521125
13431034
2919939
33047923
done5000923

prune154.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite226.0ms

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×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 → 250
Calls
4 calls:
27.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
24.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
130.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
338.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
133.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
165.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify871.0ms

Counts
262 → 262
Iterations

Useful iterations: done (862.0ms)

IterNodesCost
03116170
16474458
220984132
done50014126

prune522.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b
(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(sqrt (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
41×sqrt-prod
28×distribute-lft-out
19×flip3-+ flip-+
18×add-exp-log add-cbrt-cube
16×associate-/r/
12×pow1 add-sqr-sqrt frac-times
10×swap-sqr
9×add-cube-cbrt
6×associate-*r/ associate-*r* associate-*l* associate-*l/ add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×times-frac
2×rem-sqrt-square div-inv
1×+-commutative pow2 distribute-rgt-in frac-2neg distribute-lft-in sqrt-pow1 pow-plus pow1/2 sqrt-div pow-prod-down clear-num associate-/r* sum-log pow-sqr *-commutative pow-prod-up associate-/l* unswap-sqr
Counts
4 → 116
Calls
4 calls:
18.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
32.0ms
(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
33.0ms
(sqrt (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))
109.0ms
(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
185.0ms
(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
160.0ms
(sqrt (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))
107.0ms
(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.0s

Counts
128 → 128
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02253250
16262702
222382177
done50012169

prune265.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

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
01226
11726
done1726

end0.0ms

sample669.0ms

Algorithm
intervals
Results
148.0ms8134×body80nan
144.0ms1723×body1280valid
83.0ms1260×body640valid
78.0ms4068×body80valid
30.0ms621×body320valid
11.0ms328×body160valid