Details

Time bar (total: 14.8s)

sample42.0ms

Algorithm
intervals
Results
10.0ms70×body1280valid
7.0ms241×body80nan
4.0ms123×body80valid
4.0ms33×body640valid
2.0ms24×body320valid
0.0ms6×body160valid

simplify7.0ms

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: 31.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite87.0ms

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:
7.0ms
(sqrt (+ x 1.0))
78.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series123.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(sqrt (+ x 1.0))
85.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.7s

Counts
41 → 41
Iterations

Useful iterations: done (2.7s)

IterNodesCost
084488
1183440
2432410
31028402
42702390
done5000382

prune113.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite133.0ms

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:
10.0ms
(sqrt (+ x 1.0))
60.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
61.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series350.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(sqrt (+ x 1.0))
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
230.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.3s

Counts
80 → 80
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01521125
13431018
2891935
32607919
done5000915

prune323.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite572.0ms

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:
67.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
84.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
339.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
468.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
221.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
202.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
265.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.4s

Counts
262 → 262
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03116170
16414386
220044124
done50014023

prune714.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
34.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
40.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
8.0ms
(cbrt (+ x 1.0))
7.0ms
(cbrt (+ x 1.0))

series630.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
163.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
103.0ms
(cbrt (+ x 1.0))
116.0ms
(cbrt (+ x 1.0))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03282505
18512346
230582209
done50002197

prune514.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes52.0ms

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

sample1.9s

Algorithm
intervals
Results
707.0ms1699×body1280valid
410.0ms8200×body80nan
222.0ms1186×body640valid
130.0ms4118×body80valid
58.0ms687×body320valid
20.0ms310×body160valid