Details

Time bar (total: 13.7s)

sample52.0ms

Algorithm
intervals
Results
15.0ms252×body80nan
9.0ms58×body1280valid
4.0ms40×body640valid
4.0ms123×body80valid
2.0ms21×body320valid
1.0ms14×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

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

rewrite90.0ms

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:
8.0ms
(sqrt (+ x 1.0))
81.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series117.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(sqrt (+ x 1.0))
77.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts
41 → 41
Iterations

Useful iterations: done (1.6s)

IterNodesCost
084488
1188440
2638410
32563402
done5000400

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite99.0ms

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:
7.0ms
(sqrt (+ x 1.0))
39.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
50.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series324.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(sqrt (+ x 1.0))
87.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
182.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.0s

Counts
80 → 80
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01521125
13611018
21505937
done5001929

prune292.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
9.0ms
(sqrt (sqrt (+ x 1.0)))
9.0ms
(sqrt (sqrt (+ x 1.0)))
97.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
81.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sqrt (sqrt (+ x 1.0)))
149.0ms
(sqrt (sqrt (+ x 1.0)))
188.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
48.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify2.0s

Counts
173 → 173
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02492955
15811839
225451721
done50001692

prune496.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

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)))))

rewrite593.0ms

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:
79.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
63.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
70.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
360.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
503.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
203.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
198.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
238.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.1s

Counts
262 → 262
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03116170
17034400
232204128
done50024073

prune784.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes62.0ms

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

sample2.1s

Algorithm
intervals
Results
470.0ms338×body160valid
457.0ms8028×body80nan
401.0ms1755×body1280valid
170.0ms4070×body80valid
159.0ms1232×body640valid
57.0ms605×body320valid