Details

Time bar (total: 7.9s)

sample24.0ms

Algorithm
intervals
Results
5.0ms58×body1280valid
4.0ms226×body80nan
3.0ms42×body640valid
2.0ms123×body80valid
1.0ms23×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: 31.7b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
27.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series69.0ms

Counts
1 → 3
Calls
1 calls:
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify694.0ms

Counts
22 → 22
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
059310
1133285
2392263
31543257
done5000257

prune45.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
31×distribute-lft-out
24×times-frac sqrt-prod
14×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
3×flip3-+ flip-+
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 64
Calls
2 calls:
18.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
34.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series206.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify574.0ms

Counts
70 → 70
Iterations

Useful iterations: done (572.0ms)

IterNodesCost
01391225
13401005
21195906
done5001902

prune142.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
78×*-un-lft-identity
34×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×flip3-+ swap-sqr flip-+
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/
5×pow-prod-up
4×times-frac associate-*r/ associate-*l/ associate-/l* add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod associate-/l/
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 139
Calls
4 calls:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
107.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
167.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
145.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
69.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.3s

Counts
151 → 151
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02323527
15582241
225102022
done50002018

prune337.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0))))))
0.2b
(* (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(cbrt (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
32×sqrt-prod
18×cbrt-prod
16×add-sqr-sqrt distribute-lft-out
15×associate-*r*
14×sqrt-div
12×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
10×cbrt-div associate-*l* associate-*l/
9×flip3-+ flip-+
4×frac-times pow-prod-down prod-exp cbrt-unprod add-log-exp
2×pow1/3 associate-*r/ *-commutative unswap-sqr
Counts
4 → 94
Calls
4 calls:
53.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0))))))
107.0ms
(* (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
13.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(cbrt (+ (sqrt x) (sqrt (+ x 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0))))))
346.0ms
(* (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (fabs (cbrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
297.0ms
(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
483.0ms
(cbrt (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.0s

Counts
106 → 106
Iterations

Useful iterations: 2 (253.0ms)

IterNodesCost
02963357
17533004
228872698
done50002698

prune419.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes42.0ms

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: 2 (1.0ms)

IterNodesCost
0911
11211
2169
done169

end0.0ms

sample679.0ms

Algorithm
intervals
Results
153.0ms1746×body1280valid
140.0ms7984×body80nan
88.0ms1276×body640valid
77.0ms4049×body80valid
31.0ms615×body320valid
11.0ms314×body160valid