Details

Time bar (total: 17.1s)

sample32.0ms

Algorithm
intervals
Results
7.0ms334×body80nan
6.0ms63×body1280valid
3.0ms130×body80valid
2.0ms32×body640valid
1.0ms17×body320valid
1.0ms14×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

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))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series135.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(sqrt (+ x 1.0))
92.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.0s

Counts
41 → 41
Iterations

Useful iterations: done (3.0s)

IterNodesCost
084488
1183440
2432410
31028402
42702390
done5000382

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

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:
14.0ms
(sqrt (+ x 1.0))
49.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
55.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series304.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(sqrt (+ x 1.0))
100.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
167.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.1s

Counts
80 → 80
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01521125
13431018
2891935
32607919
done5000915

prune264.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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

rewrite467.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
73.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
63.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
63.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
207.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
199.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
203.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
455.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
208.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.8s

Counts
457 → 457
Iterations

Useful iterations: done (1.7s)

IterNodesCost
044015237
1103112250
2220811576
done500010949

prune920.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
0.3b
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
0.4b
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
1804×*-un-lft-identity
1674×times-frac
1600×sqrt-prod
840×cbrt-prod
684×add-sqr-sqrt add-cube-cbrt
640×distribute-lft-out
324×unpow-prod-down cube-prod
64×sqrt-div
60×associate-/r/
36×cube-mult unpow3 associate-/r* associate-/l* sqr-pow
32×flip3-+ flip-+
30×div-inv
12×add-exp-log
10×add-cbrt-cube
6×pow1 cube-div
4×cbrt-undiv cbrt-div div-exp add-log-exp
3×pow-unpow pow-pow
2×frac-2neg clear-num
1×pow-to-exp sqrt-pow1 pow1/2 pow1/3 pow-exp sqrt-pow2 rem-cbrt-cube associate-/l/ rem-cube-cbrt
Counts
4 → 1096
Calls
4 calls:
49.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
307.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
78.0ms
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
62.0ms
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

series1.2s

Counts
4 → 12
Calls
4 calls:
434.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
163.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
178.0ms
(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
456.0ms
(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

simplify2.5s

Counts
1108 → 1108
Iterations

Useful iterations: done (2.4s)

IterNodesCost
084346896
1165231392
2375129037
done500128447

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes53.0ms

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

sample991.0ms

Algorithm
intervals
Results
196.0ms1713×body1280valid
190.0ms8104×body80nan
113.0ms1318×body640valid
98.0ms4060×body80valid
45.0ms605×body320valid
13.0ms304×body160valid