Details

Time bar (total: 14.0s)

sample33.0ms

Algorithm
intervals
Results
6.0ms250×body80nan
5.0ms47×body1280valid
3.0ms142×body80valid
3.0ms38×body640valid
1.0ms17×body320valid
1.0ms12×body160valid

simplify8.0ms

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: 27.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite117.0ms

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:
14.0ms
(sqrt (+ x 1.0))
101.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series118.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(sqrt (+ x 1.0))
84.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts
41 → 41
Iterations

Useful iterations: done (1.7s)

IterNodesCost
084488
1188440
2638410
32563402
done5000400

prune140.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
20×sqrt-prod
18×times-frac
17×distribute-lft-out
15×add-sqr-sqrt
14×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube
3×pow1 associate-/l*
2×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 57
Calls
2 calls:
15.0ms
(sqrt (+ x 1.0))
95.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series279.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
226.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify768.0ms

Counts
63 → 63
Iterations

Useful iterations: done (765.0ms)

IterNodesCost
0140893
1328811
21362752
done5000748

prune215.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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)))))

rewrite553.0ms

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:
51.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
82.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
69.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
328.0ms
(* (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:
484.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
190.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
188.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
239.0ms
(* (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

prune826.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
100×*-un-lft-identity
82×sqrt-prod
46×times-frac
40×distribute-lft-out
34×add-sqr-sqrt
30×add-cube-cbrt
15×associate-/r*
11×add-exp-log add-cbrt-cube
6×pow1 sqrt-div associate-/r/
4×flip3-+ flip-+ associate-/l* add-log-exp
3×cbrt-undiv rem-sqrt-square div-exp div-inv
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv sqrt-unprod associate-*l/ prod-exp cbrt-unprod associate-/l/
Counts
4 → 132
Calls
4 calls:
61.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
64.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
105.0ms
(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
500.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
213.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
229.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
250.0ms
(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.0s

Counts
144 → 144
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02983063
17342733
236742514
done50012505

prune473.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11522
done1522

end0.0ms

sample1.9s

Algorithm
intervals
Results
578.0ms4105×body80valid
364.0ms1754×body1280valid
237.0ms1236×body640valid
236.0ms7835×body80nan
63.0ms627×body320valid
57.0ms278×body160valid