Details

Time bar (total: 10.5s)

sample27.0ms

Algorithm
intervals
Results
5.0ms58×body1280valid
4.0ms226×body80nan
3.0ms10×body160valid
3.0ms42×body640valid
2.0ms123×body80valid
1.0ms23×body320valid

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))

rewrite23.0ms

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:
22.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series75.0ms

Counts
1 → 3
Calls
1 calls:
75.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
22 → 22
Iterations

Useful iterations: done (1.5s)

IterNodesCost
059310
1133285
2351263
3904257
42555252
done5000251

prune45.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
17.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series217.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.4s

Counts
61 → 61
Iterations

Useful iterations: 3 (590.0ms)

IterNodesCost
0128947
1297865
2820788
32979774
done5000774

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

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

rewrite335.0ms

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:
24.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
79.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
29.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series852.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
176.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
151.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
349.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.2s

Counts
457 → 457
Iterations

Useful iterations: done (1.1s)

IterNodesCost
044015237
1103812250
2244011578
done500111574

prune573.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
476×sqrt-prod
326×*-un-lft-identity
223×times-frac
188×add-sqr-sqrt
124×add-cube-cbrt
112×distribute-lft-out
56×swap-sqr
36×associate-*r* associate-*l*
27×associate-/r*
22×sqrt-div
19×pow1
16×unswap-sqr
15×add-exp-log add-cbrt-cube
14×associate-/r/
8×sqrt-pow1 pow1/2
7×flip3-+ flip-+ div-inv associate-/l*
5×pow-prod-up
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg pow-prod-down clear-num pow-sqr associate-/l/
2×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp cbrt-unprod
1×pow2 sqrt-undiv pow-plus rem-square-sqrt *-commutative
Counts
4 → 317
Calls
4 calls:
64.0ms
(/ (* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
27.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
28.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
147.0ms
(* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
359.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
359.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
392.0ms
(* (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify1.2s

Counts
329 → 329
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03979797
17996671
226756151
done50016139

prune677.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes26.0ms

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

sample682.0ms

Algorithm
intervals
Results
146.0ms1746×body1280valid
142.0ms7984×body80nan
83.0ms1276×body640valid
80.0ms4049×body80valid
30.0ms615×body320valid
14.0ms314×body160valid