Details

Time bar (total: 17.4s)

sample47.0ms

Algorithm
intervals
Results
9.0ms291×body80nan
8.0ms57×body1280valid
5.0ms43×body640valid
4.0ms128×body80valid
2.0ms19×body320valid
1.0ms9×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ 1.0 x))
2.4b
(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite43.0ms

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-cbrt-cube sqrt-div add-exp-log distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 35
Calls
2 calls:
6.0ms
(sqrt (+ 1.0 x))
36.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

series136.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(sqrt (+ 1.0 x))
93.0ms
(- (sqrt (+ 1.0 x)) (sqrt x))

simplify1.8s

Counts
41 → 41
Iterations
IterNodes
done5000
32897
2676
1193
086

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

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-cbrt-cube add-exp-log add-log-exp
4×pow1
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
3 → 71
Calls
3 calls:
6.0ms
(sqrt (+ 1.0 x))
32.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
57.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series337.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ 1.0 x))
88.0ms
(+ (sqrt (+ 1.0 x)) (sqrt x))
218.0ms
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify802.0ms

Counts
80 → 80
Iterations
IterNodes
done5001
21549
1371
0156

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite399.0ms

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-cbrt-cube add-exp-log
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 clear-num frac-2neg div-exp
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
34.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x)))))
44.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
46.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
247.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
444.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x)))))
214.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
241.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
250.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))))

simplify1.5s

Counts
262 → 262
Iterations
IterNodes
done5000
23225
1702
0310

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite940.0ms

Algorithm
rewrite-expression-head
Rules
1687×sqrt-prod
1429×*-un-lft-identity
1208×times-frac
570×add-sqr-sqrt
540×distribute-lft-out
484×add-cube-cbrt
306×associate-*r*
48×sqrt-div associate-/r/
39×associate-/l*
27×associate-*l*
24×associate-/r* flip3-+ flip-+ div-inv unswap-sqr
15×add-cbrt-cube add-exp-log
8×pow1
5×cbrt-undiv div-exp
4×add-log-exp
3×clear-num frac-2neg pow-prod-down
2×sqrt-pow1 pow1/2
1×frac-times sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod associate-/l/
Counts
4 → 824
Calls
4 calls:
41.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
36.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
128.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
632.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
473.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
195.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))
493.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
825.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))))

simplify1.3s

Counts
836 → 836
Iterations
IterNodes
done5001
11833
0881

prune2.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done9
19
07

end0.0ms

sample1.8s

Algorithm
intervals
Results
409.0ms1768×body1280valid
367.0ms8152×body80nan
314.0ms4038×body80valid
171.0ms1259×body640valid
68.0ms632×body320valid
21.0ms303×body160valid