Details

Time bar (total: 15.4s)

sample43.0ms

Algorithm
intervals
Results
11.0ms60×body1280valid
9.0ms267×body80nan
6.0ms40×body640valid
4.0ms116×body80valid
3.0ms28×body320valid
1.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
312
212
111
06

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1))
3.4b
(- (sqrt (+ x 1)) (sqrt x))

rewrite59.0ms

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 insert-posit16 distribute-lft-out
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 37
Calls
2 calls:
9.0ms
(sqrt (+ x 1))
49.0ms
(- (sqrt (+ x 1)) (sqrt x))

series105.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(sqrt (+ x 1))
68.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify2.7s

Counts
43 → 43
Iterations
IterNodes
54088
41554
3730
2352
1161
081

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite89.0ms

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
7×add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×flip3-+ flip-+ insert-posit16 associate-/l*
2×sqrt-div div-exp associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 78
Calls
3 calls:
9.0ms
(sqrt (+ x 1))
36.0ms
(+ (sqrt (+ x 1)) (sqrt x))
41.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series194.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(sqrt (+ x 1))
61.0ms
(+ (sqrt (+ x 1)) (sqrt x))
107.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify905.0ms

Counts
87 → 87
Iterations
IterNodes
42176
31028
2524
1238
0120

prune635.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1)))
0.1b
(sqrt (sqrt (+ x 1)))
0.2b
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×pow1 sqrt-div
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l* add-exp-log
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×div-exp associate-*l/ associate-*r/ associate-/r/
1×pow2 cbrt-undiv rec-exp clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod 1-exp prod-exp *-commutative cbrt-unprod div-inv pow-flip inv-pow
Counts
4 → 169
Calls
4 calls:
5.0ms
(sqrt (sqrt (+ x 1)))
5.0ms
(sqrt (sqrt (+ x 1)))
41.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
54.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (sqrt (+ x 1)))
62.0ms
(sqrt (sqrt (+ x 1)))
121.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
38.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify926.0ms

Counts
181 → 181
Iterations
IterNodes
32182
2952
1433
0211

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (sqrt (+ x 1))))
0.2b
(/ 1 (+ (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt x)))
0.2b
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1)))))
0.2b
(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1)))))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
180×sqrt-div
138×sqrt-pow1
116×sqrt-prod
71×pow1
62×add-sqr-sqrt
53×pow-prod-up
50×pow1/2
35×flip3-+ flip-+
34×*-un-lft-identity
32×frac-times
26×associate-*r* add-cube-cbrt
16×pow-prod-down associate-*l/
15×add-exp-log
13×add-cbrt-cube
12×unswap-sqr
11×associate-*l*
10×associate-*r/
9×times-frac pow3
4×prod-exp cbrt-unprod insert-posit16 distribute-lft-out add-log-exp
3×rem-sqrt-square associate-/r* pow-plus sqrt-unprod associate-/l*
2×div-exp associate-/r/ *-commutative
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
4 → 222
Calls
4 calls:
6.0ms
(sqrt (sqrt (sqrt (+ x 1))))
132.0ms
(/ 1 (+ (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt x)))
45.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1)))))
80.0ms
(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1)))))

series238.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (sqrt (sqrt (+ x 1))))
94.0ms
(/ 1 (+ (* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt x)))
60.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1)))))
36.0ms
(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (sqrt (+ x 1))))) (sqrt (sqrt (sqrt (+ x 1)))))

simplify1.6s

Counts
234 → 234
Iterations
IterNodes
34034
21879
1798
0335

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
211
111
07

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s1788×body1280valid
463.0ms8102×body80nan
372.0ms1234×body640valid
285.0ms4068×body80valid
99.0ms607×body320valid
37.0ms303×body160valid