Details

Time bar (total: 7.3s)

sample101.0ms

Algorithm
intervals
Results
58.0ms271×body80nan
10.0ms54×body1280valid
7.0ms50×body640valid
5.0ms125×body80valid
2.0ms20×body320valid
1.0ms7×body160valid

simplify1.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite86.0ms

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:
26.0ms
(sqrt (+ x 1.0))
58.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series160.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(sqrt (+ x 1.0))
107.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify114.0ms

Counts
41 → 41

prune94.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite126.0ms

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:
9.0ms
(sqrt (+ x 1.0))
40.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
74.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series313.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(sqrt (+ x 1.0))
81.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
189.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify104.0ms

Counts
80 → 80

prune244.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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

rewrite398.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
74×*-un-lft-identity
32×distribute-lft-out
30×add-sqr-sqrt
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×swap-sqr
14×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/
5×pow-prod-up
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×times-frac pow-prod-down pow-sqr associate-/l*
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 135
Calls
4 calls:
63.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
65.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
187.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
233.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
150.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
70.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify61.0ms

Counts
147 → 147

prune453.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite459.0ms

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:
71.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
76.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
69.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
224.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series992.0ms

Counts
4 → 12
Calls
4 calls:
499.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
172.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify92.0ms

Counts
262 → 262

prune761.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

46.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify305.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
620.0ms1684×body1280valid
294.0ms8052×body80nan
173.0ms1267×body640valid
148.0ms4041×body80valid
82.0ms679×body320valid
17.0ms329×body160valid