Details

Time bar (total: 1.1m)

sample101.0ms

Algorithm
intervals
Results
24.0ms256×body80nan
24.0ms68×body640valid
10.0ms30×body1280valid
9.0ms123×body80valid
5.0ms26×body320valid
1.0ms9×body160valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.0b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite381.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
63.0ms
(sqrt (+ x 1.0))
30.0ms
(/ 1.0 (sqrt (+ x 1.0)))
18.0ms
(/ 1.0 (sqrt x))
191.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (+ x 1.0))
498.0ms
(/ 1.0 (sqrt (+ x 1.0)))
143.0ms
(/ 1.0 (sqrt x))
733.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify10.1s

Counts
145 → 145
Iterations
IterNodes
done5000
33847
21200
1463
0215

prune2.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 22.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
3.1b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-exp-log add-cube-cbrt add-cbrt-cube
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×associate-*r/ unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-lft-out
1×sub-neg rem-sqrt-square frac-2neg sqrt-unprod diff-log div-sub clear-num associate-/r* *-commutative div-inv
Counts
4 → 87
Calls
4 calls:
14.0ms
(sqrt (+ x 1.0))
100.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
165.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series2.6s

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ x 1.0))
1.0s
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
679.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
867.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify7.5s

Counts
99 → 99
Iterations
IterNodes
done5000
21998
1540
0191

prune2.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 22.0b

localize515.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.3b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
2.4b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite586.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-exp-log add-cbrt-cube
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r/
14×sqrt-div
11×sqrt-prod
10×*-un-lft-identity
9×associate-*r*
8×add-cube-cbrt associate-*l* pow-sqr pow-prod-up
7×flip3-+ flip-+
6×add-log-exp
4×frac-times pow-plus unswap-sqr
3×*-commutative
2×pow2 sqrt-pow1 pow1/2 swap-sqr associate-*l/
1×sub-neg flip3-- sqrt-unprod diff-log flip-- distribute-lft-out difference-of-squares
Counts
4 → 122
Calls
4 calls:
53.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
136.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
88.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
297.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
787.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
113.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
117.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
209.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify7.1s

Counts
134 → 134
Iterations
IterNodes
done5000
21429
1470
0174

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize102.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.2b
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.6b
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

rewrite785.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×pow1 *-un-lft-identity
11×add-cube-cbrt sqrt-prod
10×associate-*r*
8×frac-times associate-/r/
7×associate-*l* prod-exp cbrt-unprod
6×pow-prod-down add-log-exp
4×associate-*l/ unswap-sqr
3×cbrt-undiv times-frac div-exp associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in sqrt-unprod clear-num associate-/r* sum-log div-inv distribute-lft-out
Counts
4 → 103
Calls
4 calls:
33.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
254.0ms
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
65.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
384.0ms
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

series5.3s

Counts
4 → 12
Calls
4 calls:
332.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
1.4s
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
359.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
3.3s
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

simplify8.7s

Counts
115 → 115
Iterations
IterNodes
done5049
23231
1812
0265

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes472.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done18
118
012

end0.0ms

sample11.0s

Algorithm
intervals
Results
4.2s7895×body80nan
2.9s1098×body1280valid
1.8s1828×body640valid
1.2s4133×body80valid
211.0ms621×body320valid
68.0ms320×body160valid