Details

Time bar (total: 15.1s)

sample81.0ms

Algorithm
intervals
Results
17.0ms67×body640valid
16.0ms312×body80nan
10.0ms30×body1280valid
9.0ms123×body80valid
5.0ms28×body320valid
1.0ms8×body160valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite150.0ms

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-cbrt-cube add-exp-log distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
11.0ms
(sqrt (+ x 1.0))
22.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
99.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (+ x 1.0))
107.0ms
(/ 1.0 (sqrt (+ x 1.0)))
43.0ms
(/ 1.0 (sqrt x))
178.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts
145 → 145
Iterations
IterNodes
done5002
33464
21158
1462
0216

prune786.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.4b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-cbrt-cube add-exp-log add-cube-cbrt
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/ cbrt-unprod flip-- distribute-lft-out associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 87
Calls
4 calls:
5.0ms
(sqrt (+ x 1.0))
59.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
34.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
15.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series658.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
392.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
82.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
148.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.9s

Counts
99 → 99
Iterations
IterNodes
done5001
21997
1545
0193

prune618.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 22.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
1.7b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-cbrt-cube add-exp-log
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×associate-*l* pow-sqr pow-prod-up add-cube-cbrt
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:
52.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
45.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
82.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series176.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
70.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
30.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
19.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.4s

Counts
134 → 134
Iterations
IterNodes
done5001
21411
1458
0172

prune579.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
40×add-sqr-sqrt
35×*-un-lft-identity
31×add-cube-cbrt
20×add-cbrt-cube add-exp-log
18×associate-/l*
15×sqrt-prod
9×pow1
8×associate-/r/
7×cbrt-undiv div-exp associate-*r*
6×flip3-+ sqrt-div associate-*l* flip-+
4×associate-/r* associate-*r/ div-inv add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg distribute-lft-out
1×rem-sqrt-square sqrt-unprod *-commutative associate-/l/
Counts
4 → 130
Calls
4 calls:
5.0ms
(sqrt (+ x 1.0))
17.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
58.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (+ x 1.0))
201.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
630.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.9s

Counts
142 → 142
Iterations
IterNodes
done5004
22680
1767
0282

prune715.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done21
121
013

end0.0ms

sample1.7s

Algorithm
intervals
Results
447.0ms7998×body80nan
377.0ms669×body320valid
280.0ms1817×body640valid
220.0ms4129×body80valid
190.0ms1102×body1280valid
19.0ms283×body160valid