Details

Time bar (total: 15.9s)

sample71.0ms

Algorithm
intervals
Results
14.0ms50×body640valid
13.0ms334×body80nan
11.0ms46×body1280valid
6.0ms130×body80valid
2.0ms16×body320valid
1.0ms14×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite128.0ms

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:
7.0ms
(sqrt (+ x 1.0))
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
10.0ms
(/ 1.0 (sqrt x))
93.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ x 1.0))
103.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
217.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.8s

Counts
145 → 145
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02151942
14441778
210511698
326471673
done50001657

prune525.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.5b
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
105×times-frac
65×add-sqr-sqrt
53×add-cube-cbrt
52×sqrt-prod
35×distribute-lft-out
27×associate-/r*
13×add-exp-log add-cbrt-cube
9×div-inv
8×distribute-lft-out--
7×associate-/l*
6×add-log-exp
5×associate-/r/
4×pow1 cbrt-undiv div-exp difference-of-squares
3×frac-2neg associate-*r/ clear-num associate-/l/
2×flip3-- flip3-+ sqrt-div frac-sub flip-- flip-+
1×sub-neg diff-log frac-add prod-exp cbrt-unprod
Counts
4 → 158
Calls
4 calls:
25.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ 1.0 (sqrt x))
211.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
47.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

series787.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ 1.0 (sqrt (+ x 1.0)))
60.0ms
(/ 1.0 (sqrt x))
544.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
66.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

simplify2.0s

Counts
170 → 170
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03393045
18222803
225572592
done50022590

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
0.2b
(/ 1.0 (sqrt x))
2.4b
(- (* 1.0 (+ x 1.0)) (* x 1.0))
7.1b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite457.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
37×times-frac
32×add-exp-log add-cbrt-cube
26×add-sqr-sqrt add-cube-cbrt
24×sqrt-prod
22×associate-*r/
14×flip3-+ associate-*l* flip-+ distribute-lft-out
12×frac-times prod-exp cbrt-unprod
11×associate-/r/
9×pow1
7×cbrt-undiv div-exp associate-/r*
6×associate-*l/ frac-add add-log-exp
5×distribute-rgt-in distribute-lft-in
4×div-inv associate-/l*
3×pow-prod-down
2×flip3-- frac-2neg associate--l+ clear-num flip-- associate-/l/
1×sub-neg diff-log associate-*r* *-commutative
Counts
4 → 135
Calls
4 calls:
128.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
11.0ms
(/ 1.0 (sqrt x))
25.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
287.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
599.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
41.0ms
(/ 1.0 (sqrt x))
2.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
361.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify2.2s

Counts
147 → 147
Iterations

Useful iterations: 2 (983.0ms)

IterNodesCost
03333744
110073614
246252955
done50002955

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.6b
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
7.1b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
58×times-frac
42×add-sqr-sqrt add-cube-cbrt
40×sqrt-prod
34×add-exp-log add-cbrt-cube
20×associate-*r/
18×distribute-lft-out
15×flip3-+ flip-+
14×associate-*l* associate-/r*
13×associate-/r/
12×frac-times prod-exp cbrt-unprod
9×pow1
8×cbrt-undiv div-exp
7×associate-/l*
6×associate-*l/ frac-add
5×div-inv
4×distribute-rgt-in distribute-lft-in add-log-exp
3×frac-2neg pow-prod-down clear-num
2×sqrt-div
1×associate-*r* *-commutative
Counts
4 → 164
Calls
4 calls:
14.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
119.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
261.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 1.0 (sqrt (+ x 1.0)))
47.0ms
(/ 1.0 (sqrt x))
686.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
342.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify1.6s

Counts
176 → 176
Iterations

Useful iterations: 2 (725.0ms)

IterNodesCost
03593687
19883475
241123014
done50003014

prune404.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

regimes45.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11621
done1621

end0.0ms

sample971.0ms

Algorithm
intervals
Results
189.0ms8104×body80nan
188.0ms1894×body640valid
148.0ms1147×body1280valid
111.0ms4054×body80valid
47.0ms600×body320valid
15.0ms305×body160valid