Details

sample68.0ms

Algorithm

intervals

Results

39.0ms	90×	body	1280	valid
7.0ms	129×	body	80	valid
7.0ms	25×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	37	12
done	37	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 48

Calls

3 calls:

0.0ms	(hypot 1.0 x)
7.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series150.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(hypot 1.0 x)
10.0ms	(/ 1.0 (hypot 1.0 x))
138.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.3s

Counts

57 → 57

Iterations

Useful iterations: 3 (569.0ms)

Iter	Nodes	Cost
0	86	675
1	169	639
2	537	587
3	2794	583
done	5000	583

prune298.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

10.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(/ 1.0 (hypot 1.0 x))
61.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify899.0ms

Counts

92 → 92

Iterations

Useful iterations: done (896.0ms)

Iter	Nodes	Cost
0	109	1174
1	277	1112
2	1351	1012
done	5000	1007

prune473.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `associate--l+`
3×	`sub-neg`
2×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `flip3--` `div-exp` `associate-l/` `associate-r/` `frac-sub` `div-inv` `flip--`
1×	`diff-log`

Counts

4 → 79

Calls

4 calls:

0.0ms	(hypot 1.0 x)
8.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(/ 1.0 (hypot 1.0 x))
25.0ms	(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

series80.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
7.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
62.0ms	(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

simplify660.0ms

Counts

91 → 91

Iterations

Useful iterations: done (658.0ms)

Iter	Nodes	Cost
0	104	1033
1	253	998
2	988	916
done	5000	912

prune446.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)) (+ (* (* (/ 1.0 (hypot 1.0 x)) 0.5) (+ (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.1b	(pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)
1.6b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

194×	`associate-*r/`
104×	`frac-add`
103×	`associate-*l/`
74×	`flip3--` `associate-/r/` `flip--`
68×	`frac-times`
47×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
36×	`times-frac`
27×	`add-cube-cbrt`
21×	`sqr-pow`
20×	`difference-of-squares`
17×	`flip3-+` `flip-+`
14×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
9×	`cube-div`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
5×	`difference-cubes` `distribute-lft-out--`
4×	`frac-sub` `associate-/l/`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `pow-exp` `rem-cube-cbrt`
2×	`clear-num` `pow-pow` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `diff-log` `unpow3` `div-sub` `cube-prod` `pow-prod-down`

Counts

4 → 202

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
152.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)) (+ (* (* (/ 1.0 (hypot 1.0 x)) 0.5) (+ (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
16.0ms	(pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)
32.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3))

series436.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1.0 (hypot 1.0 x))
272.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)) (+ (* (* (/ 1.0 (hypot 1.0 x)) 0.5) (+ (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
47.0ms	(pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3)
104.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* (/ 1.0 (hypot 1.0 x)) 0.5) 3))

simplify905.0ms

Counts

214 → 214

Iterations

Useful iterations: done (884.0ms)

Iter	Nodes	Cost
0	556	13161
1	1935	12590
done	5002	12246

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

regimes194.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	104
1	41	104
done	41	104

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.7s	2906×	body	1280	valid
268.0ms	646×	body	640	valid
238.0ms	3977×	body	80	valid
60.0ms	306×	body	320	valid
19.0ms	165×	body	160	valid