Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	67×	body	640	valid
11.0ms	135×	body	80	valid
7.0ms	31×	body	320	valid
5.0ms	12×	body	1280	valid
2.0ms	11×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
11	3125
10	1361
9	669
8	342
7	182
6	162
5	131
4	93
3	45
2	35
1	21
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (- x 1))
2.6b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

8.0ms	(/ 1 (+ x 1))
38.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
8.0ms	(/ 1 (- x 1))
158.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (+ x 1))
42.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
31.0ms	(/ 1 (- x 1))
104.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.5s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	2338
1	536
0	219

prune502.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
0.0b	(- (* 1 x) (* (+ x 1) 2))
0.0b	(* (* (+ x 1) x) (- x 1))
16.0b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
12×	`associate-*r/`
11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1`
8×	`associate-/r/` `add-log-exp`
7×	`associate-r` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`difference-of-squares`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `diff-log` `difference-of-sqr-1` `associate-l` `-commutative` `div-inv` `distribute-lft-out--`

Counts

4 → 130

Calls

4 calls:

115.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
8.0ms	(- (* 1 x) (* (+ x 1) 2))
42.0ms	(* (* (+ x 1) x) (- x 1))
28.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series263.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
37.0ms	(- (* 1 x) (* (+ x 1) 2))
128.0ms	(* (* (+ x 1) x) (- x 1))
3.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
1	1079
0	283

prune651.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1) x)
0.0b	(* (* (+ x 1) x) (- x 1))
0.1b	(/ 2 (* (* (+ x 1) x) (- x 1)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-*l/`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`pow1` `associate-r`
8×	`frac-times` `associate-/r/` `add-cube-cbrt`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`pow-prod-down` `associate-*r/`
3×	`cbrt-undiv` `times-frac` `div-exp` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative` `difference-of-squares`
1×	`clear-num` `associate-/r*` `frac-2neg` `difference-of-sqr-1` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 89

Calls

3 calls:

28.0ms	(* (+ x 1) x)
63.0ms	(* (* (+ x 1) x) (- x 1))
27.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (+ x 1) x)
138.0ms	(* (* (+ x 1) x) (- x 1))
88.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify2.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	3397
1	492
0	156

prune325.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1) x)
0.2b	(/ (sqrt 2) (- x 1))
0.3b	(* (/ (sqrt 2) (* (+ x 1) x)) (/ (sqrt 2) (- x 1)))
1.2b	(/ (sqrt 2) (* (+ x 1) x))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `times-frac`
57×	`add-cube-cbrt`
55×	`sqrt-prod`
51×	`associate-r`
34×	`add-cbrt-cube` `add-exp-log`
26×	`difference-of-squares`
16×	`associate-l`
13×	`difference-of-sqr-1` `distribute-lft-out--`
12×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1` `associate-/r*` `associate-/r/`
7×	`associate-*l/`
4×	`insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`frac-times` `associate-*r/` `distribute-lft-out`

Counts

4 → 210

Calls

4 calls:

29.0ms	(* (+ x 1) x)
19.0ms	(/ (sqrt 2) (- x 1))
58.0ms	(* (/ (sqrt 2) (* (+ x 1) x)) (/ (sqrt 2) (- x 1)))
13.0ms	(/ (sqrt 2) (* (+ x 1) x))

series485.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (+ x 1) x)
83.0ms	(/ (sqrt 2) (- x 1))
224.0ms	(* (/ (sqrt 2) (* (+ x 1) x)) (/ (sqrt 2) (- x 1)))
115.0ms	(/ (sqrt 2) (* (+ x 1) x))

simplify1.1s

Counts

222 → 222

Iterations

Iter	Nodes
done	5000
1	776
0	264

prune800.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	8

end0.0ms

sample2.8s

Algorithm

intervals

Results

918.0ms	1908×	body	640	valid
789.0ms	594×	body	1280	valid
488.0ms	4086×	body	80	valid
364.0ms	972×	body	320	valid
124.0ms	441×	body	160	valid