Details

sample27.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 1 expressions with local error:

14.1b

(/ x (+ (* x x) 1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

21.0ms

(/ x (+ (* x x) 1))

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

(/ x (+ (* x x) 1))

simplify1.1s

Counts

33 → 33

Iterations

Iter	Nodes
done	2011
3	2011
2	562
1	163
0	69

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1)
0.1b	(* (* x x) (* x x))
1.2b	(/ x (+ (* (* x x) (* x x)) -1))
18.8b	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
29×	`add-sqr-sqrt`
25×	`times-frac`
24×	`*-un-lft-identity` `pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr` `add-cube-cbrt`
19×	`associate-l`
18×	`pow-plus`
13×	`pow2`
10×	`prod-exp` `cbrt-unprod`
7×	`difference-of-sqr--1` `associate-r`
6×	`add-log-exp`
4×	`associate-/r*` `associate-/r/` `insert-posit16` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--` `associate-/l*` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `distribute-lft-in` `flip3-+` `difference-of-sqr-1` `div-exp` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`clear-num` `frac-2neg` `diff-log` `swap-sqr` `associate-*l/`

Counts

4 → 163

Calls

4 calls:

15.0ms	(- (* x x) 1)
46.0ms	(* (* x x) (* x x))
68.0ms	(/ x (+ (* (* x x) (* x x)) -1))
154.0ms	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

series398.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x x) 1)
61.0ms	(* (* x x) (* x x))
181.0ms	(/ x (+ (* (* x x) (* x x)) -1))
103.0ms	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

simplify1.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	2003
2	2003
1	634
0	208

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (+ (* x x) 1))
13.5b	(* (/ 1 (+ (* x x) 1)) (* (/ x (- (* x x) 1)) (- (* x x) 1)))
14.1b	(/ x (- (* x x) 1))
14.1b	(* (/ x (- (* x x) 1)) (- (* x x) 1))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

55×	`times-frac`
54×	`add-sqr-sqrt` `add-exp-log`
49×	`*-un-lft-identity`
41×	`add-cube-cbrt`
39×	`associate-l`
34×	`add-cbrt-cube`
22×	`prod-exp`
16×	`difference-of-squares`
14×	`div-exp`
12×	`pow1` `cbrt-unprod`
11×	`frac-times` `associate-*r/`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-/r*`
8×	`cbrt-undiv` `flip3--` `difference-of-sqr-1` `associate-/r/` `flip--`
7×	`associate-r`
6×	`sub-neg` `associate-/l*`
4×	`rec-exp` `1-exp` `pow-prod-down` `associate-*l/` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 195

Calls

4 calls:

13.0ms	(/ 1 (+ (* x x) 1))
179.0ms	(* (/ 1 (+ (* x x) 1)) (* (/ x (- (* x x) 1)) (- (* x x) 1)))
13.0ms	(/ x (- (* x x) 1))
70.0ms	(* (/ x (- (* x x) 1)) (- (* x x) 1))

series176.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (+ (* x x) 1))
57.0ms	(* (/ 1 (+ (* x x) 1)) (* (/ x (- (* x x) 1)) (- (* x x) 1)))
68.0ms	(/ x (- (* x x) 1))
17.0ms	(* (/ x (- (* x x) 1)) (- (* x x) 1))

simplify1.3s

Counts

207 → 207

Iterations

Iter	Nodes
done	2001
2	2001
1	816
0	270

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ (/ 1 x) (* x x)))
0.1b	(/ (/ 1 x) (* x x))
0.1b	(/ 1 (pow x 5))
19.0b	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (pow x 5)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
65×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
35×	`add-exp-log`
34×	`add-cube-cbrt`
18×	`pow1` `add-cbrt-cube` `div-exp`
16×	`associate-/l*`
12×	`unpow-prod-down` `difference-of-squares`
11×	`add-log-exp`
10×	`div-inv`
8×	`associate-/r*` `pow-div`
7×	`cbrt-undiv`
6×	`distribute-lft-out` `distribute-lft-out--`
5×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
4×	`prod-exp` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `frac-add` `pow-exp`
2×	`pow2` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `pow-sqr` `pow-prod-up` `frac-sub` `cbrt-unprod` `flip--`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

22.0ms	(- (/ 1 x) (/ (/ 1 x) (* x x)))
23.0ms	(/ (/ 1 x) (* x x))
12.0ms	(/ 1 (pow x 5))
106.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (pow x 5)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (/ 1 x) (/ (/ 1 x) (* x x)))
43.0ms	(/ (/ 1 x) (* x x))
69.0ms	(/ 1 (pow x 5))
54.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (pow x 5)))

simplify1.3s

Counts

178 → 178

Iterations

Iter	Nodes
done	2001
3	2001
2	1694
1	589
0	263

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.0b

bsearch118.0ms

Steps

Iters	Range		Point
10	186.95626557948964	3373396396890550.5	8137.871959944802
9	-265991755648.13324	-24078.920296370652	-484064.81338059285

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end0.0ms

sample1.0s

Algorithm

intervals

Results

888.0ms

8000×

body

valid