Details

sample24.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	8
1	8
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize8.0ms

Local error

Found 1 expressions with local error:

17.8b

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

rewrite10.0ms

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:

10.0ms

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

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

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

simplify935.0ms

Counts

33 → 33

Iterations

Iter	Nodes
4	2726
3	839
2	333
1	149
0	69

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1)))
0.0b	(/ 1 (sqrt (+ (* x x) 1)))
17.7b	(sqrt (+ (* x x) 1))
17.7b	(sqrt (+ (* x x) 1))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
30×	`sqrt-prod`
12×	`associate-/r*`
10×	`add-exp-log`
8×	`pow1` `add-cbrt-cube` `sqrt-div`
6×	`associate-/l*`
4×	`flip3-+` `associate-/r/` `flip-+` `insert-posit16` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `div-exp` `pow-flip`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-inv`
1×	`rec-exp` `1-exp` `inv-pow`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/ x (sqrt (+ (* x x) 1)))
14.0ms	(/ 1 (sqrt (+ (* x x) 1)))
13.0ms	(sqrt (+ (* x x) 1))
8.0ms	(sqrt (+ (* x x) 1))

series235.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ x (sqrt (+ (* x x) 1)))
55.0ms	(/ 1 (sqrt (+ (* x x) 1)))
47.0ms	(sqrt (+ (* x x) 1))
52.0ms	(sqrt (+ (* x x) 1))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
4	3829
3	1615
2	706
1	336
0	172

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1)
0.1b	(* (* x x) (* x x))
2.2b	(/ x (+ (* (* x x) (* x x)) -1))
23.9b	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

rewrite254.0ms

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)
42.0ms	(* (* x x) (* x x))
32.0ms	(/ x (+ (* (* x x) (* x x)) -1))
159.0ms	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

series408.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* x x) 1)
64.0ms	(* (* x x) (* x x))
148.0ms	(/ x (+ (* (* x x) (* x x)) -1))
142.0ms	(* (/ x (+ (* (* x x) (* x x)) -1)) (- (* x x) 1))

simplify5.9s

Counts

175 → 175

Iterations

Iter	Nodes
3	9135
2	1919
1	585
0	208

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.3b	(/ 1 (* (* x x) x))
0.3b	(/ 1 (* (* x x) (* (* x x) x)))
14.4b	(- (/ 1 (* (* x x) (* (* x x) x))) (/ 1 (* (* x x) x)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

166×	`pow1`
103×	`add-exp-log`
81×	`pow-prod-up`
57×	`prod-exp`
55×	`pow-flip`
47×	`add-cbrt-cube`
45×	`pow-plus`
21×	`pow2` `pow-prod-down` `pow-sqr` `cbrt-unprod`
20×	`div-exp`
18×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `times-frac`
11×	`add-cube-cbrt`
10×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`div-inv` `distribute-lft-out--`
6×	`pow3` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-r`
2×	`clear-num` `associate-/r*` `frac-2neg` `distribute-rgt-out--` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `frac-sub` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 186

Calls

4 calls:

14.0ms	(* (* x x) x)
34.0ms	(/ 1 (* (* x x) x))
148.0ms	(/ 1 (* (* x x) (* (* x x) x)))
287.0ms	(- (/ 1 (* (* x x) (* (* x x) x))) (/ 1 (* (* x x) x)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* x x) x)
57.0ms	(/ 1 (* (* x x) x))
65.0ms	(/ 1 (* (* x x) (* (* x x) x)))
149.0ms	(- (/ 1 (* (* x x) (* (* x x) x))) (/ 1 (* (* x x) x)))

simplify5.2s

Counts

198 → 198

Iterations

Iter	Nodes
3	6309
2	1166
1	510
0	190

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch77.0ms

Steps

Iters	Range		Point
10	1.6697130628152668	4649870806659.843	402.2628134253315
7	-1114767421.731762	-13815450.6135218	-487177471.4868003

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	22

end0.0ms

sample660.0ms

Algorithm

intervals

Results

529.0ms

8000×

body

valid