Details

sample29.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	6
1	6
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize21.0ms

Local error

Found 1 expressions with local error:

16.6b

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

rewrite21.0ms

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:

20.0ms

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

series76.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

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

simplify1.2s

Counts

33 → 33

Iterations

Iter	Nodes
4	2810
3	858
2	333
1	147
0	69

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1)))
16.6b	(sqrt (+ (* x x) 1))
16.6b	(sqrt (+ (* x x) 1))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*` `sqrt-div`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 74

Calls

3 calls:

16.0ms	(/ x (sqrt (+ (* x x) 1)))
14.0ms	(sqrt (+ (* x x) 1))
12.0ms	(sqrt (+ (* x x) 1))

series181.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ x (sqrt (+ (* x x) 1)))
55.0ms	(sqrt (+ (* x x) 1))
34.0ms	(sqrt (+ (* x x) 1))

simplify2.8s

Counts

83 → 83

Iterations

Iter	Nodes
4	3191
3	1219
2	517
1	235
0	119

prune776.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1)))
0.1b	(* x (/ 1 (sqrt (+ (* x x) 1))))
16.6b	(sqrt (+ (* x x) 1))
16.6b	(sqrt (+ (* x x) 1))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
29×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
8×	`sqrt-div`
6×	`associate-/r*`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+` `insert-posit16` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `associate-l` `pow-flip` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 130

Calls

4 calls:

24.0ms	(/ 1 (sqrt (+ (* x x) 1)))
29.0ms	(* x (/ 1 (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))
12.0ms	(sqrt (+ (* x x) 1))

series226.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (sqrt (+ (* x x) 1)))
80.0ms	(* x (/ 1 (sqrt (+ (* x x) 1))))
37.0ms	(sqrt (+ (* x x) 1))
60.0ms	(sqrt (+ (* x x) 1))

simplify3.7s

Counts

142 → 142

Iterations

Iter	Nodes
3	2640
2	995
1	413
0	170

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ (/ 1 x) (* x x))
0.3b	(/ 1 (* (* (* x x) x) (* x x)))
19.2b	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

160×	`pow1`
104×	`add-exp-log`
77×	`pow-prod-up`
52×	`prod-exp`
50×	`add-cbrt-cube`
47×	`pow-flip`
41×	`pow-plus`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`div-exp`
22×	`add-sqr-sqrt`
21×	`pow2` `pow-sqr` `add-cube-cbrt`
20×	`cbrt-unprod`
18×	`pow-prod-down`
16×	`associate-/l*`
13×	`cbrt-undiv`
9×	`rec-exp` `1-exp` `div-inv` `add-log-exp`
8×	`pow-div`
6×	`distribute-lft-out`
5×	`pow3` `inv-pow`
4×	`insert-posit16` `distribute-lft-out--`
3×	`associate-r` `frac-add`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg`
1×	`+-commutative` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-l` `*-commutative` `frac-sub` `associate-+l-` `flip-+` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

15.0ms	(* (* x x) x)
14.0ms	(/ (/ 1 x) (* x x))
162.0ms	(/ 1 (* (* (* x x) x) (* x x)))
158.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) x)
65.0ms	(/ (/ 1 x) (* x x))
62.0ms	(/ 1 (* (* (* x x) x) (* x x)))
42.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

simplify1.2s

Counts

215 → 215

Iterations

Iter	Nodes
2	2116
1	705
0	269

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.4b

bsearch101.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	393.77334187402573
10	-9.857583095580377e+159	-1.0895875309198726e+143	-1.3765989384353292e+154

simplify14.0ms

Iterations

Iter	Nodes
2	29
1	29
0	21

end0.0ms

sample690.0ms

Algorithm

intervals

Results

546.0ms

8000×

body

valid