Details

sample16.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	8
1	8
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize9.0ms

Local error

Found 1 expressions with local error:

13.8b

(/ 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))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

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

simplify1.2s

Counts

33 → 33

Iterations

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

prune178.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1))) (/ x (sqrt (+ (* x x) 1))))
0.0b	(/ x (sqrt (+ (* x x) 1)))
13.7b	(sqrt (+ (* x x) 1))
13.7b	(sqrt (+ (* x x) 1))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 162

Calls

4 calls:

65.0ms	(* (/ 1 (sqrt (+ (* x x) 1))) (/ x (sqrt (+ (* x x) 1))))
18.0ms	(/ x (sqrt (+ (* x x) 1)))
11.0ms	(sqrt (+ (* x x) 1))
7.0ms	(sqrt (+ (* x x) 1))

series297.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (/ 1 (sqrt (+ (* x x) 1))) (/ x (sqrt (+ (* x x) 1))))
119.0ms	(/ x (sqrt (+ (* x x) 1)))
53.0ms	(sqrt (+ (* x x) 1))
46.0ms	(sqrt (+ (* x x) 1))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
3	3616
2	1521
1	574
0	212

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) (* x x))
1.4b	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
11.8b	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
22.9b	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

rewrite977.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

42.0ms	(* (* x x) (* x x))
245.0ms	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
99.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
584.0ms	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* x x) (* x x))
289.0ms	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
45.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
196.0ms	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

simplify807.0ms

Counts

163 → 163

Iterations

Iter	Nodes
2	2261
1	623
0	197

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (* (* (* x x) (* x x)) x))
0.1b	(/ (/ 1 x) (* x x))
0.2b	(* (* x x) (* x x))
20.9b	(- (+ (/ 1 (* (* (* x x) (* x x)) x)) (/ 1 x)) (/ (/ 1 x) (* x x)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

282×	`pow1`
116×	`pow-prod-up`
101×	`add-exp-log`
66×	`pow-plus`
57×	`times-frac`
56×	`pow-sqr`
54×	`pow-flip`
53×	`add-cbrt-cube`
52×	`*-un-lft-identity`
51×	`prod-exp`
36×	`pow-prod-down`
35×	`pow2`
29×	`add-sqr-sqrt`
24×	`div-exp`
23×	`cbrt-unprod`
20×	`add-cube-cbrt`
17×	`div-inv`
16×	`associate-/l*`
14×	`distribute-lft-out--`
12×	`cbrt-undiv`
9×	`distribute-rgt-out` `add-log-exp`
8×	`rec-exp` `1-exp` `pow-div`
5×	`inv-pow`
4×	`insert-posit16` `distribute-lft-out` `difference-of-squares`
3×	`frac-sub`
2×	`clear-num` `associate-/r*` `frac-2neg` `diff-log`
1×	`sum-log` `sub-neg` `flip3-+` `flip3--` `swap-sqr` `associate-r` `associate-l` `frac-add` `associate--l+` `*-commutative` `flip-+` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 252

Calls

4 calls:

167.0ms	(/ 1 (* (* (* x x) (* x x)) x))
11.0ms	(/ (/ 1 x) (* x x))
26.0ms	(* (* x x) (* x x))
2.1s	(- (+ (/ 1 (* (* (* x x) (* x x)) x)) (/ 1 x)) (/ (/ 1 x) (* x x)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1 (* (* (* x x) (* x x)) x))
38.0ms	(/ (/ 1 x) (* x x))
62.0ms	(* (* x x) (* x x))
48.0ms	(- (+ (/ 1 (* (* (* x x) (* x x)) x)) (/ 1 x)) (/ (/ 1 x) (* x x)))

simplify4.3s

Counts

264 → 264

Iterations

Iter	Nodes
3	6854
2	1806
1	749
0	293

prune2.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch125.0ms

Steps

Iters	Range		Point
10	3.724243043503383e-05	335086.0623706297	370.7004599643339
8	-8222859.820370512	-1352.1675980196485	-45266.24690235777

simplify11.0ms

Iterations

Iter	Nodes
2	38
1	38
0	25

end0.0ms

sample781.0ms

Algorithm

intervals

Results

628.0ms

8000×

body

valid