Details

sample32.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	7
1	7
0	5

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) 1)
17.5b	(/ x (+ (* x x) 1))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 45

Calls

2 calls:

12.0ms	(+ (* x x) 1)
20.0ms	(/ x (+ (* x x) 1))

series138.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(+ (* x x) 1)
78.0ms	(/ x (+ (* x x) 1))

simplify2.9s

Counts

51 → 51

Iterations

Iter	Nodes
4	4186
3	1463
2	538
1	189
0	83

prune375.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
17.5b	(sqrt (+ (* x x) 1))
17.5b	(sqrt (+ (* x x) 1))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
166×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
162×	`add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `hypot-def` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 274

Calls

4 calls:

15.0ms	(/ x (sqrt (+ (* x x) 1)))
32.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
10.0ms	(sqrt (+ (* x x) 1))
13.0ms	(sqrt (+ (* x x) 1))

series222.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ x (sqrt (+ (* x x) 1)))
59.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
44.0ms	(sqrt (+ (* x x) 1))
38.0ms	(sqrt (+ (* x x) 1))

simplify2.4s

Counts

286 → 286

Iterations

Iter	Nodes
3	5112
2	1591
1	731
0	324

prune2.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1)
0.1b	(fma (* x x) (* x x) -1)
2.9b	(/ x (fma (* x x) (* x x) -1))
22.6b	(* (/ x (fma (* x x) (* x x) -1)) (- (* x x) 1))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
19×	`times-frac`
14×	`add-exp-log`
13×	`associate-l`
11×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1` `associate-r` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `sub-neg` `flip3--` `prod-exp` `flip--` `associate-/l`
2×	`frac-times` `cbrt-undiv` `expm1-def` `difference-of-sqr-1` `div-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 113

Calls

4 calls:

12.0ms	(- (* x x) 1)
0.0ms	(fma (* x x) (* x x) -1)
6.0ms	(/ x (fma (* x x) (* x x) -1))
35.0ms	(* (/ x (fma (* x x) (* x x) -1)) (- (* x x) 1))

series526.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* x x) 1)
163.0ms	(fma (* x x) (* x x) -1)
174.0ms	(/ x (fma (* x x) (* x x) -1))
130.0ms	(* (/ x (fma (* x x) (* x x) -1)) (- (* x x) 1))

simplify6.2s

Counts

125 → 125

Iterations

Iter	Nodes
3	4945
2	1315
1	482
0	184

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (* x (* (* x x) (* x x))))
0.1b	(/ (/ 1 x) x)
0.1b	(* (* x x) (* x x))
17.9b	(+ (- (/ 1 x) (/ (/ (/ 1 x) x) x)) (/ 1 (* x (* (* x x) (* x x)))))

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

5579×	`times-frac`
2985×	`add-sqr-sqrt`
2957×	`*-un-lft-identity`
2919×	`add-cube-cbrt`
1731×	`associate-+l+`
1729×	`prod-diff`
325×	`div-inv`
215×	`pow1`
88×	`add-exp-log`
86×	`pow-prod-up`
47×	`prod-exp`
46×	`add-cbrt-cube`
38×	`pow-sqr`
36×	`pow-prod-down`
30×	`pow-plus`
29×	`fma-def` `pow-flip`
23×	`pow2`
21×	`cbrt-unprod`
18×	`div-exp` `difference-of-squares`
16×	`associate-/l*`
9×	`cbrt-undiv` `distribute-lft-out` `distribute-lft-out--` `add-log-exp`
7×	`rec-exp` `1-exp`
6×	`distribute-rgt-out--`
4×	`expm1-log1p-u` `associate-/r*` `frac-add` `log1p-expm1-u`
2×	`clear-num` `sum-log` `frac-2neg` `inv-pow` `pow-div`
1×	`+-commutative` `sub-neg` `flip3-+` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `*-commutative` `frac-sub` `associate-+l-` `flip-+` `flip--` `sub-div` `unswap-sqr` `associate-/l/`

Counts

4 → 2001

Calls

4 calls:

152.0ms	(/ 1 (* x (* (* x x) (* x x))))
16.0ms	(/ (/ 1 x) x)
40.0ms	(* (* x x) (* x x))
166.0ms	(+ (- (/ 1 x) (/ (/ (/ 1 x) x) x)) (/ 1 (* x (* (* x x) (* x x)))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (* x (* (* x x) (* x x))))
30.0ms	(/ (/ 1 x) x)
66.0ms	(* (* x x) (* x x))
93.0ms	(+ (- (/ 1 x) (/ (/ (/ 1 x) x) x)) (/ 1 (* x (* (* x x) (* x x)))))

simplify2.0s

Counts

2013 → 2013

Iterations

Iter	Nodes
1	2763
0	1019

prune29.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch80.0ms

Steps

Iters	Range		Point
8	0.9676876931049737	32461.898498684495	580.2919375789389
6	-6889706126056.061	-1067456184327.3741	-6258382897202.597

simplify9.0ms

Iterations

Iter	Nodes
2	28
1	28
0	22

end0.0ms

sample717.0ms

Algorithm

intervals

Results

601.0ms

8000×

body

valid