Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) 1)
14.3b	(/ x (+ (* x x) 1))

rewrite41.0ms

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×	`pow1` `flip3-+` `associate-/r/` `flip-+` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 42

Calls

2 calls:

14.0ms	(+ (* x x) 1)
25.0ms	(/ x (+ (* x x) 1))

series103.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (* x x) 1)
54.0ms	(/ x (+ (* x x) 1))

simplify2.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5472
3	3084
2	699
1	209
0	81

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1)))
0.0b	(/ x (sqrt (+ (* x x) 1)))
14.3b	(sqrt (+ (* x x) 1))
14.3b	(sqrt (+ (* x x) 1))

rewrite75.0ms

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:

29.0ms	(/ 1 (sqrt (+ (* x x) 1)))
14.0ms	(/ x (sqrt (+ (* x x) 1)))
9.0ms	(sqrt (+ (* x x) 1))
18.0ms	(sqrt (+ (* x x) 1))

series239.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (sqrt (+ (* x x) 1)))
78.0ms	(/ x (sqrt (+ (* x x) 1)))
56.0ms	(sqrt (+ (* x x) 1))
55.0ms	(sqrt (+ (* x x) 1))

simplify2.2s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
3	2534
2	869
1	364
0	172

prune423.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (+ (* x x) 1) -1/2) (/ x (sqrt (+ (* x x) 1))))
0.0b	(/ x (sqrt (+ (* x x) 1)))
14.3b	(sqrt (+ (* x x) 1))
14.3b	(pow (+ (* x x) 1) -1/2)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
42×	`times-frac`
37×	`*-un-lft-identity` `add-cube-cbrt`
27×	`sqrt-prod`
24×	`associate-r`
20×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`unpow-prod-down` `unswap-sqr`
7×	`associate-l`
6×	`pow1` `associate-/r*` `sqrt-div` `prod-exp`
5×	`sqr-pow`
4×	`div-exp` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `flip3-+` `pow-exp` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative`

Counts

4 → 134

Calls

4 calls:

77.0ms	(* (pow (+ (* x x) 1) -1/2) (/ x (sqrt (+ (* x x) 1))))
14.0ms	(/ x (sqrt (+ (* x x) 1)))
12.0ms	(sqrt (+ (* x x) 1))
12.0ms	(pow (+ (* x x) 1) -1/2)

series256.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (pow (+ (* x x) 1) -1/2) (/ x (sqrt (+ (* x x) 1))))
63.0ms	(/ x (sqrt (+ (* x x) 1)))
45.0ms	(sqrt (+ (* x x) 1))
95.0ms	(pow (+ (* x x) 1) -1/2)

simplify1.4s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
2	1551
1	539
0	204

prune519.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 1 x) x) x)
0.1b	(/ (/ 1 x) x)
0.2b	(/ 1 (pow x 5))
18.9b	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ (/ (/ 1 x) x) x)))

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

492×	`times-frac`
263×	`*-un-lft-identity`
246×	`add-sqr-sqrt` `add-cube-cbrt`
59×	`associate-/l*`
37×	`add-exp-log`
28×	`div-inv`
23×	`div-exp`
20×	`add-cbrt-cube`
13×	`associate-/r*`
12×	`pow1` `unpow-prod-down`
10×	`cbrt-undiv`
9×	`add-log-exp`
7×	`distribute-lft-out`
6×	`pow-div`
5×	`rec-exp` `1-exp` `distribute-lft-out--`
4×	`frac-add` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp` `pow-flip` `inv-pow`
2×	`associate-+r+` `sum-log` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--` `sub-div`

Counts

4 → 353

Calls

4 calls:

32.0ms	(/ (/ (/ 1 x) x) x)
16.0ms	(/ (/ 1 x) x)
8.0ms	(/ 1 (pow x 5))
442.0ms	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ (/ (/ 1 x) x) x)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (/ (/ 1 x) x) x)
18.0ms	(/ (/ 1 x) x)
67.0ms	(/ 1 (pow x 5))
48.0ms	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ (/ (/ 1 x) x) x)))

simplify2.0s

Counts

365 → 365

Iterations

Iter	Nodes
done	5010
2	3014
1	1241
0	523

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes77.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.5b

bsearch61.0ms

Steps

Iters	Range		Point
8	29.100869698027953	73049.03827748532	486.478699858977
6	-8.387157242043076e+38	-1.348344988670491e+38	-7.683354923764348e+38

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample417.0ms

Algorithm

intervals

Results

325.0ms

8000×

body

valid