Details

sample90.0ms

Algorithm

intervals

Results

54.0ms	91×	body	1280	valid
10.0ms	131×	body	80	valid
7.0ms	21×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	90
5	90
4	71
3	55
2	39
1	21
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
1.7b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `sqrt-prod` `insert-posit16` `difference-of-squares`
3×	`associate-/r` `associate-/l` `distribute-lft-out--`
2×	`distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 69

Calls

4 calls:

0.0ms	(hypot 1 x)
19.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
9.0ms	(/ 1/2 (hypot 1 x))
91.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1 x)
44.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
11.0ms	(/ 1/2 (hypot 1 x))
85.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
3	2090
2	703
1	234
0	107

prune358.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
1.2b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
11×	`flip3-+` `flip-+` `add-log-exp`
10×	`pow1` `sqrt-div`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-l` `sqrt-prod`
6×	`distribute-lft-out`
4×	`frac-times` `associate-r` `frac-add` `insert-posit16`
3×	`associate-/r` `sum-log` `distribute-rgt-out` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `pow-prod-up` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `sub-neg` `frac-2neg` `distribute-lft1-in` `flip3--` `diff-log` `cube-unmult` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--`

Counts

4 → 107

Calls

4 calls:

10.0ms	(/ 1/2 (hypot 1 x))
146.0ms	(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
142.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
15.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1/2 (hypot 1 x))
84.0ms	(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
124.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
123.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify2.2s

Counts

119 → 119

Iterations

Iter	Nodes
done	5004
2	2138
1	498
0	187

prune676.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.2b	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
1.2b	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2))
1.2b	(- 1 (/ (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) 1/8)) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`times-frac`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
5×	`div-inv`
4×	`insert-posit16` `unswap-sqr`
3×	`associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`pow2` `frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `distribute-rgt-out--` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `-commutative` `pow-prod-up` `distribute-lft-out--`

Counts

4 → 122

Calls

4 calls:

31.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
27.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
8.0ms	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2))
166.0ms	(- 1 (/ (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) 1/8)) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2)))))

series765.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
39.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
54.0ms	(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2))
638.0ms	(- 1 (/ (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))) 1/8)) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2)))))

simplify2.2s

Counts

134 → 134

Iterations

Iter	Nodes
done	5015
2	2968
1	731
0	240

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.5b	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
1.2b	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite632.0ms

Algorithm

rewrite-expression-head

Rules

264×	`sqrt-div`
144×	`frac-times`
134×	`sqrt-pow1`
129×	`pow1`
120×	`flip3-+` `flip-+`
63×	`pow-prod-up`
48×	`associate-l/` `associate-r/`
46×	`pow1/2`
37×	`pow-plus`
33×	`add-sqr-sqrt`
31×	`pow-prod-down`
23×	`*-un-lft-identity`
18×	`associate-l`
15×	`pow-sqr`
14×	`add-cube-cbrt` `sqrt-prod`
12×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
8×	`cube-unmult`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`swap-sqr` `insert-posit16` `distribute-lft-out`
3×	`prod-exp` `*-commutative` `cbrt-unprod`
2×	`distribute-rgt-in` `distribute-lft-in` `difference-of-squares`
1×	`pow2` `sub-neg` `rem-square-sqrt` `flip3--` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 260

Calls

4 calls:

140.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
142.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
309.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
10.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
79.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
113.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
97.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

simplify2.3s

Counts

272 → 272

Iterations

Iter	Nodes
done	5001
2	1668
1	616
0	305

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.7b

regimes88.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	2892×	body	1280	valid
373.0ms	3996×	body	80	valid
186.0ms	639×	body	640	valid
62.0ms	320×	body	320	valid
23.0ms	153×	body	160	valid