Details

sample38.0ms

Algorithm

intervals

Results

19.0ms	94×	body	1280	valid
5.0ms	131×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
6	37
5	35
4	30
3	28
2	24
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot 1.0 x)
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 21

Calls

2 calls:

0.0ms	(hypot 1.0 x)
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series117.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(hypot 1.0 x)
115.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

27 → 27

Iterations

Iter	Nodes
done	5000
3	1468
2	296
1	96
0	50

prune132.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
0.0b	(* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
0.0b	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
1.0b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
91.0ms	(* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
341.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
98.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

series906.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
195.0ms	(* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
439.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
167.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

simplify3.1s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	4481
1	674
0	220

prune740.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.3b

localize96.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
0.0b	(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))))
1.0b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
1.0b	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

90×	`sqrt-prod`
72×	`add-sqr-sqrt`
51×	`times-frac`
44×	`*-un-lft-identity` `add-cube-cbrt`
41×	`associate-*r/`
30×	`associate-/r/`
25×	`flip3-+` `flip-+`
24×	`swap-sqr`
22×	`associate-r` `associate-l`
20×	`frac-add`
19×	`pow1`
9×	`unswap-sqr`
8×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate--r+` `add-log-exp`
5×	`pow-prod-up` `div-inv`
4×	`sqrt-div`
3×	`associate-/r` `flip3--` `pow-prod-down` `pow-sqr` `flip--` `associate-/l`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `div-exp` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`

Counts

4 → 173

Calls

4 calls:

439.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
1.1s	(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))))
135.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
141.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

466.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
525.0ms	(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))))
246.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
225.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

simplify2.4s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
1	782
0	299

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 13.3b

regimes335.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2942×	body	1280	valid
712.0ms	3991×	body	80	valid
157.0ms	623×	body	640	valid
52.0ms	302×	body	320	valid
25.0ms	142×	body	160	valid