Details

sample72.0ms

Algorithm

intervals

Results

36.0ms	94×	body	1280	valid
9.0ms	131×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	24
1	19
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize24.0ms

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))))))

rewrite11.0ms

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)
9.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series141.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(hypot 1.0 x)
139.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.0s

Counts

27 → 27

Iterations

Iter	Nodes
done	5002
4	3468
3	834
2	259
1	96
0	50

prune157.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.3b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite659.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
18×	`associate-*l/`
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×	`add-log-exp`
6×	`sqrt-pow1` `sqrt-div` `associate-*r/` `associate-/r/` `pow-prod-up`
4×	`frac-times` `associate-l` `frac-add`
3×	`associate-/r` `pow-plus` `pow1/2` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`flip3--` `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 → 96

Calls

4 calls:

112.0ms	(* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))
24.0ms	(+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0)
405.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))
114.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

series1.0s

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))
105.0ms	(+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0)
551.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))
177.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

simplify3.0s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	2951
1	630
0	203

prune788.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.3b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

90×	`sqrt-prod`
72×	`add-sqr-sqrt`
51×	`times-frac`
44×	`*-un-lft-identity` `add-cube-cbrt`
30×	`associate-/r/`
25×	`flip3-+` `flip-+`
24×	`swap-sqr`
22×	`associate-r` `associate-l`
21×	`associate-l/` `associate-r/`
20×	`frac-add`
19×	`pow1`
9×	`unswap-sqr`
8×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `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` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

389.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))
1.3s	(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))))
157.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))
121.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

series1.5s

Counts

4 → 12

Calls

4 calls:

526.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))
483.0ms	(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 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) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))))
195.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))
253.0ms	(- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)))

simplify3.1s

Counts

177 → 177

Iterations

Iter	Nodes
done	5004
2	3086
1	733
0	289

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 13.3b

regimes257.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2942×	body	1280	valid
627.0ms	623×	body	640	valid
295.0ms	3991×	body	80	valid
163.0ms	302×	body	320	valid
59.0ms	142×	body	160	valid