Details

sample60.0ms

Algorithm

intervals

Results

25.0ms	76×	body	1280	valid
8.0ms	28×	body	640	valid
8.0ms	136×	body	80	valid
2.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

9.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
51.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
14.0ms	(/ 1.0 (hypot 1.0 x))
154.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify694.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	842
1	238
0	112

prune337.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b	(- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`distribute-lft-out`
4×	`pow1` `flip3--` `associate--l+` `associate-*r/` `frac-sub` `flip--` `associate-/l/`
3×	`sub-neg`
2×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`+-commutative` `sum-log` `diff-log` `div-sub`

Counts

4 → 95

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
52.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
22.0ms	(- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
134.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
230.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
49.0ms	(- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x)))

simplify1.1s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1903
1	450
0	174

prune624.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
1.3b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0)))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
48×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-*l/`
14×	`associate-/r/`
12×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
11×	`distribute-lft-out`
8×	`frac-sub` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
6×	`flip3--` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`div-sub`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log`

Counts

4 → 127

Calls

4 calls:

8.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
124.0ms	(/ (/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
189.0ms	(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
77.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
284.0ms	(/ (/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
90.0ms	(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
61.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (* 1.0 (hypot 1.0 x))) (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) (* 0.5 1.0)))

simplify512.0ms

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
1	818
0	251

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))
1.2b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0))))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

422×	`times-frac`
249×	`*-un-lft-identity`
241×	`add-sqr-sqrt`
205×	`add-cube-cbrt`
61×	`associate-*r/`
45×	`add-cbrt-cube` `add-exp-log`
44×	`swap-sqr` `associate-r` `associate-l`
26×	`associate-/r/`
24×	`flip3--` `frac-sub` `flip--`
22×	`div-inv` `distribute-lft-out`
21×	`frac-times` `cbrt-undiv` `div-exp`
20×	`associate-/l*`
16×	`difference-of-squares`
15×	`associate-*l/`
11×	`pow1`
10×	`frac-add`
9×	`prod-exp` `cbrt-unprod` `unswap-sqr`
8×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-log-exp`
7×	`flip3-+` `flip-+`
5×	`sub-neg`
4×	`associate-/r*`
2×	`div-sub`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `associate-/l/`

Counts

4 → 354

Calls

4 calls:

270.0ms	(/ (/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
8.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
72.0ms	(* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))
93.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
98.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
47.0ms	(* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))
76.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (/ 0.5 (/ (hypot 1.0 x) 1.0)) (/ 0.5 (/ (hypot 1.0 x) 1.0))))

simplify1.2s

Counts

366 → 366

Iterations

Iter	Nodes
done	5001
1	2516
0	704

prune2.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.7b

regimes172.0ms

Accuracy

0% (0.4b remaining)

Error of 15.8b against oracle of 15.3b and baseline of 15.8b

bsearch0.0ms

simplify31.0ms

Iterations

Iter	Nodes
done	62
3	62
2	60
1	58
0	42

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	2806×	body	1280	valid
325.0ms	664×	body	640	valid
274.0ms	4038×	body	80	valid
58.0ms	342×	body	320	valid
16.0ms	150×	body	160	valid