Details

sample45.0ms

Algorithm

intervals

Results

21.0ms	86×	body	1280	valid
5.0ms	130×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite49.0ms

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-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
94.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
128.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify592.0ms

Counts

78 → 78

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	112	1034
1	238	951
2	839	887
done	5001	885

prune287.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(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))))))
2.3b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
16.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
136.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
107.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
54.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts

78 → 78

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	130	1119
1	327	1028
2	1567	946
done	5000	941

prune271.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(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))))))
2.3b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
9×	`add-sqr-sqrt`
7×	`pow1`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `associate-*r/` `sum-log` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

12.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
21.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
131.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
119.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
63.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify535.0ms

Counts

64 → 64

Iterations

Useful iterations: done (533.0ms)

Iter	Nodes	Cost
0	100	929
1	239	860
2	959	784
done	5000	782

prune185.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize33.0ms

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 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
2.2b	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite588.0ms

Algorithm

rewrite-expression-head

Rules

287×	`add-sqr-sqrt`
157×	`times-frac`
120×	`difference-of-squares`
109×	`*-un-lft-identity`
103×	`unpow-prod-down` `cube-prod`
57×	`add-cube-cbrt`
51×	`sqr-pow`
33×	`associate-/l*`
25×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/` `rem-cube-cbrt`
1×	`+-commutative` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `sum-log` `distribute-lft-out`

Counts

4 → 252

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
484.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
10.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
59.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series524.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
272.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
45.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
84.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify2.7s

Counts

264 → 264

Iterations

Useful iterations: 2 (843.0ms)

Iter	Nodes	Cost
0	330	10160
1	983	9725
2	4393	9449
done	5001	9449

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

regimes277.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	36
1	20	36
done	20	36

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	2812×	body	1280	valid
278.0ms	660×	body	640	valid
251.0ms	4036×	body	80	valid
61.0ms	332×	body	320	valid
20.0ms	160×	body	160	valid