Details

sample32.0ms

Algorithm

intervals

Results

17.0ms

269×

body

valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	70	15
done	70	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
24.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

9.0ms	(- (* b c) (* a d))
29.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (* b c) (* a d))
133.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.2s

Counts

50 → 50

Iterations

Useful iterations: 3 (684.0ms)

Iter	Nodes	Cost
0	88	954
1	252	936
2	857	854
3	2867	850
done	5000	850

prune190.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.1b	(sqrt (+ (* c c) (* d d)))
30.1b	(sqrt (+ (* c c) (* d d)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

20.0ms	(- (* b c) (* a d))
51.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b c) (* a d))
162.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
51.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (689.0ms)

Iter	Nodes	Cost
0	120	1814
1	306	1682
2	888	1574
3	2547	1558
done	5000	1558

prune417.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.1b	(sqrt (+ (* c c) (* d d)))
30.1b	(sqrt (+ (* c c) (* d d)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (* b c) (* a d))
53.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b c) (* a d))
175.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts

98 → 98

Iterations

Useful iterations: 3 (552.0ms)

Iter	Nodes	Cost
0	120	1814
1	306	1682
2	888	1574
3	2547	1558
done	5000	1558

prune434.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
0.7b	(- (* b c) (* a d))
24.1b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `pow-flip` `flip3-+` `diff-log` `flip-+` `inv-pow`

Counts

3 → 127

Calls

3 calls:

31.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
9.0ms	(- (* b c) (* a d))
42.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series340.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
62.0ms	(- (* b c) (* a d))
91.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify2.3s

Counts

136 → 136

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	194	3518
1	466	3269
2	1207	2998
3	4084	2962
done	5001	2962

prune639.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.1b

regimes268.0ms

Accuracy

24.6% (2.5b remaining)

Error of 25.3b against oracle of 22.8b and baseline of 26.1b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	43
1	19	43
done	19	43

end0.0ms

sample1.0s

Algorithm

intervals

Results

583.0ms

8494×

body

valid