Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

277×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* a c) (* b d))
24.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite15.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify818.0ms

Counts

48 → 48

Iterations

Useful iterations: 3 (235.0ms)

Iter	Nodes	Cost
0	85	924
1	242	906
2	754	824
3	2254	820
done	5000	820

prune144.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
15.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* a c) (* b d))
12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a c) (* b d))
106.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify795.0ms

Counts

96 → 96

Iterations

Useful iterations: 3 (240.0ms)

Iter	Nodes	Cost
0	116	1780
1	281	1657
2	781	1543
3	2148	1527
done	5000	1527

prune302.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
15.4b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* c c) (* d d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

14.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
10.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b))))
75.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* d b)))
33.0ms	(sqrt (+ (* c c) (* d d)))
220.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.5s

Counts

205 → 205

Iterations

Useful iterations: 3 (898.0ms)

Iter	Nodes	Cost
0	242	5680
1	586	5184
2	1827	4723
3	4728	4665
done	5000	4665

prune445.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 1 (/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))))
15.3b	(/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))
28.1b	(sqrt (+ (* c c) (* d d)))
28.1b	(sqrt (+ (* d d) (* c c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

753×	`times-frac`
357×	`add-sqr-sqrt`
355×	`add-cube-cbrt` `*-un-lft-identity`
126×	`sqrt-prod`
83×	`associate-/r*`
49×	`add-exp-log`
36×	`div-exp`
31×	`associate-/r/`
30×	`sqrt-div`
18×	`div-inv`
16×	`flip3-+` `flip-+`
15×	`add-cbrt-cube`
13×	`rec-exp` `1-exp`
8×	`pow1`
7×	`cbrt-undiv`
6×	`associate-/l*`
4×	`pow-flip` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/` `inv-pow`
1×	`remove-double-div`

Counts

4 → 424

Calls

4 calls:

28.0ms	(/ 1 (/ 1 (/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))))
12.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* d d) (* c c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ 1 (/ 1 (/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))))
85.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* d d) (* c c))))
37.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* d d) (* c c)))

simplify2.9s

Counts

436 → 436

Iterations

Useful iterations: 2 (597.0ms)

Iter	Nodes	Cost
0	639	15435
1	1507	13220
2	4510	10961
done	5000	10961

prune608.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.1b

regimes229.0ms

Accuracy

1% (3.6b remaining)

Error of 25.8b against oracle of 22.2b and baseline of 25.8b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	30	56
done	30	56

end0.0ms

sample477.0ms

Algorithm

intervals

Results

278.0ms

8488×

body

valid