Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

272×

body

valid

simplify5.0ms

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: 25.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(+ (* a c) (* b d))
25.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
33.0ms	(+ (* a c) (* b d))
83.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.5s

Counts

62 → 62

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	98	1090
1	270	1067
2	965	951
3	3914	951
done	5000	951

prune187.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(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))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts

96 → 96

Iterations

Useful iterations: 3 (490.0ms)

Iter	Nodes	Cost
0	116	1780
1	274	1649
2	768	1541
3	2269	1525
done	5001	1525

prune281.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
25.0b	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`add-sqr-sqrt` `flip3-+` `flip-+`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity` `associate-/r/`
6×	`pow1` `sqrt-prod` `add-log-exp`
4×	`frac-times`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
19.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a c) (* b d))
81.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
41.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify998.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (298.0ms)

Iter	Nodes	Cost
0	112	1662
1	294	1304
2	875	1142
3	2570	1110
done	5000	1110

prune242.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.6b

localize14.0ms

Local error

Found 4 expressions with local error:

16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify841.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (265.0ms)

Iter	Nodes	Cost
0	105	1833
1	244	1680
2	660	1570
3	1922	1548
done	5000	1548

prune325.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

regimes151.0ms

Accuracy

0% (2.9b remaining)

Error of 26.4b against oracle of 23.5b and baseline of 26.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	17	25
done	17	25

end0.0ms

sample528.0ms

Algorithm

intervals

Results

294.0ms

8482×

body

valid