Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

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: 27.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.6b	(+ (* a c) (* b d))
26.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

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)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
37.0ms	(+ (* a c) (* b d))
86.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.0s

Counts

62 → 62

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	98	1090
1	277	1067
2	1110	951
3	4288	951
done	5000	951

prune190.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(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:

2.0ms	(+ (* 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)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a c) (* b d))
113.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.0s

Counts

96 → 96

Iterations

Useful iterations: 3 (288.0ms)

Iter	Nodes	Cost
0	116	1780
1	281	1657
2	808	1541
3	2487	1525
done	5000	1525

prune304.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(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:

2.0ms	(+ (* 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)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a c) (* b d))
113.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.0s

Counts

96 → 96

Iterations

Useful iterations: 3 (290.0ms)

Iter	Nodes	Cost
0	116	1780
1	281	1657
2	808	1541
3	2487	1525
done	5000	1525

prune319.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.4b

localize19.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (+ (* a c) (* b d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.9b	(cbrt (+ (* c c) (* d d)))
29.9b	(cbrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

12.0ms	(/ (+ (* a c) (* b d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
3.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ (+ (* a c) (* b d)) (* (fabs (cbrt (+ (* c c) (* d d)))) (sqrt (cbrt (+ (* c c) (* d d))))))
43.0ms	(sqrt (+ (* c c) (* d d)))
97.0ms	(cbrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))

simplify494.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	154	1722
1	399	1641
2	1444	1387
done	5001	1387

prune355.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.4b

regimes256.0ms

Accuracy

0.1% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch37.0ms

Steps

Iters	Range		Point
8	1.5974682383539887e+61	1.4744290377191018e+65	1.4473657936297032e+65

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	20	29
done	20	29

end0.0ms

sample496.0ms

Algorithm

intervals

Results

287.0ms

8511×

body

valid