Details

sample37.0ms

Algorithm

intervals

Results

16.0ms

283×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

10.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(+ (* a c) (* b d))
109.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	4513
2	925
1	235
0	83

prune301.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.7b	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 264

Calls

4 calls:

62.0ms	(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
33.0ms	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
162.0ms	(/ (+ (* b d) (* a c)) (sqrt (+ (* c c) (* d d))))
52.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
2	3738
1	755
0	302

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.5b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* d b) (* a c))
0.7b	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
24.4b	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

834×	`times-frac`
380×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
144×	`sqrt-prod`
49×	`associate-/r/`
41×	`div-inv`
27×	`add-exp-log`
26×	`flip3-+` `flip-+`
25×	`associate-/l*`
18×	`associate-/r*`
17×	`add-cbrt-cube` `div-exp`
9×	`cbrt-undiv`
5×	`add-log-exp`
3×	`pow1` `associate-/l/`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`+-commutative` `sum-log`

Counts

3 → 433

Calls

3 calls:

6.0ms	(+ (* d b) (* a c))
41.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
41.0ms	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* d b) (* a c))
160.0ms	(/ (/ 1 (sqrt 1)) (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
76.0ms	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

simplify1.7s

Counts

442 → 442

Iterations

Iter	Nodes
done	5000
1	2250
0	623

prune567.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))))
14.7b	(/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
49×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
45×	`add-exp-log`
36×	`sqrt-prod`
28×	`associate-/l*`
27×	`add-cbrt-cube`
23×	`div-exp`
12×	`cbrt-undiv`
10×	`sqrt-div`
8×	`prod-exp`
7×	`associate-/r/`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r*` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/l/`
2×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`associate-*r/`

Counts

4 → 152

Calls

4 calls:

31.0ms	(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))))
25.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))))
87.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* c a) (* b d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
2	2598
1	684
0	241

prune571.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.5b

regimes356.0ms

Accuracy

-6.9% (3.1b remaining)

Error of 26.2b against oracle of 23.1b and baseline of 26.0b

bsearch46.0ms

Steps

Iters	Range		Point
9	-1.3194991668433843e+53	-7.867138586923555e+46	-1.3001792014151386e+53

simplify3.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample863.0ms

Algorithm

intervals

Results

522.0ms

8478×

body

valid