Details

sample40.0ms

Algorithm

intervals

Results

19.0ms

268×

body

valid

simplify8.0ms

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: 28.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(+ (* a c) (* b d))
27.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ (* c c) (* d d))
9.0ms	(+ (* a c) (* b d))
56.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series224.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* c c) (* d d))
53.0ms	(+ (* a c) (* b d))
132.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
3	3905
2	997
1	279
0	96

prune335.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
17.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

9.0ms	(+ (* a c) (* b d))
36.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* a c) (* b d))
153.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
41.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	2246
2	768
1	278
0	114

prune560.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
17.2b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ (* a c) (* b d))
22.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* a c) (* b d))
91.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
43.0ms	(sqrt (+ (* c c) (* d d)))
52.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
4	4986
3	1893
2	738
1	268
0	112

prune622.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(+ (* a c) (* b d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
27.2b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

6.0ms	(+ (* c c) (* d d))
6.0ms	(+ (* a c) (* b d))
19.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
30.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* c c) (* d d))
43.0ms	(+ (* a c) (* b d))
137.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
63.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	1916
1	568
0	204

prune813.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

regimes356.0ms

Accuracy

0% (3.0b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample772.0ms

Algorithm

intervals

Results

534.0ms

8480×

body

valid