Details

sample43.0ms

Algorithm

intervals

Results

28.0ms

269×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite100.0ms

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` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

14.0ms	(+ (* c c) (* d d))
15.0ms	(+ (* a c) (* b d))
69.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series234.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (* c c) (* d d))
63.0ms	(+ (* a c) (* b d))
118.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.4s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	3987
2	1000
1	282
0	99

prune386.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.4b	(sqrt (+ (* c c) (* d d)))
28.4b	(sqrt (+ (* c c) (* d d)))

rewrite124.0ms

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` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

56.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
50.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
113.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
46.0ms	(sqrt (+ (* c c) (* d d)))
69.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.3s

Counts

280 → 280

Iterations

Iter	Nodes
done	5000
2	1755
1	724
0	305

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (+ (* c c) (* d d)))
24.5b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
7.0ms	(+ (* c c) (* d d))
10.0ms	(/ 1 (+ (* c c) (* d d)))
38.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* a c) (* b d))
29.0ms	(+ (* c c) (* d d))
48.0ms	(/ 1 (+ (* c c) (* d d)))
88.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1472
1	413
0	141

prune517.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.2b

localize43.0ms

Local error

Found 4 expressions with local error:

15.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.4b	(sqrt (+ (* c c) (* d d)))
28.4b	(sqrt (+ (* c c) (* d d)))
28.4b	(sqrt (+ (* c c) (* d d)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 92

Calls

4 calls:

36.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
42.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	1969
2	661
1	251
0	107

prune570.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.2b

regimes314.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8439×

body

valid