Details

sample38.0ms

Algorithm

intervals

Results

27.0ms

270×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
28.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite51.0ms

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

Counts

2 → 44

Calls

2 calls:

13.0ms	(+ (* a c) (* b d))
37.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (* a c) (* b d))
89.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify640.0ms

Counts

50 → 50

Iterations

Iter	Nodes
3	2599
2	777
1	236
0	85

prune464.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 27.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
18.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.4b	(sqrt (+ (* c c) (* d d)))
33.4b	(sqrt (+ (* c c) (* d d)))

rewrite108.0ms

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:

46.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
38.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
13.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
120.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
55.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.4s

Counts

280 → 280

Iterations

Iter	Nodes
3	6045
2	1718
1	721
0	305

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
18.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.4b	(sqrt (+ (* c c) (* d d)))
33.4b	(sqrt (+ (* c c) (* d d)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

56.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
28.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (/ 1 (sqrt (+ (* c c) (* d d)))) (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts

176 → 176

Iterations

Iter	Nodes
3	7439
2	1941
1	594
0	196

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
18.8b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
33.4b	(sqrt (+ (* c c) (* d d)))
33.4b	(sqrt (+ (* c c) (* d d)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 197

Calls

4 calls:

17.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
17.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d))))
81.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
37.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.3s

Counts

209 → 209

Iterations

Iter	Nodes
3	4739
2	1574
1	633
0	245

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 25.1b

regimes316.0ms

Accuracy

0% (2.7b remaining)

Error of 26.2b against oracle of 23.5b and baseline of 26.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

764.0ms

8484×

body

valid