Details

sample57.0ms

Algorithm

intervals

Results

29.0ms

263×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
28.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite47.0ms

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:

11.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))
28.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* c c) (* d d))
41.0ms	(+ (* a c) (* b d))
121.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify882.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
2	1580
1	294
0	96

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 28.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* d b) (* a c))
18.0b	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
30.7b	(sqrt (+ (* c c) (* d d)))
30.7b	(sqrt (+ (* c c) (* d d)))

rewrite73.0ms

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:

12.0ms	(+ (* d b) (* a c))
31.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* d b) (* a c))
128.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
46.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify750.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1128
1	280
0	116

prune610.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* d b) (* a c))
18.1b	(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
30.7b	(sqrt (+ (* c c) (* d d)))
30.7b	(sqrt (+ (* c c) (* d d)))

rewrite82.0ms

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:

17.0ms	(+ (* d b) (* a c))
36.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
12.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* d b) (* a c))
107.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* d b) (* a c)))
60.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4161
2	980
1	270
0	114

prune425.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* d b) (* a c))
18.1b	(* (+ (* d b) (* a c)) (/ 1 (sqrt (+ (* c c) (* d d)))))
30.7b	(sqrt (+ (* c c) (* d d)))
30.7b	(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(+ (* d b) (* a c))
45.0ms	(* (+ (* d b) (* a c)) (/ 1 (sqrt (+ (* c c) (* d d)))))
11.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* d b) (* a c))
96.0ms	(* (+ (* d b) (* a c)) (/ 1 (sqrt (+ (* c c) (* d d)))))
38.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	2314
1	408
0	145

prune414.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 25.2b

regimes358.0ms

Accuracy

35.1% (2.0b remaining)

Error of 25.4b against oracle of 23.4b and baseline of 26.4b

bsearch2.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample821.0ms

Algorithm

intervals

Results

489.0ms

8502×

body

valid