Details

sample51.0ms

Algorithm

intervals

Results

22.0ms

270×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
24.6b	(/ (+ (* 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:

12.0ms	(+ (* c c) (* d d))
12.0ms	(+ (* a c) (* b d))
49.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series240.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
68.0ms	(+ (* a c) (* b d))
142.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify880.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
2	1580
1	294
0	96

prune416.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* d b) (* a c))
16.4b	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite91.0ms

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))
50.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* d b) (* a c))
146.0ms	(/ (+ (* d b) (* a c)) (sqrt (+ (* c c) (* d d))))
50.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify815.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1128
1	280
0	116

prune783.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(/ 1 (+ (* c c) (* d d)))
0.5b	(+ (* a c) (* b d))
24.7b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite95.0ms

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/`
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 → 97

Calls

4 calls:

14.0ms	(+ (* c c) (* d d))
18.0ms	(/ 1 (+ (* c c) (* d d)))
6.0ms	(+ (* a c) (* b d))
51.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* c c) (* d d))
51.0ms	(/ 1 (+ (* c c) (* d d)))
48.0ms	(+ (* a c) (* b d))
122.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify3.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	3600
1	427
0	137

prune579.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* d b) (* a c))
0.9b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
24.3b	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

rewrite77.0ms

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:

10.0ms	(+ (* c c) (* d d))
6.0ms	(+ (* d b) (* a c))
24.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
31.0ms	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* c c) (* d d))
50.0ms	(+ (* d b) (* a c))
180.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* d b) (* a c))))
88.0ms	(/ (+ (* c c) (* d d)) (+ (* d b) (* a c)))

simplify1.9s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	3471
1	590
0	206

prune888.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.6b

regimes480.0ms

Accuracy

0% (3.0b remaining)

Error of 26.0b against oracle of 23.0b and baseline of 26.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

714.0ms

8493×

body

valid