Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

265×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
27.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

8.0ms	(+ (* a c) (* b d))
37.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ (* a c) (* b d))
94.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.5s

Counts

48 → 48

Iterations

Useful iterations: 3 (544.0ms)

Iter	Nodes	Cost
0	85	924
1	232	906
2	767	824
3	2337	820
done	5001	820

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
16.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.2b	(sqrt (+ (* c c) (* d d)))
33.2b	(sqrt (+ (* c c) (* d d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
41.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* a c) (* b d))
124.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
42.0ms	(sqrt (+ (* c c) (* d d)))
43.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (464.0ms)

Iter	Nodes	Cost
0	116	1780
1	275	1649
2	777	1541
3	2052	1525
done	5000	1525

prune359.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
16.3b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
33.2b	(sqrt (+ (* c c) (* d d)))
33.2b	(sqrt (+ (* c c) (* d d)))

rewrite122.0ms

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` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(+ (* a c) (* b d))
86.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* a c) (* b d))
135.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
41.0ms	(sqrt (+ (* c c) (* d d)))
47.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.5s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	145	1886
1	378	1642
2	1153	1474
3	3771	1458
done	5000	1458

prune386.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.6b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.7b	(+ (* a c) (* b d))
27.4b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

40.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
15.0ms	(+ (* a c) (* b d))
58.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series298.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
42.0ms	(+ (* a c) (* b d))
93.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify2.8s

Counts

135 → 135

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	193	3510
1	468	3261
2	1275	2982
3	4169	2954
done	5002	2954

prune408.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 26.2b

regimes155.0ms

Accuracy

0% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 25.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	17	25
done	17	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

749.0ms

8453×

body

valid