Details

sample41.0ms

Algorithm

intervals

Results

15.0ms

271×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize20.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
27.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite66.0ms

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:

9.0ms	(+ (* a c) (* b d))
55.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series225.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(+ (* a c) (* b d))
152.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (678.0ms)

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

prune228.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* b d) (* a c))
27.9b	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

rewrite55.0ms

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:

9.0ms	(+ (* b d) (* a c))
45.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (* b d) (* a c))
120.0ms	(/ (+ (* b d) (* a c)) (+ (* c c) (* d d)))

simplify1.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (628.0ms)

Iter	Nodes	Cost
0	85	924
1	232	906
2	767	824
3	2335	820
done	5001	820

prune233.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* b d) (* a c))))
0.7b	(+ (* b d) (* a c))
27.5b	(/ (+ (* c c) (* d d)) (+ (* b d) (* a c)))

rewrite130.0ms

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:

43.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* b d) (* a c))))
14.0ms	(+ (* b d) (* a c))
64.0ms	(/ (+ (* c c) (* d d)) (+ (* b d) (* a c)))

series369.0ms

Counts

3 → 9

Calls

3 calls:

201.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* b d) (* a c))))
55.0ms	(+ (* b d) (* a c))
113.0ms	(/ (+ (* c c) (* d d)) (+ (* b d) (* a c)))

simplify3.4s

Counts

135 → 135

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	193	3510
1	468	3261
2	1275	2982
3	4173	2954
done	5000	2954

prune402.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 27.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
17.2b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.4b	(sqrt (+ (* c c) (* d d)))
30.4b	(sqrt (+ (* c c) (* d d)))

rewrite121.0ms

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:

9.0ms	(+ (* a c) (* b d))
73.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
17.0ms	(sqrt (+ (* c c) (* d d)))
17.0ms	(sqrt (+ (* c c) (* d d)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* a c) (* b d))
159.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
67.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (552.0ms)

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

prune410.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 25.2b

regimes314.0ms

Accuracy

0% (2.9b remaining)

Error of 26.1b against oracle of 23.2b and baseline of 26.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

668.0ms

8500×

body

valid