Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	284
1	19	284
2	36	284
3	48	284
4	66	284
5	72	284
done	72	284

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
23.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite46.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

9.0ms	(- (* b c) (* a d))
36.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series163.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (* b c) (* a d))
112.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.9s

Counts

50 → 50

Iterations

Useful iterations: 2 (275.0ms)

Iter	Nodes	Cost
0	86	17471
1	254	16526
2	980	16446
3	4329	16446
done	5001	16446

prune344.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.8b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))

rewrite118.0ms

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*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`flip3--` `flip--`

Counts

4 → 266

Calls

4 calls:

41.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
30.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
170.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
65.0ms	(sqrt (+ (* c c) (* d d)))
48.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.6s

Counts

278 → 278

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	307	189751
1	764	176147
2	3205	173626
done	5000	172826

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.3b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* b c) (* a d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
22.8b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

10.0ms	(- (* b c) (* a d))
38.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
29.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* b c) (* a d))
203.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
85.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify2.3s

Counts

136 → 136

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	192	67718
1	533	58679
2	2790	57583
done	5002	55816

prune648.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.3b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* c b) (* d a))
23.2b	(/ (- (* c b) (* d a)) (+ (* c c) (* d d)))

rewrite49.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

6.0ms	(- (* c b) (* d a))
42.0ms	(/ (- (* c b) (* d a)) (+ (* c c) (* d d)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (* c b) (* d a))
107.0ms	(/ (- (* c b) (* d a)) (+ (* c c) (* d d)))

simplify1.0s

Counts

50 → 50

Iterations

Useful iterations: 2 (193.0ms)

Iter	Nodes	Cost
0	89	17471
1	258	16566
2	1074	16446
done	5000	16446

prune238.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.3b

regimes339.0ms

Accuracy

0% (2.8b remaining)

Error of 26.3b against oracle of 23.6b and baseline of 26.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	364
1	16	364
done	16	364

end0.0ms

sample860.0ms

Algorithm

intervals

Results

597.0ms

8438×

body

valid