Details

sample50.0ms

Algorithm

intervals

Results

22.0ms

265×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
24.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite54.0ms

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

Counts

2 → 42

Calls

2 calls:

11.0ms	(+ (* a c) (* b d))
42.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series168.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (* a c) (* b d))
128.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.9s

Counts

48 → 48

Iterations

Useful iterations: 3 (912.0ms)

Iter	Nodes	Cost
0	83	924
1	235	906
2	925	824
3	4513	820
done	5000	820

prune274.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.2b	(sqrt (+ (* c c) (* d d)))
26.2b	(sqrt (+ (* c c) (* d d)))

rewrite114.0ms

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

Counts

4 → 264

Calls

4 calls:

56.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
26.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
184.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
46.0ms	(sqrt (+ (* c c) (* d d)))
73.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

276 → 276

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	302	11076
1	755	9987
2	3738	9426
done	5000	9054

prune899.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d)))))
15.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.2b	(sqrt (+ (* c c) (* d d)))
26.2b	(sqrt (+ (* c c) (* d d)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 161

Calls

4 calls:

69.0ms	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d)))))
25.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (/ 1 (sqrt (+ (* c c) (* d d)))))
127.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.7s

Counts

173 → 173

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	196	4846
1	608	4527
2	3837	4052
done	5000	4038

prune886.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.6b	(/ (/ 1 1) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
23.7b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

474×	`times-frac`
221×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
38×	`add-exp-log`
32×	`div-inv`
31×	`associate-/r/`
30×	`div-exp`
18×	`associate-/r*`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/l*`
10×	`1-exp`
9×	`cbrt-undiv`
5×	`add-log-exp`
4×	`rec-exp`
3×	`pow1` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

3 → 295

Calls

3 calls:

8.0ms	(+ (* a c) (* b d))
25.0ms	(/ (/ 1 1) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
23.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* a c) (* b d))
133.0ms	(/ (/ 1 1) (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
58.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify875.0ms

Counts

304 → 304

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	478	11053
1	1816	9038
done	5000	8745

prune431.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.8b

regimes297.0ms

Accuracy

3.7% (2.7b remaining)

Error of 25.7b against oracle of 23.0b and baseline of 25.8b

bsearch38.0ms

Steps

Iters	Range		Point
8	2.586892949274192e+85	1.392645936715808e+88	1.2655629246867158e+88

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	21	39
done	21	39

end0.0ms

sample810.0ms

Algorithm

intervals

Results

502.0ms

8448×

body

valid