Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

276×

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* a c) (* b d))
29.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite41.0ms

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))
32.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (* a c) (* b d))
145.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (527.0ms)

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

prune197.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 29.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* a c) (* b d))
17.5b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))

rewrite86.0ms

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))
47.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* a c) (* b d))
150.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.9s

Counts

96 → 96

Iterations

Useful iterations: 3 (722.0ms)

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

prune425.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 26.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* a c) (* b d))
17.6b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))

rewrite100.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

16.0ms	(+ (* a c) (* b d))
45.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
15.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* a c) (* b d))
111.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
54.0ms	(sqrt (+ (* c c) (* d d)))
60.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.5s

Counts

96 → 96

Iterations

Useful iterations: 3 (546.0ms)

Iter	Nodes	Cost
0	114	1774
1	265	1656
2	723	1554
3	1731	1540
4	4577	1540
done	5000	1540

prune304.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 26.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.8b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.9b	(+ (* a c) (* b d))
28.5b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite75.0ms

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:

25.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
8.0ms	(+ (* a c) (* b d))
35.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
37.0ms	(+ (* a c) (* b d))
62.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify2.1s

Counts

135 → 135

Iterations

Useful iterations: 3 (960.0ms)

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

prune247.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 26.0b

regimes252.0ms

Accuracy

3% (2.9b remaining)

Error of 26.6b against oracle of 23.7b and baseline of 26.7b

bsearch34.0ms

Steps

Iters	Range		Point
8	2.5603685361688665e+88	1.193256888551369e+92	1.0220962851570888e+92

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample616.0ms

Algorithm

intervals

Results

298.0ms

8487×

body

valid