Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

266×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* a c) (* b d))
28.4b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite42.0ms

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))
33.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series120.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* a c) (* b d))
85.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: 3 (443.0ms)

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

prune148.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
32.6b	(sqrt (+ (* c c) (* d d)))
32.6b	(sqrt (+ (* c c) (* d d)))

rewrite60.0ms

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))
34.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* a c) (* b d))
116.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: 3 (424.0ms)

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

prune273.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* a c) (* b d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
28.0b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite70.0ms

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:

8.0ms	(+ (* a c) (* b d))
27.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
31.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series243.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* a c) (* b d))
146.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
57.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify2.1s

Counts

135 → 135

Iterations

Useful iterations: 3 (955.0ms)

Iter	Nodes	Cost
0	193	3510
1	468	3261
2	1271	2982
3	4154	2954
done	5000	2954

prune252.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))))
16.6b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
32.6b	(sqrt (+ (* c c) (* d d)))
32.6b	(sqrt (+ (* c c) (* d d)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
18×	`sqrt-prod`
15×	`add-cbrt-cube`
10×	`sqrt-div` `div-exp`
9×	`pow1` `associate-/l*`
7×	`associate-/r/`
6×	`flip3-+` `prod-exp` `flip-+`
5×	`cbrt-undiv`
4×	`associate-/r*` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-times` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*l/` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`associate-*r/` `pow-prod-down` `inv-pow`

Counts

4 → 110

Calls

4 calls:

50.0ms	(/ 1 (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))))
22.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (* (sqrt (+ (* c c) (* d d))) (/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))))
82.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.4s

Counts

122 → 122

Iterations

Useful iterations: 3 (933.0ms)

Iter	Nodes	Cost
0	157	2812
1	370	2308
2	1020	2070
3	3258	2006
done	5002	2006

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 26.4b

regimes170.0ms

Accuracy

22.9% (2.4b remaining)

Error of 25.6b against oracle of 23.2b and baseline of 26.3b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	20	43
done	20	43

end0.0ms

sample549.0ms

Algorithm

intervals

Results

268.0ms

8444×

body

valid