Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

277×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize21.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (* a c) (* b d))
24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite41.0ms

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:

6.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series168.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(+ (* a c) (* b d))
117.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	4513
2	925
1	235
0	83

prune310.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.1b	(sqrt (+ (* c c) (* d d)))
29.1b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ (* a c) (* b 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)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* a c) (* b d))
139.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
52.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	4727
2	1003
1	278
0	114

prune725.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
1.2b	(+ (* a c) (* b d))
24.4b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite88.0ms

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`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow`

Counts

3 → 126

Calls

3 calls:

31.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
7.0ms	(+ (* a c) (* b d))
41.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
41.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify2.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	3224
1	537
0	191

prune668.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.7b

localize19.0ms

Local error

Found 3 expressions with local error:

1.2b	(+ (* d b) (* c a))
1.2b	(/ 1 (+ (* c c) (* d d)))
23.8b	(* (/ 1 (+ (* c c) (* d d))) (+ (* d b) (* c a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `associate-r` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 87

Calls

3 calls:

6.0ms	(+ (* d b) (* c a))
12.0ms	(/ 1 (+ (* c c) (* d d)))
54.0ms	(* (/ 1 (+ (* c c) (* d d))) (+ (* d b) (* c a)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* d b) (* c a))
51.0ms	(/ 1 (+ (* c c) (* d d)))
171.0ms	(* (/ 1 (+ (* c c) (* d d))) (+ (* d b) (* c a)))

simplify2.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	4204
1	502
0	135

prune426.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 21.7b

regimes437.0ms

Accuracy

54.8% (1.0b remaining)

Error of 24.7b against oracle of 23.7b and baseline of 25.9b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	22

end0.0ms

sample726.0ms

Algorithm

intervals

Results

483.0ms

8465×

body

valid