Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	1519
6	575
5	339
4	177
3	95
2	46
1	22
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
16.1b	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

2 → 47

Calls

2 calls:

12.0ms	(+ (* x x) (* y y))
43.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

series147.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (* x x) (* y y))
98.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

simplify1.4s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	897
1	267
0	92

prune287.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (* x x) (* y y))
14.2b	(/ (* x x) (+ (* x x) (* y y)))
22.2b	(/ (* y y) (+ (* x x) (* y y)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
6×	`associate-/r*` `times-frac`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
2×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

9.0ms	(+ (* x x) (* y y))
13.0ms	(+ (* x x) (* y y))
28.0ms	(/ (* x x) (+ (* x x) (* y y)))
28.0ms	(/ (* y y) (+ (* x x) (* y y)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* x x) (* y y))
38.0ms	(+ (* x x) (* y y))
60.0ms	(/ (* x x) (+ (* x x) (* y y)))
55.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5022
2	1497
1	336
0	96

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
2.3b	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
14.2b	(/ (* x x) (+ (* x x) (* y y)))
22.2b	(/ (* y y) (+ (* x x) (* y y)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`log-pow`
9×	`exp-prod` `times-frac`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
3×	`log-prod` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sum-log` `rem-log-exp`

Counts

4 → 78

Calls

4 calls:

13.0ms	(+ (* x x) (* y y))
29.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
19.0ms	(/ (* x x) (+ (* x x) (* y y)))
17.0ms	(/ (* y y) (+ (* x x) (* y y)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x x) (* y y))
81.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
59.0ms	(/ (* x x) (+ (* x x) (* y y)))
64.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1533
1	376
0	128

prune523.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes110.0ms

Accuracy

75.1% (4.9b remaining)

Error of 5.4b against oracle of 0.5b and baseline of 20.2b

bsearch121.0ms

Steps

Iters	Range	Point
7	4.9913496161306e-166	8.204998353780088e-165	8.136310300271012e-165
9	-1.1589213588247953e-150	-9.80703630762879e-160	-1.096966360472084e-152
11	-1.1194373462677982e+167	-1.9832728243821866e+140	-1.9320202372956998e+146

Iters

Range

Point

4.9913496161306e-166

8.204998353780088e-165

8.136310300271012e-165

-1.1589213588247953e-150

-9.80703630762879e-160

-1.096966360472084e-152

-1.1194373462677982e+167

-1.9832728243821866e+140

-1.9320202372956998e+146

simplify13.0ms

Iterations

Iter	Nodes
done	29
1	29
0	26

end0.0ms

sample983.0ms

Algorithm

intervals

Results

594.0ms	8000×	body	80	valid
178.0ms	8000×	pre	80	true