Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	47	15
3	86	15
4	166	15
5	291	15
6	520	15
7	867	15
8	2679	15
done	5000	15

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* x x) (* y y))
64.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify694.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	91	826
1	305	802
2	1393	662
done	5001	662

prune112.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
19.6b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
29×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`frac-times`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp`
10×	`associate-r/` `associate-l/`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `prod-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 130

Calls

3 calls:

2.0ms	(+ (* x x) (* y y))
18.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
18.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
61.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
66.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify965.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	220	3376
1	597	3136
2	2258	2794
done	5001	2794

prune219.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (+ (* x x) (* y y))) (+ x y))
0.0b	(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
18.8b	(sqrt (+ (* x x) (* y y)))
18.8b	(sqrt (+ (* x x) (* y y)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

2922×	`times-frac`
1935×	`*-un-lft-identity`
1479×	`add-sqr-sqrt`
1105×	`add-cube-cbrt`
930×	`sqrt-prod`
229×	`distribute-lft-out`
186×	`distribute-lft-out--` `difference-of-squares`
139×	`associate-/r/`
72×	`flip3-+` `flip-+`
70×	`div-inv`
68×	`sqrt-div`
42×	`associate-/l*`
34×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num`

Counts

4 → 1247

Calls

4 calls:

13.0ms	(/ (sqrt (+ (* x x) (* y y))) (+ x y))
47.0ms	(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
6.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sqrt (+ (* x x) (* y y))) (+ x y))
60.0ms	(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
41.0ms	(sqrt (+ (* x x) (* y y)))
36.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.9s

Counts

1259 → 1259

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1114	65187
1	3470	58370
done	5000	58330

prune1.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

76.4% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 20.6b

bsearch96.0ms

Steps

Iters	Range	Point
9	9.986525913041322e-165	9.314421598598523e-160	2.87578004264954e-160
8	-3.916123509756297e-159	-1.316095757551224e-163	-1.9177316652177307e-160
9	-9.454570341338981e+157	-6.679228854675776e+149	-1.693074810444792e+150

Iters

Range

Point

9.986525913041322e-165

9.314421598598523e-160

2.87578004264954e-160

-3.916123509756297e-159

-1.316095757551224e-163

-1.9177316652177307e-160

-9.454570341338981e+157

-6.679228854675776e+149

-1.693074810444792e+150

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	46
1	27	46
done	27	46

end0.0ms

sample516.0ms

Algorithm

intervals

Results

253.0ms	8000×	body	80	valid
118.0ms	8000×	pre	80	true