Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	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

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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:

3.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
60.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify744.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (172.0ms)

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

prune110.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
18.8b	(sqrt (+ (* x x) (* y y)))
18.8b	(sqrt (+ (* x x) (* y y)))
19.6b	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `sqrt-div`
24×	`sqrt-prod`
21×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`frac-times`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr` `associate-/r/` `associate-/l/`
6×	`associate-r/` `associate-r` `associate-l` `associate-l/`
5×	`prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `pow-sqr` `flip--`
2×	`rem-sqrt-square`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 124

Calls

4 calls:

20.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
6.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
18.0ms	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
36.0ms	(sqrt (+ (* x x) (* y y)))
35.0ms	(sqrt (+ (* x x) (* y y)))
65.0ms	(/ (* (- x y) (+ x y)) (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))))

simplify1.0s

Counts

136 → 136

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	149	3134
1	443	2122
2	2210	1726
done	5001	1726

prune267.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow y 2) (pow x 2))
0.0b	(/ 1 (/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y))))
19.6b	(/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
59×	`*-un-lft-identity`
41×	`associate-/r/`
31×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`add-exp-log`
20×	`frac-times`
18×	`associate-/r*`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
15×	`flip3--` `flip--`
14×	`unpow-prod-down` `div-exp` `distribute-lft-out`
10×	`associate-r/` `associate-l/`
8×	`associate-/l*`
7×	`cbrt-undiv`
6×	`div-inv`
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 → 144

Calls

3 calls:

9.0ms	(+ (pow y 2) (pow x 2))
33.0ms	(/ 1 (/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y))))
32.0ms	(/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (pow y 2) (pow x 2))
59.0ms	(/ 1 (/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y))))
64.0ms	(/ (+ (pow y 2) (pow x 2)) (* (- x y) (+ x y)))

simplify1.1s

Counts

153 → 153

Iterations

Useful iterations: 2 (322.0ms)

Iter	Nodes	Cost
0	226	3610
1	604	3306
2	2247	2990
done	5000	2990

prune260.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize2.0ms

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

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

76.3% (4.7b remaining)

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

bsearch92.0ms

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

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	60
1	36	58
done	36	58

end0.0ms

sample505.0ms

Algorithm

intervals

Results

235.0ms	8000×	body	80	valid
122.0ms	8000×	pre	80	true