Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	101	15
4	188	15
5	346	15
6	579	15
7	875	15
8	2271	15
done	5000	15

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
23.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite47.0ms

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:

8.0ms	(+ (* x x) (* y y))
37.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* x x) (* y y))
68.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify931.0ms

Counts

48 → 48

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	91	826
1	303	802
2	1443	662
done	5000	655

prune134.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune6.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
22.5b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 89

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
66.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
27.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x x) (* y y))
68.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
52.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify1.5s

Counts

98 → 98

Iterations

Useful iterations: 2 (287.0ms)

Iter	Nodes	Cost
0	133	1685
1	374	1626
2	1536	1452
done	5000	1452

prune284.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) (* y y))
0.1b	(* (- (* x x) (* y y)) (+ x y))
0.1b	(* (+ x y) (+ (* x x) (* y y)))
32.2b	(/ (* (- (* x x) (* y y)) (+ x y)) (* (+ x y) (+ (* x x) (* y y))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
18×	`flip3-+` `flip-+`
16×	`frac-times`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`pow1` `add-cube-cbrt` `associate-r/` `associate-l` `associate-l/` `associate-/r/` `associate-/l/`
7×	`flip3--` `associate-r` `flip--`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 109

Calls

4 calls:

14.0ms	(- (* x x) (* y y))
68.0ms	(* (- (* x x) (* y y)) (+ x y))
65.0ms	(* (+ x y) (+ (* x x) (* y y)))
69.0ms	(/ (* (- (* x x) (* y y)) (+ x y)) (* (+ x y) (+ (* x x) (* y y))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* x x) (* y y))
65.0ms	(* (- (* x x) (* y y)) (+ x y))
41.0ms	(* (+ x y) (+ (* x x) (* y y)))
79.0ms	(/ (* (- (* x x) (* y y)) (+ x y)) (* (+ x y) (+ (* x x) (* y y))))

simplify2.5s

Counts

121 → 121

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	169	2616
1	616	2481
2	3993	1803
done	5000	1789

prune356.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes89.0ms

Accuracy

71.2% (6.0b remaining)

Error of 6.5b against oracle of 0.5b and baseline of 21.4b

bsearch109.0ms

Steps

Iters	Range		Point
7	1.9471739123443656e-169	2.0859602484492992e-167	2.0411774748009583e-167
5	-3.988702589505791e-215	-1.2751600830229018e-215	-3.929967420140984e-215
8	-2.444588034602567e-164	-6.369895171969084e-169	-9.045484095441609e-169
8	-6.41463231543233e-36	-1.1244907348468388e-39	-6.267281322841903e-36

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	49
1	28	49
done	28	49

end0.0ms

sample728.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
138.0ms	8000×	pre	80	true