Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify4.3s

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite60.0ms

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))
50.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x x) (* y y))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify913.0ms

Counts

48 → 48

Iterations

Useful iterations: done (911.0ms)

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

prune122.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (pow y 2))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

rewrite68.0ms

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:

11.0ms	(+ (* x x) (pow y 2))
55.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(+ (* x x) (pow y 2))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (pow y 2)))

simplify933.0ms

Counts

48 → 48

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	91	826
1	296	794
2	1358	666
done	5001	661

prune160.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (pow y 2))
0.0b	(/ 1 (/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y))))
18.4b	(/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y)))

rewrite205.0ms

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:

16.0ms	(+ (* x x) (pow y 2))
79.0ms	(/ 1 (/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y))))
93.0ms	(/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y)))

series246.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* x x) (pow y 2))
102.0ms	(/ 1 (/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y))))
93.0ms	(/ (+ (* x x) (pow y 2)) (* (- x y) (+ x y)))

simplify1.6s

Counts

139 → 139

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	221	3376
1	580	3134
2	2280	2796
done	5000	2759

prune317.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/l/`
19×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`cbrt-prod` `flip3--` `associate-/r*` `flip--`
8×	`associate-/r/`
6×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`cbrt-div` `pow1/3`

Counts

4 → 111

Calls

4 calls:

14.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
58.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
30.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
99.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
101.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
91.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.0s

Counts

123 → 123

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	108	2452
1	316	2386
2	1452	2036
done	5000	1990

prune549.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes135.0ms

Accuracy

75.7% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 19.9b

bsearch115.0ms

Steps

Iters	Range		Point
9	9.133840493531702e-163	9.628535965427897e-156	7.168109854324842e-160
9	-1.1690025963777955e-148	-8.983747944314465e-154	-1.1129546130770477e-151
7	-108.09236434424712	-0.7718806003288846	-106.30606884619185

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	23	48
1	31	30
done	31	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

664.0ms	8000×	pre	80	true
489.0ms	8000×	body	80	valid