Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
7.0ms	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: 22.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y y) (* x x))
0.0b	(+ (* x x) (* y y))
22.1b	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

12.0ms	(- (* y y) (* x x))
12.0ms	(+ (* x x) (* y y))
31.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (* y y) (* x x))
37.0ms	(+ (* x x) (* y y))
103.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

simplify3.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4834
2	951
1	285
0	98

prune404.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize4.0ms

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

prune16.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ (+ y x) (/ (+ (* x x) (* y y)) (- y x)))
21.3b	(/ (+ (* x x) (* y y)) (- y x))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
162×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
26×	`associate-/r*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `flip3-+` `flip-+`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

3 → 176

Calls

3 calls:

6.0ms	(+ (* x x) (* y y))
41.0ms	(/ (+ y x) (/ (+ (* x x) (* y y)) (- y x)))
49.0ms	(/ (+ (* x x) (* y y)) (- y x))

series239.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* x x) (* y y))
104.0ms	(/ (+ y x) (/ (+ (* x x) (* y y)) (- y x)))
85.0ms	(/ (+ (* x x) (* y y)) (- y x))

simplify2.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	5002
2	2496
1	676
0	243

prune807.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ y x))
21.3b	(/ (+ (* x x) (* y y)) (- y x))
21.3b	(/ (+ (* x x) (* y y)) (- y x))
21.3b	(/ (+ (* x x) (* y y)) (- y x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
45×	`times-frac`
35×	`add-cube-cbrt`
15×	`associate-/r*`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`associate-/r/` `associate-/l/`
4×	`cbrt-prod` `pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`cbrt-div`
1×	`pow1/3` `distribute-lft-out`

Counts

4 → 131

Calls

4 calls:

3.0ms	(cbrt (+ y x))
25.0ms	(/ (+ (* x x) (* y y)) (- y x))
29.0ms	(/ (+ (* x x) (* y y)) (- y x))
28.0ms	(/ (+ (* x x) (* y y)) (- y x))

series444.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (+ y x))
87.0ms	(/ (+ (* x x) (* y y)) (- y x))
70.0ms	(/ (+ (* x x) (* y y)) (- y x))
100.0ms	(/ (+ (* x x) (* y y)) (- y x))

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
3	2646
2	795
1	287
0	127

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes179.0ms

Accuracy

77.4% (4.9b remaining)

Error of 5.3b against oracle of 0.5b and baseline of 22.0b

bsearch149.0ms

Steps

Iters	Range	Point
8	1.054098417937684e-163	2.235821800100019e-159	1.4972378188996695e-159
10	-3.849078315748194e-151	-3.393129705632957e-163	-1.0335226845348844e-155
8	-1.8020288129482739e+158	-7.020206400485694e+153	-7.975608354837673e+153

Iters

Range

Point

1.054098417937684e-163

2.235821800100019e-159

1.4972378188996695e-159

-3.849078315748194e-151

-3.393129705632957e-163

-1.0335226845348844e-155

-1.8020288129482739e+158

-7.020206400485694e+153

-7.975608354837673e+153

simplify6.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

551.0ms	8000×	body	80	valid
506.0ms	8000×	pre	80	true