Details

sample34.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify276.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	252
7	252
6	244
5	199
4	133
3	77
2	39
1	19
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.6b	(- (* x x) (* (* y 4.0) y))
32.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 64

Calls

3 calls:

12.0ms	(+ (* x x) (* (* y 4.0) y))
12.0ms	(- (* x x) (* (* y 4.0) y))
45.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ (* x x) (* (* y 4.0) y))
66.0ms	(- (* x x) (* (* y 4.0) y))
92.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1796
1	279
0	98

prune510.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize0.0ms

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

prune10.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

3.6b	(- (* x x) (* (* y 4.0) y))
32.0b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 48

Calls

2 calls:

13.0ms	(- (* x x) (* (* y 4.0) y))
32.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (* x x) (* (* y 4.0) y))
117.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify1.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1475
1	246
0	90

prune329.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
0.5b	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
3.6b	(- (* x x) (* (* y 4.0) y))
32.0b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 70

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
1.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
13.0ms	(- (* x x) (* (* y 4.0) y))
27.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))))
149.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))))
66.0ms	(- (* x x) (* (* y 4.0) y))
124.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1466
1	284
0	113

prune562.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes308.0ms

Accuracy

59.1% (13.0b remaining)

Error of 13.4b against oracle of 0.4b and baseline of 32.1b

bsearch245.0ms

Steps

Iters	Range		Point
11	1.4811311028475771e+262	7.570381961298086e+285	1.4962584659013787e+262
8	2.6202151264562232e+244	8.301180575196618e+248	8.170638210533042e+248
9	1.7653732899602565e+85	3.7806436988263344e+90	1.7922671628902882e+85
11	2.7912168670898916e-38	4.1094300843342833e-13	3.691663792214943e-13
10	4.603331812003636e-293	3.704681433897876e-282	7.027808530107358e-286

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	28

end0.0ms

sample719.0ms

Algorithm

intervals

Results

543.0ms

8000×

body

valid