Details

sample37.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify226.0ms

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: 30.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.2b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite64.0ms

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:

7.0ms	(+ (* x x) (* (* y 4.0) y))
17.0ms	(- (* x x) (* (* y 4.0) y))
39.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(+ (* x x) (* (* y 4.0) y))
76.0ms	(- (* x x) (* (* y 4.0) y))
76.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1796
1	279
0	98

prune452.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 2 expressions with local error:

4.2b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite46.0ms

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)))

series164.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (* x x) (* (* y 4.0) y))
103.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1475
1	246
0	90

prune338.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(fma (* y 4.0) (- y) (* x x))
30.1b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
30.1b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
30.1b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (* y 4.0) (- y) (* x x))
4.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
4.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
4.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (* y 4.0) (- y) (* x x))
152.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
140.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
113.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

simplify1.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
3	2061
2	344
1	118
0	67

prune842.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize1.0ms

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

prune1.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes420.0ms

Accuracy

53% (14.4b remaining)

Error of 14.7b against oracle of 0.3b and baseline of 31.0b

bsearch313.0ms

Steps

Iters	Range		Point
8	1.554980890507146e+50	6.447507513983036e+53	6.357559912396234e+53
10	6.350418665017979e-153	1.5267098419003533e-142	6.823576610928472e-152
10	-1.2554389614223213e-180	-1.5147693389286864e-190	-1.239928607796128e-180
3	-1.0426208093273308e-128	-8.529105409937888e-129	-8.647674327646353e-129
7	-1.0247974828914149e-73	-2.6388757619776774e-75	-5.393824270148449e-74
6	-5.10986653714767e-17	-1.173305502329754e-17	-3.4780572575898166e-17
10	-3.307435552146123e+26	-23371946804750188.0	-2.1328351164470982e+17
3	-1.1611654526548658e+117	-8.48111626998625e+116	-9.850726757232305e+116

simplify10.0ms

Iterations

Iter	Nodes
done	47
1	47
0	42

end0.0ms

sample925.0ms

Algorithm

intervals

Results

618.0ms

8000×

body

valid