Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify222.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.7b	(- (* x x) (* (* y 4.0) y))
28.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite48.0ms

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))
7.0ms	(- (* x x) (* (* y 4.0) y))
33.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(+ (* x x) (* (* y 4.0) y))
87.0ms	(- (* x x) (* (* y 4.0) y))
106.0ms	(/ (- (* 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

prune405.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma (* y 4.0) (- y) (* x x))
28.0b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
28.0b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
28.0b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

rewrite24.0ms

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))
6.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
7.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
8.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma (* y 4.0) (- y) (* x x))
169.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
130.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
129.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

simplify1.3s

Counts

109 → 109

Iterations

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

prune844.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize83.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma 4.0 (* y (- y)) (* x x))
28.0b	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))
28.0b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
28.0b	(/ (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 4.0 (* y (- y)) (* x x))
4.0ms	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))
4.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
5.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma 4.0 (* y (- y)) (* x x))
128.0ms	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))
137.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))
145.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

simplify2.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	4564
2	723
1	206
0	119

prune946.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

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

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes249.0ms

Accuracy

58.9% (12.8b remaining)

Error of 13.2b against oracle of 0.4b and baseline of 31.6b

bsearch252.0ms

Steps

Iters	Range		Point
9	2.608500637638846e+49	6.787836348837619e+54	6.680131771318429e+54
10	5.867135609902031e-137	1.3413289066181662e-120	5.430501749338193e-128
9	-5.902380441646539e-162	-2.084140915635644e-170	-5.780522729495913e-162
7	-4.644078595127857e+56	-4.6999773453873415e+54	-4.542162861981963e+56

simplify14.0ms

Iterations

Iter	Nodes
done	47
3	47
2	45
1	43
0	35

end0.0ms

sample848.0ms

Algorithm

intervals

Results

573.0ms

8000×

body

valid