Details

sample57.0ms

Algorithm

intervals

Results

25.0ms

264×

body

valid

simplify169.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize71.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
28.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite130.0ms

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×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
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 → 58

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(- (* x.im y.re) (* x.re y.im))
67.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* y.re y.re) (* y.im y.im))
56.0ms	(- (* x.im y.re) (* x.re y.im))
166.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

67 → 67

Iterations

Iter	Nodes
done	5003
2	1248
1	306
0	104

prune960.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.6b

localize156.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

18.0ms	(- (* x.im y.re) (* x.re y.im))
63.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
22.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
23.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* x.im y.re) (* x.re y.im))
207.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5004
3	2697
2	922
1	315
0	124

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.9b

localize82.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* y.re x.im) (* y.im x.re))
28.8b	(/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))

rewrite155.0ms

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×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
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 → 58

Calls

3 calls:

38.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* y.re x.im) (* y.im x.re))
77.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))

series380.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ (* y.re y.re) (* y.im y.im))
105.0ms	(- (* y.re x.im) (* y.im x.re))
207.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (+ (* y.re y.re) (* y.im y.im)))

simplify8.2s

Counts

67 → 67

Iterations

Iter	Nodes
done	5005
3	4898
2	1123
1	301
0	101

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.9b

localize168.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* y.re x.im) (* y.im x.re))
0.3b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re))))
28.7b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 142

Calls

4 calls:

32.0ms	(+ (* y.re y.re) (* y.im y.im))
18.0ms	(- (* y.re x.im) (* y.im x.re))
90.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re))))
103.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* y.re y.re) (* y.im y.im))
85.0ms	(- (* y.re x.im) (* y.im x.re))
279.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re))))
132.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* y.re x.im) (* y.im x.re)))

simplify3.6s

Counts

154 → 154

Iterations

Iter	Nodes
done	5003
2	1646
1	568
0	208

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.9b

regimes1.3s

Accuracy

-1.5% (3.2b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.4b

bsearch108.0ms

Steps

Iters	Range		Point
4	2.99988769581893e+36	5.314606313626179e+36	5.2422713568197025e+36
8	-7.171553699074835e+91	-1.194776095236265e+88	-7.846283352613039e+90

simplify11.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s

8412×

body

valid