Details

sample64.0ms

Algorithm

intervals

Results

41.0ms

479×

body

valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1970
5	833
4	340
3	156
2	58
1	21
0	11

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.im) (* x.im x.re))
0.1b	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
7.0b	(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-*l/`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
7×	`associate-l`
6×	`associate-r`
4×	`flip3-+` `flip3--` `frac-sub` `flip-+` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

6.0ms	(+ (* x.re x.im) (* x.im x.re))
40.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
35.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
41.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

series225.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re x.im) (* x.im x.re))
75.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
44.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
67.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5029
2	1679
1	401
0	136

prune426.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.im) (* x.im x.re))
0.1b	(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.2b	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.2b	(* (+ x.re x.im) (* (- x.re x.im) x.re))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*l/`
19×	`flip3-+` `flip-+`
16×	`frac-sub`
12×	`frac-times`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`flip3--` `flip--`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`associate-l` `add-cube-cbrt`
6×	`associate-*r/`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `distribute-lft-out` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(+ (* x.re x.im) (* x.im x.re))
54.0ms	(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
21.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
64.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.re))

series289.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x.re x.im) (* x.im x.re))
97.0ms	(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
55.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
99.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify3.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	4174
1	721
0	198

prune593.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
13.0b	(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.0b	(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.0b	(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

65.0ms	(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
7.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
8.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
7.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
159.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
116.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
128.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	2066
2	808
1	298
0	119

prune622.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x.im)
1.0b	(cbrt 2)
13.0b	(cbrt (+ (* x.re x.im) (* x.im x.re)))
13.0b	(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-log-exp`
2×	`flip3-+` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt x.im)
1.0ms	(cbrt 2)
7.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
7.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

series611.0ms

Counts

4 → 10

Calls

4 calls:

318.0ms	(cbrt x.im)
0.0ms	(cbrt 2)
130.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
162.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
3	1662
2	565
1	223
0	97

prune471.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.0b

regimes224.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	11

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

14457×

body

valid