Details

sample35.0ms

Algorithm

intervals

Results

22.0ms

479×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1689
4	447
3	160
2	58
1	21
0	11

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize20.0ms

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)

rewrite101.0ms

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:

9.0ms	(+ (* x.re x.im) (* x.im x.re))
22.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
29.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
38.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

series221.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re x.im) (* x.im x.re))
69.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
51.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
69.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify2.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	2778
1	413
0	136

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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))

rewrite152.0ms

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:

8.0ms	(+ (* 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))
29.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
57.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.re))

series237.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x.re x.im) (* x.im x.re))
87.0ms	(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
45.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
67.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
1	723
0	198

prune629.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

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)))

rewrite75.0ms

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:

50.0ms	(* (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)))
7.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
8.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
160.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
140.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))
135.0ms	(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify1.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1071
1	303
0	119

prune725.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
0.6b	(cbrt (+ x.re x.im))
0.6b	(cbrt (+ x.re x.im))
0.6b	(cbrt (+ x.re x.im))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`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 → 95

Calls

4 calls:

46.0ms	(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
3.0ms	(cbrt (+ x.re x.im))
3.0ms	(cbrt (+ x.re x.im))
3.0ms	(cbrt (+ x.re x.im))

series764.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
191.0ms	(cbrt (+ x.re x.im))
174.0ms	(cbrt (+ x.re x.im))
177.0ms	(cbrt (+ x.re x.im))

simplify1.3s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1127
1	278
0	116

prune764.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
3	20
2	18
1	16
0	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

14457×

body

valid