Details

sample49.0ms

Algorithm

intervals

Results

36.0ms

458×

body

valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2763
5	1086
4	382
3	146
2	55
1	24
0	11

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x.re x.re) (* x.im x.im))
0.2b	(- (* (- (* 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)
6.3b	(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite129.0ms

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`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(- (* x.re x.re) (* x.im x.im))
28.0ms	(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
43.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)
46.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

series235.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x.re x.re) (* x.im x.im))
77.0ms	(- (* (- (* 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)
77.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify2.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1905
1	445
0	158

prune445.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*l/`
18×	`flip3-+` `flip-+`
16×	`frac-sub`
15×	`add-sqr-sqrt`
13×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
12×	`frac-times` `associate-l`
11×	`flip3--` `flip--`
9×	`add-cube-cbrt`
7×	`associate-r`
6×	`associate-*r/` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

15.0ms	(* (- x.re x.im) x.re)
52.0ms	(- (* (+ 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.re x.im) x.re))
24.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)

series233.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (- x.re x.im) x.re)
81.0ms	(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
59.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.re))
31.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.im)

simplify2.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	4132
1	803
0	228

prune615.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`flip3-+` `distribute-rgt-out` `count-2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `neg-mul-1` `sum-log` `fma-def` `flip3--` `distribute-rgt-neg-out` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

14.0ms	(+ (* x.re x.im) (* x.re x.im))
17.0ms	(* (- x.re x.im) x.re)
0.0ms	(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* (+ (* x.re x.im) (* x.re x.im)) (- x.im)))
29.0ms	(* (+ (* x.re x.im) (* x.re x.im)) (- x.im))

series224.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x.re x.im) (* x.re x.im))
61.0ms	(* (- x.re x.im) x.re)
93.0ms	(fma (+ x.re x.im) (* (- x.re x.im) x.re) (* (+ (* x.re x.im) (* x.re x.im)) (- x.im)))
44.0ms	(* (+ (* x.re x.im) (* x.re x.im)) (- x.im))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1360
1	318
0	135

prune517.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
16.3b	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
16.3b	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
16.3b	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

176×	`associate-*l/`
168×	`cbrt-div`
148×	`frac-times`
63×	`flip3-+` `flip3--` `flip-+` `flip--`
50×	`associate-*r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

91.0ms	(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
42.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
31.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
32.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
152.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
192.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
206.0ms	(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

simplify2.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	4707
2	1174
1	447
0	257

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
4	28
3	23
2	20
1	16
0	10

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

14424×

body

valid