Details

sample36.0ms

Algorithm

intervals

Results

23.0ms

455×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1115
4	335
3	127
2	51
1	20
0	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize31.0ms

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.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
6.5b	(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite97.0ms

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×	`frac-add`
3×	`flip3--` `flip--`
2×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`difference-of-squares`

Counts

4 → 67

Calls

4 calls:

12.0ms	(+ (* x.re x.im) (* x.im x.re))
36.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
20.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
26.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)

series262.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* x.re x.im) (* x.im x.re))
96.0ms	(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
37.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
92.0ms	(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	2761
1	419
0	135

prune517.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*l/`
20×	`flip3-+` `flip-+`
16×	`frac-add`
12×	`frac-times`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `*-un-lft-identity` `flip3--` `flip--`
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` `sum-log` `*-commutative`
1×	`distribute-lft-out` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

9.0ms	(+ (* x.re x.im) (* x.im x.re))
44.0ms	(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
28.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
56.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.im))

series259.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* x.re x.im) (* x.im x.re))
98.0ms	(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
31.0ms	(* (+ (* x.re x.im) (* x.im x.re)) x.re)
84.0ms	(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify440.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
1	715
0	197

prune574.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* x.im (+ x.re x.re)) x.re)) (cbrt (* (* x.im (+ x.re x.re)) x.re)))
26.3b	(cbrt (* (* x.im (+ x.re x.re)) x.re))
26.3b	(cbrt (* (* x.im (+ x.re x.re)) x.re))
26.3b	(cbrt (* (* x.im (+ x.re x.re)) x.re))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-l/` `associate-r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `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 → 72

Calls

4 calls:

39.0ms	(* (cbrt (* (* x.im (+ x.re x.re)) x.re)) (cbrt (* (* x.im (+ x.re x.re)) x.re)))
40.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))
39.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))
22.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))

series772.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(* (cbrt (* (* x.im (+ x.re x.re)) x.re)) (cbrt (* (* x.im (+ x.re x.re)) x.re)))
154.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))
179.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))
175.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))

simplify586.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	984
1	300
0	121

prune665.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt x.re) (cbrt x.re))
13.4b	(cbrt (* (* x.im 2) x.re))
13.4b	(cbrt (* (* x.im 2) x.re))
26.3b	(cbrt (* (* x.im (+ x.re x.re)) x.re))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

11.0ms	(* (cbrt x.re) (cbrt x.re))
10.0ms	(cbrt (* (* x.im 2) x.re))
23.0ms	(cbrt (* (* x.im 2) x.re))
30.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))

series1.1s

Counts

4 → 12

Calls

4 calls:

339.0ms	(* (cbrt x.re) (cbrt x.re))
133.0ms	(cbrt (* (* x.im 2) x.re))
130.0ms	(cbrt (* (* x.im 2) x.re))
526.0ms	(cbrt (* (* x.im (+ x.re x.re)) x.re))

simplify718.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	947
1	304
0	131

prune604.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes150.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
3	21
2	19
1	17
0	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s

14556×

body

valid