Details

sample65.0ms

Algorithm

intervals

Results

45.0ms

269×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize38.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 49

Calls

2 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
55.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
107.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify909.0ms

Counts

55 → 55

Iterations

Iter	Nodes
3	2803
2	894
1	249
0	92

prune671.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.7b

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
15.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite65.0ms

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`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* x.re y.re) (* x.im y.im))
143.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify902.0ms

Counts

111 → 111

Iterations

Iter	Nodes
3	2551
2	906
1	301
0	126

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.7b

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
16.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `fma-def` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 109

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
61.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x.re y.re) (* x.im y.im))
158.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

121 → 121

Iterations

Iter	Nodes
3	4363
2	1368
1	410
0	155

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.7b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
15.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

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`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* x.re y.re) (* x.im y.im))
131.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify947.0ms

Counts

111 → 111

Iterations

Iter	Nodes
3	2551
2	906
1	301
0	126

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 22.7b

regimes414.0ms

Accuracy

0% (2.6b remaining)

Error of 25.8b against oracle of 23.2b and baseline of 25.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s

8511×

body

valid