Details

sample46.0ms

Algorithm

intervals

Results

25.0ms

276×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.7b	(- (* x.im y.re) (* x.re y.im))
25.7b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
11.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma y.im y.im (* y.re y.re))
46.0ms	(- (* x.im y.re) (* x.re y.im))
99.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5004
3	3468
2	916
1	233
0	96

prune350.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 25.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.2b	(sqrt (fma y.im y.im (* y.re y.re)))
31.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite50.0ms

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` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 92

Calls

4 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
141.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
47.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	2174
2	761
1	267
0	114

prune645.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
31.2b	(sqrt (fma y.im y.im (* y.re y.re)))
31.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
169.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
50.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
3	3164
2	947
1	338
0	139

prune744.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
25.7b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite43.0ms

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` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 48

Calls

2 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
28.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series218.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (* x.im y.re) (* x.re y.im))
151.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	2539
2	718
1	221
0	88

prune363.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.0b

regimes439.0ms

Accuracy

-1.8% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch63.0ms

Steps

Iters	Range		Point
9	2.1675332614166088e+58	1.841919235217342e+66	1.9376700173410365e+62

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

696.0ms

8474×

body

valid