Details

sample26.0ms

Algorithm

intervals

Results

14.0ms

273×

body

valid

simplify65.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite46.0ms

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--` `insert-posit16` `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 → 50

Calls

2 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series197.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(- (* x.im y.re) (* x.re y.im))
136.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
3	2513
2	716
1	223
0	90

prune355.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.3b	(sqrt (fma y.im y.im (* y.re y.re)))
29.3b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite41.0ms

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` `insert-posit16` `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 → 96

Calls

4 calls:

9.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* x.im y.re) (* x.re y.im))
161.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
58.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2132
2	759
1	270
0	117

prune549.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
0.2b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.3b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 189

Calls

4 calls:

28.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
15.0ms	(- (* x.im y.re) (* x.re y.im))
42.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
42.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.4s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	1674
1	623
0	259

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.2b	(- (* y.re x.im) (* y.im x.re))
15.0b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 124

Calls

3 calls:

33.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
16.0ms	(- (* y.re x.im) (* y.im x.re))
40.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

series366.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
65.0ms	(- (* y.re x.im) (* y.im x.re))
150.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

simplify1.6s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1469
1	461
0	188

prune621.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes254.0ms

Accuracy

39% (6.6b remaining)

Error of 12.3b against oracle of 5.7b and baseline of 16.5b

bsearch76.0ms

Steps

Iters	Range		Point
6	2.8364102844858466e+132	3.3182823546818055e+133	7.209078410675665e+132
9	-5.99730792027498e+155	-1.8300824072553637e+149	-4.78970221325173e+151

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

969.0ms

8506×

body

valid