Details

sample55.0ms

Algorithm

intervals

Results

20.0ms

273×

body

valid

simplify190.0ms

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize27.0ms

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)))

rewrite57.0ms

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:

17.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series296.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (* x.im y.re) (* x.re y.im))
232.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify4.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
3	2473
2	747
1	224
0	90

prune979.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.7b

localize71.0ms

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)))

rewrite66.0ms

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:

19.0ms	(- (* 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)))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* x.im y.re) (* x.re y.im))
266.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
81.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
82.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify4.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
3	2063
2	743
1	269
0	117

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.7b

localize66.0ms

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)))

rewrite135.0ms

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:

44.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
16.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* 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)))

series992.0ms

Counts

4 → 12

Calls

4 calls:

512.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
100.0ms	(- (* x.im y.re) (* x.re y.im))
284.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
96.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.2s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	1636
1	621
0	259

prune3.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.6b

localize62.0ms

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))

rewrite141.0ms

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:

49.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
21.0ms	(- (* y.re x.im) (* y.im x.re))
51.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

series642.0ms

Counts

3 → 9

Calls

3 calls:

289.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
84.0ms	(- (* y.re x.im) (* y.im x.re))
268.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

simplify3.4s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1472
1	462
0	188

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

regimes1.2s

Accuracy

36.4% (7.8b remaining)

Error of 12.6b against oracle of 4.7b and baseline of 17.0b

bsearch130.0ms

Steps

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

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s

8506×

body

valid