Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

271×

body

valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.3b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite33.0ms

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))
10.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma y.im y.im (* y.re y.re))
45.0ms	(- (* x.im y.re) (* x.re y.im))
108.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1160
1	233
0	96

prune516.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.7b	(sqrt (fma y.im y.im (* y.re y.re)))
28.7b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite52.0ms

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)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* x.im y.re) (* x.re y.im))
171.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1033
1	267
0	114

prune831.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
0.5b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.7b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite73.0ms

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` `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 → 185

Calls

4 calls:

19.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
8.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
76.0ms	(- (* x.im y.re) (* x.re y.im))
186.0ms	(/ (- (* 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)))

simplify2.0s

Counts

197 → 197

Iterations

Iter	Nodes
done	5002
2	2797
1	624
0	255

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(- (* y.re x.im) (* y.im x.re))
16.4b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.im y.re)
31.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
13.0ms	(- (* y.re x.im) (* y.im x.re))
17.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

series549.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(hypot y.im y.re)
192.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re)) (hypot y.im y.re))
74.0ms	(- (* y.re x.im) (* y.im x.re))
206.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.im y.re))

simplify1.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5002
2	2290
1	483
0	192

prune943.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

regimes478.0ms

Accuracy

30.6% (7.6b remaining)

Error of 13.4b against oracle of 5.8b and baseline of 16.7b

bsearch131.0ms

Steps

Iters	Range		Point
10	1.5425824365857962e+73	1.5192017912580791e+85	2.805404912411876e+84
8	-3.35691658268957e+164	-1.5338344244864082e+161	-8.30562369060115e+163

simplify4.0ms

Iterations

Iter	Nodes
done	27
2	27
1	25
0	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

8499×

body

valid