Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

275×

body

valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize20.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
24.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite38.0ms

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:

12.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series174.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* x.im y.re) (* x.re y.im))
131.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify3.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	2514
2	718
1	221
0	88

prune421.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.2b

localize41.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.3b	(sqrt (fma y.im y.im (* y.re y.re)))
31.3b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite27.0ms

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:

7.0ms	(- (* x.im y.re) (* x.re y.im))
16.0ms	(/ (- (* 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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* x.im y.re) (* x.re y.im))
175.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
73.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts

104 → 104

Iterations

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

prune654.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
1.1b	(- (* x.im y.re) (* x.re y.im))
15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
31.3b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`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 → 179

Calls

4 calls:

28.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
6.0ms	(- (* x.im y.re) (* x.re y.im))
15.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
45.0ms	(- (* x.im y.re) (* x.re y.im))
183.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
84.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.5s

Counts

191 → 191

Iterations

Iter	Nodes
done	5003
2	1641
1	591
0	254

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
1.1b	(- (* x.im y.re) (* x.re y.im))
15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite70.0ms

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` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

26.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
12.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series380.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
51.0ms	(- (* x.im y.re) (* x.re y.im))
158.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify1.7s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1450
1	460
0	187

prune947.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

regimes638.0ms

Accuracy

34.1% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.7b

bsearch141.0ms

Steps

Iters	Range		Point
8	7.125568374099785e+144	5.300661243002492e+148	1.3360538186501758e+147
10	-1.1963497052112714e+106	-1.0713785531950437e+91	-1.477885392425796e+104

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

767.0ms

8432×

body

valid