Details

sample45.0ms

Algorithm

intervals

Results

23.0ms

275×

body

valid

simplify68.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize17.0ms

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)))

rewrite24.0ms

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:

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

series148.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
105.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	3623
2	800
1	221
0	88

prune396.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 24.2b

localize30.0ms

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)))

rewrite35.0ms

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))
20.0ms	(/ (- (* 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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* x.im y.re) (* x.re y.im))
193.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
86.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
80.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1033
1	267
0	114

prune773.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize35.0ms

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))
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)))

rewrite86.0ms

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:

30.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
13.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* 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)))

series648.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
69.0ms	(- (* x.im y.re) (* x.re y.im))
202.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
83.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.6s

Counts

197 → 197

Iterations

Iter	Nodes
done	5002
2	2797
1	624
0	255

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
1.1b	(- (* x.im y.re) (* x.re y.im))
15.6b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

25.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
7.0ms	(- (* x.im y.re) (* x.re y.im))
46.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re)))

series426.0ms

Counts

3 → 9

Calls

3 calls:

201.0ms	(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
56.0ms	(- (* x.im y.re) (* x.re y.im))
169.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.im y.re)))

simplify2.9s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	3193
1	430
0	150

prune606.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

regimes603.0ms

Accuracy

34% (7.3b remaining)

Error of 13.0b against oracle of 5.7b and baseline of 16.7b

bsearch130.0ms

Steps

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

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

802.0ms

8432×

body

valid