Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

272×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7
done	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (* x.im y.re) (* x.re y.im))
26.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
88.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify100.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421
done	5001	421

prune141.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
1.2b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
32×	`prod-exp`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 120

Calls

4 calls:

0.0ms	(hypot y.re y.im)
52.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
9.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series387.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
181.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
40.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify56.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	546	1122
1	2249	931
2	5002	929
done	5002	929

prune311.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
1.2b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot y.re y.im)
21.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
11.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series330.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot y.re y.im)
122.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
41.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify45.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	432	989
1	1705	876
2	5001	875
done	5001	875

prune312.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
1.2b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

249×	`add-exp-log`
171×	`times-frac`
120×	`div-exp`
112×	`prod-exp`
109×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
95×	`add-cube-cbrt`
64×	`1-exp`
50×	`associate-r`
47×	`add-cbrt-cube`
43×	`rec-exp`
19×	`cbrt-undiv`
18×	`associate-/r*` `associate-/r/`
12×	`pow1` `cbrt-unprod`
11×	`div-inv`
9×	`flip3--` `flip--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
5×	`pow-flip` `pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 292

Calls

4 calls:

20.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
81.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
8.0ms	(- (* x.im y.re) (* x.re y.im))
15.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
180.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
38.0ms	(- (* x.im y.re) (* x.re y.im))
95.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify100.0ms

Counts

304 → 304

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1165	3311
1	4700	2898
2	5002	2690
done	5002	2690

prune519.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes195.0ms

Accuracy

33.7% (8.3b remaining)

Error of 12.9b against oracle of 4.7b and baseline of 17.1b

bsearch77.0ms

Steps

Iters	Range		Point
10	4.4479863906389105e+146	5.819673793962513e+160	3.180043411345888e+156
10	-1.278229714437347e+143	-1.3757182438677812e+128	-1.466824429873716e+138

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	32	15
2	32	15
done	32	15

end0.0ms

sample554.0ms

Algorithm

intervals

Results

275.0ms

8516×

body

valid