Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

273×

body

valid

simplify12.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
28.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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:

3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series120.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify103.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (95.0ms)

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

prune157.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(- (* x.im y.re) (* x.re y.im))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

4.0ms	(/ 1 (* (hypot y.re y.im) 1))
3.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series387.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (* (hypot y.re y.im) 1))
38.0ms	(- (* x.im y.re) (* x.re y.im))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	555	1211
1	2307	1003
2	5001	995

prune333.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 121

Calls

3 calls:

9.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series260.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify48.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	451	1408
1	1659	1307
2	5001	1298

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.2b	(- (* x.im y.re) (* x.re y.im))
17.4b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
255×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
56×	`associate-/l*`
39×	`associate-/r/`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
21×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 359

Calls

4 calls:

23.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
11.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
117.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
39.0ms	(- (* x.im y.re) (* x.re y.im))
91.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1296	5404
1	5002	4894

prune806.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

regimes209.0ms

Accuracy

29.2% (9.0b remaining)

Error of 13.6b against oracle of 4.6b and baseline of 17.3b

bsearch83.0ms

Steps

Iters	Range		Point
8	5.265695259277909e+173	7.825150772293386e+177	1.5910699936696656e+174
9	-1.085810015494438e+65	-1.2809166914199238e+60	-1.0689057415946615e+65

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	13
1	32	13
2	32	13

end0.0ms

sample508.0ms

Algorithm

intervals

Results

295.0ms

8485×

body

valid