Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

271×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 28.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
28.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite35.0ms

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)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
82.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (99.0ms)

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

prune144.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
18.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite95.0ms

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:

11.0ms	(/ 1 (* (hypot y.re y.im) 1))
53.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
8.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series372.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (* (hypot y.re y.im) 1))
174.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
36.0ms	(- (* x.im y.re) (* x.re y.im))
111.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify62.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	555	1207
1	2306	1003
2	5003	995

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

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))
0.5b	(- (* x.im y.re) (* x.re y.im))
18.3b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite51.0ms

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:

18.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series256.0ms

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))
36.0ms	(- (* x.im y.re) (* x.re y.im))
108.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

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

prune305.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))))
9.4b	(/ (* x.im y.re) (hypot y.re y.im))
11.2b	(/ (* x.re y.im) (hypot y.re y.im))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

147×	`prod-diff`
138×	`times-frac`
103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
97×	`add-cube-cbrt`
51×	`distribute-rgt-in` `distribute-lft-in`
50×	`div-inv`
40×	`add-exp-log`
23×	`add-cbrt-cube`
18×	`prod-exp`
10×	`div-exp`
7×	`fma-neg` `associate-l`
6×	`pow1` `cbrt-undiv` `1-exp` `associate-r` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `rec-exp` `flip3--` `frac-sub` `flip--` `sub-div`
2×	`distribute-rgt-out--` `frac-2neg` `clear-num` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 270

Calls

4 calls:

22.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
95.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))))
10.0ms	(/ (* x.im y.re) (hypot y.re y.im))
10.0ms	(/ (* x.re y.im) (hypot y.re y.im))

series600.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
282.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))))
68.0ms	(/ (* x.im y.re) (hypot y.re y.im))
70.0ms	(/ (* x.re y.im) (hypot y.re y.im))

simplify133.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1076	6073
1	4858	4269
2	5001	4268

prune416.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	33
1	37	33
2	37	33

end0.0ms

sample564.0ms

Algorithm

intervals

Results

280.0ms

8475×

body

valid