Details

sample362.0ms

Algorithm

intervals

Results

30.0ms	52×	body	1280	valid
23.0ms	250×	body	80	valid
20.0ms	52×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify86.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	454
1	556	413
2	1286	411
3	2863	411
4	5002	411

prune369.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `hypot-def`

Counts

4 → 77

Calls

4 calls:

3.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
86.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	320	596
1	1020	545
2	3156	516
3	5001	484

prune316.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x.re x.im)
0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (hypot x.re x.im)) y.re)
1.5b	(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1`
8×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `hypot-udef` `flip3--` `fma-neg` `diff-log` `prod-diff` `log-pow` `flip--`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot x.re x.im)
3.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
3.0ms	(* (log (hypot x.re x.im)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series286.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot x.re x.im)
126.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
97.0ms	(* (log (hypot x.re x.im)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify71.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	247	377
1	794	346
2	2559	342
3	5002	337

prune257.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
131.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	454
1	556	413
2	1286	411
3	2863	411
4	5002	411

prune389.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.7b

regimes123.0ms

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	20	7
2	20	7

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2039×	body	1280	valid
668.0ms	7988×	body	80	valid
603.0ms	1558×	body	640	valid
179.0ms	664×	body	320	valid
49.0ms	284×	body	160	valid