Details

sample433.0ms

Algorithm

intervals

Results

43.0ms	73×	body	1280	valid
22.0ms	12×	body	160	valid
22.0ms	247×	body	80	valid
20.0ms	49×	body	640	valid
6.0ms	22×	body	320	valid

simplify38.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	456
1	556	415
2	1286	411
3	2863	411
4	5002	411

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.9b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

20.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
94.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	308	585
1	921	522
2	2504	484
3	5002	467

prune344.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (exp (log (hypot x.re x.im)))) y.re)
2.9b	(* (atan2 x.im x.re) y.im)
5.6b	(exp (log (hypot x.re x.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `exp-prod` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow` `add-log-exp`
6×	`associate-r` `exp-sum`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `rem-exp-log`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `exp-diff` `diff-log` `prod-diff`

Counts

4 → 80

Calls

4 calls:

24.0ms	(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
16.0ms	(* (log (exp (log (hypot x.re x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(exp (log (hypot x.re x.im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
112.0ms	(* (log (exp (log (hypot x.re x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
49.0ms	(exp (log (hypot x.re x.im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	258	497
1	699	434
2	2091	412
3	5001	406

prune338.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
0.3b	(* (log (exp (log (hypot x.re x.im)))) y.re)
2.9b	(* (atan2 x.im x.re) y.im)
5.6b	(exp (log (hypot x.re x.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `exp-prod` `add-cbrt-cube`
7×	`log-pow`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p` `rem-exp-log` `expm1-udef`

Counts

4 → 73

Calls

4 calls:

0.0ms	(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
15.0ms	(* (log (exp (log (hypot x.re x.im)))) y.re)
9.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(exp (log (hypot x.re x.im)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(expm1 (log1p (exp (- (* (log (exp (log (hypot x.re x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
102.0ms	(* (log (exp (log (hypot x.re x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(exp (log (hypot x.re x.im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	237	464
1	625	392
2	1740	381
3	4715	370
4	5001	370

prune317.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

regimes230.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	24	11
2	24	11

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2046×	body	1280	valid
669.0ms	7961×	body	80	valid
556.0ms	1466×	body	640	valid
169.0ms	648×	body	320	valid
57.0ms	322×	body	160	valid