Details

sample310.0ms

Algorithm

intervals

Results

24.0ms	255×	body	80	valid
12.0ms	149×	body	80	overflowed
4.0ms	6×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	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: 36.5b

localize36.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(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)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms	(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 (14.0ms)

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

prune376.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.6b

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)
2.2b	(* (atan2 x.im x.re) y.im)
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:

8.0ms	(exp (- (* (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)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (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

prune331.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im))))
0.0b	(exp (pow (hypot x.re x.im) y.re))
0.1b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
2.2b	(* (atan2 x.im x.re) y.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im))))
3.0ms	(exp (pow (hypot x.re x.im) y.re))
3.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
3.0ms	(* (atan2 x.im x.re) y.im)

series464.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im))))
129.0ms	(exp (pow (hypot x.re x.im) y.re))
148.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
20.0ms	(* (atan2 x.im x.re) y.im)

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	310	742
1	1084	679
2	5001	640

prune390.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (hypot x.re x.im) y.re))
0.1b	(log (pow (log1p (expm1 (exp (pow (hypot x.re x.im) y.re)))) (exp (- (* (atan2 x.im x.re) y.im)))))
1.0b	(expm1 (exp (pow (hypot x.re x.im) y.re)))
2.2b	(* (atan2 x.im x.re) y.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

3.0ms	(exp (pow (hypot x.re x.im) y.re))
1.0ms	(log (pow (log1p (expm1 (exp (pow (hypot x.re x.im) y.re)))) (exp (- (* (atan2 x.im x.re) y.im)))))
0.0ms	(expm1 (exp (pow (hypot x.re x.im) y.re)))
3.0ms	(* (atan2 x.im x.re) y.im)

series520.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(exp (pow (hypot x.re x.im) y.re))
183.0ms	(log (pow (log1p (expm1 (exp (pow (hypot x.re x.im) y.re)))) (exp (- (* (atan2 x.im x.re) y.im)))))
187.0ms	(expm1 (exp (pow (hypot x.re x.im) y.re)))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify140.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	329	605
1	1131	506
2	4875	491
3	5001	491

prune344.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.4b

regimes181.0ms

Accuracy

0% (0.6b remaining)

Error of 4.4b against oracle of 3.7b and baseline of 4.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	29	11
2	29	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

670.0ms	7953×	body	80	valid
331.0ms	4063×	body	80	overflowed
81.0ms	128×	body	1280	valid
69.0ms	175×	body	640	valid
29.0ms	105×	body	320	valid
12.0ms	66×	body	160	valid