Details

sample411.0ms

Algorithm

intervals

Results

56.0ms	68×	body	1280	valid
38.0ms	58×	body	640	valid
37.0ms	256×	body	80	valid
10.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid

simplify39.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite28.0ms

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

series248.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
146.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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

prune374.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.7b

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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
33.2b	(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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(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)
20.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (58.0ms)

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

prune340.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (hypot x.re x.im) y.re))
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.3b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
1.7b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `exp-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log` `log-prod` `add-log-exp`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rem-log-exp` `associate-r` `associate-l` `rem-exp-log`
2×	`sqr-pow`
1×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `exp-diff` `pow-prod-down` `neg-log` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

3.0ms	(exp (pow (hypot x.re x.im) y.re))
2.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
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)

series331.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(exp (pow (hypot x.re x.im) y.re))
24.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
154.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify132.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	294	551
1	994	487
2	4741	467
3	5001	467

prune357.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
0.9b	(cbrt (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.im)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(cbrt (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
2.0ms	(cbrt (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)
5.0ms	(* (atan2 x.im x.re) y.im)

series453.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
211.0ms	(cbrt (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
17.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.im)

simplify61.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	205	740
1	645	680
2	2209	666
3	5001	660

prune422.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

regimes165.0ms

Accuracy

0% (1.3b remaining)

Error of 5.2b against oracle of 3.8b and baseline of 5.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	34
1	36	34
2	36	34

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1986×	body	1280	valid
1.1s	7939×	body	80	valid
830.0ms	1432×	body	640	valid
287.0ms	679×	body	320	valid
90.0ms	314×	body	160	valid