Details

sample372.0ms

Algorithm

intervals

Results

40.0ms	69×	body	1280	valid
20.0ms	249×	body	80	valid
19.0ms	45×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	16×	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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
27.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series223.0ms

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)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(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

prune374.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
2.4b	(* (atan2 x.im x.re) y.im)
27.1b	(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)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
82.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (59.0ms)

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

prune329.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (* 1 (hypot x.re x.im))) y.re)
2.4b	(* (atan2 x.im x.re) y.im)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

10.0ms	(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
27.0ms	(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
16.0ms	(* (log (* 1 (hypot x.re x.im))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

series323.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im))
93.0ms	(exp (- (* (log (* 1 (hypot x.re x.im))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (log (* 1 (hypot x.re x.im))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)

simplify101.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	269	584
1	861	528
2	3384	509
3	5001	508

prune307.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(exp (atan2 x.im x.re))
0.5b	(exp (atan2 x.im x.re))
0.5b	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))
0.5b	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
96×	`unpow-prod-down`
70×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`sqr-pow`
22×	`add-exp-log`
18×	`div-exp`
14×	`associate-/r` `associate-/l`
12×	`pow-to-exp` `pow-exp`
8×	`add-cbrt-cube`
6×	`exp-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 196

Calls

4 calls:

2.0ms	(exp (atan2 x.im x.re))
2.0ms	(exp (atan2 x.im x.re))
12.0ms	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))
13.0ms	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (atan2 x.im x.re))
13.0ms	(exp (atan2 x.im x.re))
135.0ms	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))
140.0ms	(/ (pow (hypot x.re x.im) (/ y.re 2)) (pow (exp (atan2 x.im x.re)) (/ y.im 2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	324	2708
1	1145	2644
2	5002	2644

prune846.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.9b

regimes186.0ms

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	8
1	24	8
2	24	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1909×	body	1280	valid
663.0ms	8000×	body	80	valid
554.0ms	1436×	body	640	valid
166.0ms	614×	body	320	valid
50.0ms	289×	body	160	valid