Details

sample370.0ms

Algorithm

intervals

Results

41.0ms	69×	body	1280	valid
21.0ms	249×	body	80	valid
20.0ms	45×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	16×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune23.0ms

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)))

rewrite50.0ms

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×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(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)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune313.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.2b

localize16.0ms

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`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

21.0ms	(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)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(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)
33.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2118	481
3	5001	481

prune277.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (/ 1 x.re) y.re)
0.5b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
2.4b	(* (atan2 x.im x.re) y.im)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
65×	`add-sqr-sqrt` `unpow-prod-down`
63×	`add-cube-cbrt` `*-un-lft-identity`
17×	`associate-/r*`
16×	`add-exp-log`
10×	`div-exp`
8×	`pow-exp`
7×	`pow1` `add-cbrt-cube`
6×	`div-inv`
5×	`sqr-pow`
3×	`pow-unpow` `pow-pow` `associate-r` `associate-l` `associate-/l*` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `exp-neg` `pow-flip` `frac-2neg` `exp-diff` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

3 → 140

Calls

3 calls:

7.0ms	(pow (/ 1 x.re) y.re)
24.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
7.0ms	(* (atan2 x.im x.re) y.im)

series128.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(pow (/ 1 x.re) y.re)
72.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
15.0ms	(* (atan2 x.im x.re) y.im)

simplify59.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	461	1540
1	1811	1451
2	5001	1441

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ 1 x.re) y.re))
0.2b	(/ (/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re)))) (cbrt (pow (/ 1 x.re) y.re)))
0.5b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re))))
2.4b	(* (atan2 x.im x.re) y.im)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

287×	`times-frac`
153×	`cbrt-prod`
132×	`add-sqr-sqrt`
130×	`add-cube-cbrt` `*-un-lft-identity`
117×	`unpow-prod-down`
32×	`div-inv`
21×	`associate-/r*`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`sqr-pow`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`neg-sub0` `exp-neg` `exp-diff` `pow1/3` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 250

Calls

4 calls:

5.0ms	(cbrt (pow (/ 1 x.re) y.re))
50.0ms	(/ (/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re)))) (cbrt (pow (/ 1 x.re) y.re)))
26.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re))))
7.0ms	(* (atan2 x.im x.re) y.im)

series296.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(cbrt (pow (/ 1 x.re) y.re))
73.0ms	(/ (/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re)))) (cbrt (pow (/ 1 x.re) y.re)))
137.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (* (cbrt (pow (/ 1 x.re) y.re)) (cbrt (pow (/ 1 x.re) y.re))))
15.0ms	(* (atan2 x.im x.re) y.im)

simplify109.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	930	5763
1	3518	5429
2	5001	5409

prune961.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

regimes230.0ms

Accuracy

51.5% (7.6b remaining)

Error of 11.2b against oracle of 3.6b and baseline of 19.2b

bsearch504.0ms

Steps

Iters	Range		Point
10	7.626026030886938e-121	1.0552318090987947e-110	5.381096841343168e-111
8	4.642616563637219e-233	5.812451751464859e-230	8.491943082054637e-233
7	-2.4823423547568707e-293	-5.453313162155254e-295	-5.538766143941085e-295
7	-1.6994146232147158e-251	-9.545328849940457e-253	-3.9259927672133025e-252
9	-4.72130842837958e-05	-2.0303826557161976e-11	-7.902239802261551e-11

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	74
1	80	74
2	80	74

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	1909×	body	1280	valid
685.0ms	8000×	body	80	valid
550.0ms	1436×	body	640	valid
165.0ms	614×	body	320	valid
53.0ms	289×	body	160	valid