Details

sample428.0ms

Algorithm

intervals

Results

43.0ms	73×	body	1280	valid
39.0ms	49×	body	640	valid
22.0ms	247×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid

simplify42.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize31.0ms

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×	`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)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

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

prune312.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize18.0ms

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)))

rewrite46.0ms

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:

19.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
89.0ms	(* (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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (23.0ms)

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

prune289.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt 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)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`sqrt-prod`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify152.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (147.0ms)

Iter	Nodes	Cost
0	232	495
1	586	443
2	1587	439
3	4527	432
4	5002	431

prune364.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

3.6b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt 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)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-prod` `cos-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

15.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(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)))

simplify114.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	184	440
1	396	400
2	1041	398
3	3217	396
4	5001	396

prune327.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes304.0ms

Accuracy

62.9% (6.1b remaining)

Error of 9.6b against oracle of 3.6b and baseline of 19.9b

bsearch305.0ms

Steps

Iters	Range	Point
8	-1.3287558847979414e-305	4.527111501653717e-308	-1.1974408710008e-310
9	-2.141684871670345e-153	-2.352808649179745e-159	-3.011667906396995e-159
10	-3.854589780371342e+164	-1.6181289332921645e+150	-6.451247643666555e+153

Iters

Range

Point

-1.3287558847979414e-305

4.527111501653717e-308

-1.1974408710008e-310

-2.141684871670345e-153

-2.352808649179745e-159

-3.011667906396995e-159

-3.854589780371342e+164

-1.6181289332921645e+150

-6.451247643666555e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	34
1	55	34
2	55	34

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2046×	body	1280	valid
666.0ms	7961×	body	80	valid
570.0ms	1466×	body	640	valid
173.0ms	648×	body	320	valid
56.0ms	322×	body	160	valid