Details

sample369.0ms

Algorithm

intervals

Results

47.0ms	73×	body	1280	valid
22.0ms	238×	body	80	valid
16.0ms	40×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid

simplify38.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.2b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

4.0ms	(* (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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(sin (+ (* (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 (13.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize27.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sin (+ (* (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

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×	`sin-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify141.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (135.0ms)

Iter	Nodes	Cost
0	237	500
1	591	448
2	1598	444
3	4562	437
4	5002	436

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.8b

localize33.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
141.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify159.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1523	487
4	4766	486
5	5002	486

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.8b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`sin-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)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series233.0ms

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)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	427
1	506	390
2	1139	386
3	2509	386
4	5001	386

prune304.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.8b

regimes341.0ms

Accuracy

76.9% (3.3b remaining)

Error of 22.5b against oracle of 19.2b and baseline of 33.5b

bsearch424.0ms

Steps

Iters	Range	Point
9	-1.3660599968596594e-302	4.521562716650534e-309	-3.4831262277498e-310
11	-1.7126236893778652e-152	-3.963250735052942e-182	-5.998443331646264e-160
8	-1.626397734379993e-31	-1.6389762002272076e-34	-2.2874670419255224e-34

Iters

Range

Point

-1.3660599968596594e-302

4.521562716650534e-309

-3.4831262277498e-310

-1.7126236893778652e-152

-3.963250735052942e-182

-5.998443331646264e-160

-1.626397734379993e-31

-1.6389762002272076e-34

-2.2874670419255224e-34

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	119
1	63	119

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2218×	body	1280	valid
685.0ms	7950×	body	80	valid
570.0ms	1410×	body	640	valid
167.0ms	594×	body	320	valid
86.0ms	56×	body	2560	valid
47.0ms	254×	body	160	valid