Details

sample443.0ms

Algorithm

intervals

Results

81.0ms	87×	body	1280	valid
46.0ms	254×	body	80	valid
31.0ms	51×	body	640	valid
9.0ms	20×	body	320	valid
6.0ms	3×	body	2560	valid
3.0ms	9×	body	160	valid

simplify39.0ms

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: 30.6b

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(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:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

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)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune334.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize32.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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` `sin-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (* (atan2 x.im x.re) y.im))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1976	373
4	5002	371

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize33.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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` `sin-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(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)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt (* (atan2 x.im x.re) y.im))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1976	373
4	5002	371

prune398.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize37.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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` `sin-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (* (atan2 x.im x.re) y.im))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (* (atan2 x.im x.re) y.im))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify70.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1976	373
4	5002	371

prune377.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

regimes372.0ms

Accuracy

68.2% (4.4b remaining)

Error of 23.7b against oracle of 19.3b and baseline of 33.1b

bsearch646.0ms

Steps

Iters	Range		Point
9	2.3339507455991238e-125	4.6244931228009117e-119	4.281341901471708e-125
7	1.0553182922645175e-197	1.7881242210647934e-195	4.2240617406325604e-196
9	-2.1428949923893228e-303	3.863692482921592e-307	7.779861495065443e-309
8	-2.4518782512689756e-57	-9.251492437512707e-60	-9.800465451807095e-60

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	228
1	88	228
2	91	228
3	91	228

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.0s	2299×	body	1280	valid
1.4s	7943×	body	80	valid
883.0ms	1416×	body	640	valid
259.0ms	576×	body	320	valid
99.0ms	53×	body	2560	valid
74.0ms	237×	body	160	valid