Details

sample436.0ms

Algorithm

intervals

Results

52.0ms	78×	body	1280	valid
44.0ms	253×	body	80	valid
26.0ms	55×	body	640	valid
7.0ms	20×	body	320	valid
1.0ms	4×	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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.5b

localize24.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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:

3.0ms	(* (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)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (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	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune319.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
2.3b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (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)
16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	290	540
1	897	500
2	2667	491
3	5002	491

prune279.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.5b	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`cbrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`sqrt-prod`
8×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod` `associate-r`
4×	`sqrt-div` `add-log-exp`
2×	`cube-div` `cbrt-div` `flip3-+` `pow1/3` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series183.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	329	609
1	1048	548
2	3533	542
3	5002	542

prune326.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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:

3.0ms	(* (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	(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:

16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
134.0ms	(cos (+ (* (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	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune328.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

regimes276.0ms

Accuracy

72.8% (5.8b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 24.7b

bsearch375.0ms

Steps

Iters	Range		Point
10	-9.53539283584192e-295	2.2826757702542398e-303	-6.92145173333843e-310
8	-2.711512310774523e-135	-1.3702607488594748e-138	-2.6820854053599922e-135
7	-73037290446.31708	-339960223.867127	-348135322.851263

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	36
1	58	36
2	58	36

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	1983×	body	1280	valid
1.2s	7978×	body	80	valid
697.0ms	1485×	body	640	valid
227.0ms	641×	body	320	valid
71.0ms	284×	body	160	valid