Details

sample303.0ms

Algorithm

intervals

Results

23.0ms	255×	body	80	valid
12.0ms	149×	body	80	overflowed
4.0ms	6×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.5b

localize33.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (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

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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(cos (+ (* (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:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2496	381
4	5001	381

prune325.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.6b

localize16.0ms

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)
2.2b	(* (atan2 x.im x.re) y.im)
33.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:

8.0ms	(exp (- (* (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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (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)))

simplify57.0ms

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

prune291.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ -1 x.re) y.re)
0.0b	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
2.2b	(* (atan2 x.im x.re) y.im)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
67×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
17×	`associate-/r*`
13×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`exp-prod` `div-exp` `div-inv` `add-log-exp`
5×	`sqr-pow`
4×	`pow-exp`
3×	`pow-unpow` `associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `pow-to-exp` `exp-diff` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `neg-mul-1` `pow-pow` `distribute-rgt-neg-in` `frac-2neg` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

3.0ms	(pow (/ -1 x.re) y.re)
14.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
2.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series192.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ -1 x.re) y.re)
91.0ms	(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
23.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify63.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	534	1633
1	2176	1576
2	5002	1576

prune565.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
2.2b	(* (atan2 x.im x.re) y.im)
2.2b	(* (atan2 x.im x.re) y.im)
2.2b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`cbrt-prod` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-div`
1×	`neg-sub0` `exp-neg` `exp-diff` `pow1/3`

Counts

4 → 67

Calls

4 calls:

2.0ms	(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.im)

series99.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(cbrt (exp (- (* (atan2 x.im x.re) y.im))))
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.im)

simplify53.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	119	340
1	434	305
2	1846	303
3	5001	300

prune329.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

regimes307.0ms

Accuracy

53.8% (7.2b remaining)

Error of 11.4b against oracle of 4.2b and baseline of 19.8b

bsearch219.0ms

Steps

Iters	Range		Point
6	1.4752724115702747e-301	1.2498705789582403e-300	7.627135162944657e-301
4	-3.522525476992319e-285	-1.7631587368184673e-285	-2.8652139801084568e-285
10	-1.7006887056910985e-143	-1.8139680146072402e-154	-1.0812928157068453e-151
4	-9.016737826503982e-46	-6.072585905253019e-46	-6.9815058281331826e-46

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	83
1	81	83
2	81	83

end0.0ms

sample1.6s

Algorithm

intervals

Results

676.0ms	7953×	body	80	valid
342.0ms	4063×	body	80	overflowed
79.0ms	128×	body	1280	valid
70.0ms	175×	body	640	valid
29.0ms	105×	body	320	valid
12.0ms	66×	body	160	valid