Details

sample375.0ms

Algorithm

intervals

Results

41.0ms	67×	body	1280	valid
35.0ms	59×	body	640	valid
26.0ms	263×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(cos (+ (* (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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

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

series243.0ms

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)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	456
1	556	415
2	1286	411
3	2863	411
4	5002	411

prune331.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 19.4b

Counts

79 → 3

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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `exp-sum` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `prod-diff` `flip-+` `hypot-def`

Counts

4 → 79

Calls

4 calls:

5.0ms	(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)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
88.0ms	(* (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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	308	585
1	921	522
2	2504	484
3	5002	467

prune276.0ms

Filtered

91 candidates to 74 candidates (81.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Merged error: 4.2b

Counts

94 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (hypot x.re x.im)) y.re)
1.7b	(* (atan2 x.im x.re) y.im)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `exp-sum`
2×	`sub-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`flip3--` `exp-diff` `fma-neg` `log-pow` `flip--`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms	(* (log (hypot x.re x.im)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series346.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
99.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
99.0ms	(* (log (hypot x.re x.im)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify81.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	265	517
1	869	474
2	2937	463
3	5001	458

prune228.0ms

Filtered

87 candidates to 65 candidates (74.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 4.2b

Counts

92 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))))
1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.im)

rewrite17.0ms

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`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `cbrt-div` `exp-diff` `pow1/3` `prod-diff`

Counts

4 → 77

Calls

4 calls:

4.0ms	(cbrt (exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))))
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)

series177.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (exp (- (* (log (hypot x.re x.im)) y.re) (* (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)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify204.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	174	468
1	492	420
2	1302	411
3	4062	408
4	5001	408

prune296.0ms

Filtered

89 candidates to 64 candidates (71.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	89	6	95

Merged error: 4.2b

Counts

95 → 6

regimes148.0ms

Accuracy

0% (0.7b remaining)

Error of 4.2b against oracle of 3.6b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	20	7
2	20	7

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	2008×	body	1280	valid
730.0ms	7998×	body	80	valid
635.0ms	1506×	body	640	valid
198.0ms	677×	body	320	valid
59.0ms	308×	body	160	valid