Details

sample355.0ms

Algorithm

intervals

Results

36.0ms	63×	body	1280	valid
23.0ms	257×	body	80	valid
21.0ms	58×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify51.0ms

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

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 34.9b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
52×	`hypot-def`
32×	`*-un-lft-identity`
24×	`swap-sqr`
21×	`*-commutative` `unswap-sqr`
16×	`sqrt-prod`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `associate-r`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
144.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	204	486
1	528	447
2	1221	443
3	3074	443
4	5001	443

prune399.0ms

Filtered

139 candidates to 84 candidates (39.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Merged error: 19.5b

Counts

141 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
1.9b	(* (atan2 x.im x.re) y.im)
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

212×	`add-sqr-sqrt`
182×	`exp-sum`
180×	`prod-diff`
137×	`associate-l`
113×	`*-un-lft-identity`
91×	`add-cube-cbrt`
87×	`associate-r`
43×	`unswap-sqr`
41×	`log-pow`
39×	`*-commutative`
37×	`pow1`
26×	`hypot-def`
14×	`sqrt-pow1` `pow1/2`
13×	`exp-prod`
12×	`swap-sqr`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
7×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `rem-exp-log`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 298

Calls

4 calls:

36.0ms	(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)
4.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
92.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	878	5864
1	2040	4374
2	5001	2806

prune380.0ms

Filtered

310 candidates to 101 candidates (67.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	307	3	310
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	308	9	317

Merged error: 3.6b

Counts

317 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x.re x.im)
0.0b	(exp (- (* (atan2 x.im x.re) y.im)))
0.2b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
1.9b	(* (atan2 x.im x.re) y.im)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

35×	`exp-prod`
24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`log-pow`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`associate-r` `associate-l`
8×	`pow1` `add-exp-log` `pow-pow`
7×	`log-prod`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `rem-log-exp` `log1p-expm1-u`
3×	`pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-exp-log` `sqr-pow`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `neg-mul-1` `hypot-udef` `exp-diff` `pow-prod-down` `neg-log` `prod-exp` `cbrt-unprod`

Counts

4 → 104

Calls

4 calls:

1.0ms	(hypot x.re x.im)
6.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
8.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
4.0ms	(* (atan2 x.im x.re) y.im)

series243.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot x.re x.im)
25.0ms	(exp (- (* (atan2 x.im x.re) y.im)))
154.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (exp (- (* (atan2 x.im x.re) y.im)))))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify41.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	359	637
1	1228	563
2	5002	549

prune385.0ms

Filtered

116 candidates to 90 candidates (22.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	115	10	125

Merged error: 3.6b

Counts

125 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re)))
0.0b	(hypot x.re x.im)
0.2b	(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re))))
2.0b	(pow (exp (- y.im)) (atan2 x.im x.re))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow-pow`
24×	`exp-prod`
21×	`unpow-prod-down`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`pow-unpow` `log-pow`
8×	`pow1` `add-exp-log`
7×	`log-prod` `sqr-pow`
6×	`pow-exp`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `pow-to-exp` `distribute-rgt-neg-in`
1×	`neg-mul-1` `hypot-udef`

Counts

4 → 108

Calls

4 calls:

5.0ms	(pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re)))
1.0ms	(hypot x.re x.im)
6.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re))))
5.0ms	(pow (exp (- y.im)) (atan2 x.im x.re))

series443.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re)))
50.0ms	(hypot x.re x.im)
171.0ms	(log (pow (exp (pow (hypot x.re x.im) y.re)) (pow (exp (- y.im)) (atan2 x.im x.re))))
33.0ms	(pow (exp (- y.im)) (atan2 x.im x.re))

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	370	898
1	1369	832
2	5002	812

prune390.0ms

Filtered

120 candidates to 98 candidates (18.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	118	12	130

Merged error: 3.6b

Counts

130 → 12

regimes292.0ms

Accuracy

0% (0.9b remaining)

Error of 4.5b against oracle of 3.6b and baseline of 4.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	20
1	24	20
2	24	20

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	2076×	body	1280	valid
653.0ms	7973×	body	80	valid
591.0ms	1549×	body	640	valid
175.0ms	644×	body	320	valid
53.0ms	307×	body	160	valid