Details

sample369.0ms

Algorithm

intervals

Results

40.0ms	66×	body	1280	valid
24.0ms	259×	body	80	valid
21.0ms	52×	body	640	valid
9.0ms	33×	body	320	valid
1.0ms	8×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

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 (100.0%)

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: 32.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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)
23.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (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:

17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(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)))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	204	484
1	528	447
2	1221	443
3	3074	443
4	5001	443

prune402.0ms

Filtered

139 candidates to 84 candidates (60.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Merged error: 18.6b

Counts

141 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify112.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	254	422
1	709	380
2	1734	378
3	4658	378
4	5001	378

prune371.0ms

Filtered

111 candidates to 71 candidates (64.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 2.5b

Counts

116 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (* 1 (hypot x.re x.im))) y.im)
0.7b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
29.6b	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`pow1`
11×	`associate-l`
10×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cos-sum` `log-pow`
1×	`+-commutative`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (log (* 1 (hypot x.re x.im))) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (log (* 1 (hypot x.re x.im))) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
150.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	224	457
1	688	401
2	1987	394
3	5001	392

prune311.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	9	85
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 2.3b

Counts

90 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
0.7b	(* (atan2 x.im x.re) y.re)
2.3b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.6b	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
36×	`associate-r`
25×	`cbrt-prod`
18×	`unswap-sqr`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
12×	`associate-l`
11×	`pow1` `add-exp-log`
10×	`cbrt-unprod`
8×	`swap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum`
1×	`+-commutative` `pow1/3`

Counts

4 → 102

Calls

4 calls:

1.0ms	(cbrt y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
17.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
85.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
151.0ms	(cos (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify51.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	363	726
1	1388	633
2	5002	603

prune407.0ms

Filtered

114 candidates to 79 candidates (69.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 2.3b

Counts

124 → 10

regimes253.0ms

Accuracy

0% (0.6b remaining)

Error of 3.4b against oracle of 2.8b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	38	23
2	38	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2074×	body	1280	valid
679.0ms	7957×	body	80	valid
569.0ms	1463×	body	640	valid
180.0ms	653×	body	320	valid
61.0ms	339×	body	160	valid