Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

277×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Filtered

1 candidates to 0 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: 29.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
28.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
79.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	316	555
1	1343	496
2	5001	481

prune161.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 11.7b

Counts

74 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.3b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

5.0ms	(/ 1 (* (hypot y.re y.im) 1))
12.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series363.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (* (hypot y.re y.im) 1))
174.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
33.0ms	(- (* x.im y.re) (* x.re y.im))
107.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	555	1207
1	2306	1003
2	5003	995

prune268.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	147	8	155
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	150	10	160

Merged error: 4.0b

Counts

160 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series257.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
34.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	451	1408
1	1659	1307
2	5001	1298

prune258.0ms

Filtered

130 candidates to 97 candidates (74.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Merged error: 4.0b

Counts

140 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.5b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
255×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
56×	`associate-/l*`
39×	`associate-/r/`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
21×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 359

Calls

4 calls:

15.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
10.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
4.0ms	(- (* x.im y.re) (* x.re y.im))
5.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (hypot y.re y.im))
108.0ms	(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
36.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1296	5404
1	5002	4894

prune665.0ms

Filtered

371 candidates to 228 candidates (61.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	372	10	382

Merged error: 4.0b

Counts

382 → 10

regimes197.0ms

Accuracy

33.9% (8.3b remaining)

Error of 12.9b against oracle of 4.6b and baseline of 17.2b

bsearch143.0ms

Steps

Iters	Range		Point
8	1.5184330169621066e+139	6.324854275423776e+142	4.6230231189603044e+141
9	4.60987506426565e+76	1.4293103507126414e+82	2.54946443013026e+79
7	4.563194349605498e-107	7.312504672026838e-106	6.698957894855029e-106
7	-8.906213487170025e+95	-3.3207123533803692e+94	-5.122757241376907e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	42	30
2	42	30

end0.0ms

sample597.0ms

Algorithm

intervals

Results

379.0ms

8490×

body

valid