Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

268×

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: 23.6b

Counts

2 → 1

localize11.0ms

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))
23.3b	(/ (- (* 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))
3.0ms	(- (* 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)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
83.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

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

prune175.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 12.1b

Counts

74 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot y.re y.im) 1))
0.2b	(* (/ 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))
14.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite31.0ms

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

series388.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (* (hypot y.re y.im) 1))
182.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify62.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	555	1211
1	2307	1003
2	5001	995

prune284.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	9	155
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 5.7b

Counts

161 → 11

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))
14.4b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite21.0ms

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:

7.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series260.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
110.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify50.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (36.0ms)

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

prune285.0ms

Filtered

130 candidates to 99 candidates (76.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Merged error: 5.7b

Counts

141 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
0.1b	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
9.4b	(/ (* x.re y.im) (hypot y.re y.im))
10.0b	(/ (* x.im y.re) (hypot y.re y.im))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
59×	`add-sqr-sqrt` `*-un-lft-identity`
49×	`add-cube-cbrt` `prod-diff`
28×	`div-inv`
16×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`associate-/l*`
7×	`fma-neg`
6×	`add-log-exp`
5×	`cbrt-undiv` `distribute-rgt-out--` `div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 167

Calls

4 calls:

10.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
14.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
4.0ms	(/ (* x.re y.im) (hypot y.re y.im))
4.0ms	(/ (* x.im y.re) (hypot y.re y.im))

series557.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im)))
235.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ (* x.re y.im) (hypot y.re y.im))) (hypot y.re y.im))
71.0ms	(/ (* x.re y.im) (hypot y.re y.im))
67.0ms	(/ (* x.im y.re) (hypot y.re y.im))

simplify82.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	607	2530
1	2576	1870
2	5001	1867

prune320.0ms

Filtered

179 candidates to 113 candidates (63.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Merged error: 0.0b

Counts

188 → 6

regimes109.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	30
1	31	30
2	31	30

end0.0ms

sample535.0ms

Algorithm

intervals

Results

322.0ms

8493×

body

valid