Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

265×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	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: 27.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
26.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series137.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
79.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune168.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	5	63

Merged error: 26.7b

Counts

63 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
103.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune271.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 24.4b

Counts

101 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.4b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
78.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify57.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	393	853
1	2037	749
2	5003	720

prune228.0ms

Filtered

109 candidates to 70 candidates (64.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Merged error: 24.4b

Counts

117 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

26.4b	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
32.0b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.0b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.0b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
96×	`associate-r`
80×	`cbrt-div`
69×	`add-sqr-sqrt`
57×	`cbrt-prod`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
50×	`associate-/r/`
42×	`flip3-+` `flip-+`
32×	`add-exp-log`
26×	`frac-times`
14×	`associate-*l/`
13×	`associate-*r/` `add-cbrt-cube`
11×	`div-exp` `prod-exp`
7×	`div-inv` `unswap-sqr`
6×	`pow1`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow1/3` `associate-l`
2×	`rec-exp` `1-exp`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 171

Calls

4 calls:

44.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (* (cbrt (+ (* y.re y.re) (* y.im y.im))) (cbrt (+ (* y.re y.re) (* y.im y.im))))) (cbrt (+ (* y.re y.re) (* y.im y.im)))))
90.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
93.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
92.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1003	3370
1	5002	3012

prune609.0ms

Filtered

183 candidates to 148 candidates (80.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	182	9	191

Merged error: 24.4b

Counts

191 → 9

regimes135.0ms

Accuracy

0% (2.8b remaining)

Error of 26.1b against oracle of 23.2b and baseline of 26.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample493.0ms

Algorithm

intervals

Results

288.0ms

8478×

body

valid