Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

264×

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(+ (* x.re y.re) (* x.im y.im))
26.5b	(/ (+ (* x.re y.re) (* x.im 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`
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:

2.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series139.0ms

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))
81.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

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

prune174.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
13.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* 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))))
33.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune274.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(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:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

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

prune299.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.4b

localize21.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

12.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
95.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
94.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	399	908
1	1522	808
2	5002	804

prune356.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.4b

regimes258.0ms

Accuracy

0.1% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch39.0ms

Steps

Iters	Range		Point
8	1.5974682383539887e+61	1.4744290377191018e+65	1.4473657936297032e+65

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample536.0ms

Algorithm

intervals

Results

304.0ms

8511×

body

valid