Details

Time bar (total: 3.7s)

sample23.0ms

Algorithm
intervals
Results
12.0ms272×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* x.re y.re) (* x.im y.im))
27.6b
(/ (+ (* 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:
3.0ms
(+ (* 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)))

series139.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* 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)))

simplify130.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune188.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
21.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms
(/ (+ (* 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)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
105.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms
(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
276 → 276
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
07145680
125165201
250015144

prune547.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
17.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative
Counts
4 → 161
Calls
4 calls:
24.0ms
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
9.0ms
(/ (+ (* 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)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
107.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05782493
127602257
250012142

prune449.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.9b

localize16.0ms

Local error

Found 4 expressions with local error:

17.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
10×flip3-+ flip-+
9×add-exp-log add-cube-cbrt *-un-lft-identity sqrt-prod add-cbrt-cube
8×associate-/r/
7×pow1
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/l/
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
16.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (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)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0272873
1784804
22307804
35002804

prune309.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.9b

regimes198.0ms

Accuracy

-28% (3.9b remaining)

Error of 27.2b against oracle of 23.3b and baseline of 26.3b

bsearch44.0ms

Steps
ItersRangePoint
8
-2.6377723203856948e+209
-9.359040239694252e+204
-1.8333306916678013e+209

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02619
12619

end0.0ms

sample530.0ms

Algorithm
intervals
Results
312.0ms8456×body80valid