Details

Time bar (total: 3.8s)

sample21.0ms

Algorithm
intervals
Results
8.0ms266×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: 23.0b

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))
22.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
34.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series127.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* y.re y.re) (* y.im y.im))
28.0ms
(+ (* x.re y.re) (* x.im y.im))
74.0ms
(/ (+ (* 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 (29.0ms)

IterNodesCost
0272527
11164479
24451477
35003477

prune160.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize12.0ms

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))))
12.3b
(/ (+ (* 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)))

rewrite120.0ms

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:
55.0ms
(/ (/ (+ (* 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))))
34.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (/ (+ (* 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))))
97.0ms
(/ (+ (* 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)))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify86.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
07145680
125165201
250015144

prune540.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

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)))))
12.3b
(/ (+ (* 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)))

rewrite143.0ms

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:
83.0ms
(* (/ (+ (* 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)))))
35.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (/ (+ (* 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)))))
99.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify70.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05782495
127752257
250012142

prune427.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.1b

localize15.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
32×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
10×sqrt-div
9×associate-/r*
7×pow1
6×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02941227
18711172
225451144
350011144

prune322.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.1b

regimes143.0ms

Accuracy

0% (2.9b remaining)

Error of 25.8b against oracle of 22.9b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01713
11713

end0.0ms

sample562.0ms

Algorithm
intervals
Results
272.0ms8491×body80valid