Details

Time bar (total: 14.7s)

sample31.0ms

Algorithm
intervals
Results
15.0ms283×body80valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done15
115
011

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
24.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* flip3-+ flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 42
Calls
2 calls:
23.0ms
(+ (* x.re y.re) (* x.im y.im))
51.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series200.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (* x.re y.re) (* x.im y.im))
135.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
48 → 48
Iterations
IterNodes
done5001
34323
2906
1237
086

prune367.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.7b
(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r* flip3-+ flip-+
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 264
Calls
4 calls:
52.0ms
(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms
(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
152.0ms
(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
276 → 276
Iterations
IterNodes
done5000
23738
1755
0302

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.5b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.im x.im) (* x.re y.re))
0.7b
(/ (/ 1 (sqrt 1)) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re))))
24.4b
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
834×times-frac
380×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
49×associate-/r/
41×div-inv
27×add-exp-log
26×flip3-+ flip-+
25×associate-/l*
18×associate-/r*
17×add-cbrt-cube div-exp
9×cbrt-undiv
5×add-log-exp
3×pow1 associate-/l/
2×rec-exp clear-num frac-2neg 1-exp
1×+-commutative sum-log
Counts
3 → 433
Calls
3 calls:
12.0ms
(+ (* y.im x.im) (* x.re y.re))
69.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re))))
48.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re)))

series325.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (* y.im x.im) (* x.re y.re))
200.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re))))
80.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* x.re y.re)))

simplify1.7s

Counts
442 → 442
Iterations
IterNodes
done5001
12250
0623

prune768.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))))
14.7b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
49×add-sqr-sqrt
47×*-un-lft-identity add-cube-cbrt
45×add-exp-log
36×sqrt-prod
28×associate-/l*
27×add-cbrt-cube
23×div-exp
12×cbrt-undiv
10×sqrt-div
8×prod-exp
7×associate-/r/
6×pow1 flip3-+ flip-+
4×associate-/r* cbrt-unprod div-inv add-log-exp
3×rec-exp 1-exp associate-/l/
2×frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l/
1×associate-*r/
Counts
4 → 152
Calls
4 calls:
47.0ms
(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))))
34.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(/ (/ 1 (sqrt 1)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))))
139.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* y.re x.re)))
61.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
164 → 164
Iterations
IterNodes
done5000
22598
1684
0241

prune750.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.5b

regimes457.0ms

Accuracy

-6.9% (3.1b remaining)

Error of 26.2b against oracle of 23.1b and baseline of 26.0b

bsearch68.0ms

Steps
ItersRangePoint
9
-1.3194991668433843e+53
-7.867138586923555e+46
-1.3001792014151386e+53

simplify3.0ms

Iterations
IterNodes
done29
129
021

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s8478×body80valid