Details

Time bar (total: 8.7s)

sample20.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
24.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series113.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
82.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify833.0ms

Counts
48 → 48
Iterations

Useful iterations: 3 (241.0ms)

IterNodesCost
086924
1243906
2763824
32266820
done5000820

prune146.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
15.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(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:
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))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
108.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify786.0ms

Counts
96 → 96
Iterations

Useful iterations: 3 (242.0ms)

IterNodesCost
01171780
12811657
27811543
321481527
done50001527

prune306.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re))))
15.4b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
100×add-sqr-sqrt
98×add-cube-cbrt *-un-lft-identity
54×sqrt-prod
27×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
9×associate-/l*
8×flip3-+ div-exp flip-+
7×pow1
6×sqrt-div div-inv
4×cbrt-undiv add-log-exp
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 193
Calls
4 calls:
13.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re))))
10.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re))))
82.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts
205 → 205
Iterations

Useful iterations: 3 (901.0ms)

IterNodesCost
02425680
15865184
218274723
347334665
done50004665

prune475.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt 1) (/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))))
15.3b
(/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.im y.im) (* y.re y.re)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
1473×times-frac
681×add-sqr-sqrt
679×add-cube-cbrt *-un-lft-identity
522×sqrt-prod
155×associate-/r*
55×associate-/r/
54×sqrt-div
30×div-inv
28×flip3-+ flip-+
27×add-exp-log
16×div-exp
15×add-cbrt-cube
7×pow1 cbrt-undiv
6×associate-/l*
4×add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
1×pow-flip inv-pow
Counts
4 → 697
Calls
4 calls:
39.0ms
(/ 1 (/ (sqrt 1) (/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))))
11.0ms
(/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1 (/ (sqrt 1) (/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))))
97.0ms
(/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (+ (* y.im y.im) (* y.re y.re))))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(sqrt (+ (* y.im y.im) (* y.re y.re)))

simplify655.0ms

Counts
709 → 709
Iterations

Useful iterations: done (618.0ms)

IterNodesCost
087328454
1206624143
done500022249

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.1b

regimes243.0ms

Accuracy

1.3% (2.8b remaining)

Error of 25.8b against oracle of 23.0b and baseline of 25.8b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02456
13056
done3056

end0.0ms

sample507.0ms

Algorithm
intervals
Results
294.0ms8488×body80valid