Details

Time bar (total: 15.3s)

sample52.0ms

Algorithm
intervals
Results
35.0ms269×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done15
115
011

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
4×flip3-+ flip-+
3×pow1 associate-/r* insert-posit16 associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 56
Calls
3 calls:
12.0ms
(+ (* x.re y.re) (* x.im y.im))
10.0ms
(+ (* y.re y.re) (* y.im y.im))
52.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series190.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ (* x.re y.re) (* x.im y.im))
49.0ms
(+ (* y.re y.re) (* y.im y.im))
83.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts
65 → 65
Iterations
IterNodes
done5007
34530
21142
1284
0101

prune466.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.3b

localize59.0ms

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))))
15.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite168.0ms

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 insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 268
Calls
4 calls:
80.0ms
(/ (/ (+ (* 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))))
54.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (/ (+ (* 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))))
162.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
59.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
68.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts
280 → 280
Iterations
IterNodes
done5000
21755
1724
0305

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.5b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×times-frac add-cube-cbrt
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
6×flip3-+ flip-+
4×div-exp prod-exp associate-/r/ insert-posit16
3×associate-/r* associate-*l* associate-/l* unswap-sqr
2×frac-times cbrt-undiv +-commutative rec-exp sum-log 1-exp associate-*l/ cbrt-unprod div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 101
Calls
4 calls:
14.0ms
(+ (* x.re y.re) (* x.im y.im))
14.0ms
(+ (* y.re y.re) (* y.im y.im))
21.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
77.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* x.re y.re) (* x.im y.im))
31.0ms
(+ (* y.re y.re) (* y.im y.im))
54.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
135.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify1.6s

Counts
113 → 113
Iterations
IterNodes
done5001
21565
1414
0143

prune558.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.2b

localize35.0ms

Local error

Found 4 expressions with local error:

15.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.4b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
21×sqrt-prod
18×times-frac
8×sqrt-div
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
5×flip3-+ flip-+
4×insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 92
Calls
4 calls:
42.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts
104 → 104
Iterations
IterNodes
done5000
31969
2661
1251
0107

prune648.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.2b

regimes464.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done20
120
013

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8439×body80valid