Details

Time bar (total: 10.7s)

sample23.0ms

Algorithm
intervals
Results
12.0ms272×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.0b
(fma y.re y.re (* y.im y.im))
25.0b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
0.0ms
(fma y.re y.re (* y.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series164.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma x.re y.re (* x.im y.im))
34.0ms
(fma y.re y.re (* y.im y.im))
90.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify770.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
074833
1112819
2320707
31307707
done5001707

prune175.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
16.6b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ 1 (hypot y.re y.im))
14.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series387.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma x.re y.re (* x.im y.im))
55.0ms
(/ 1 (hypot y.re y.im))
180.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.2s

Counts
142 → 142
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
01542192
13722009
211311759
345041759
done50011759

prune344.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x.re y.re (* y.im x.im))
0.1b
(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
16.6b
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
3 → 111
Calls
3 calls:
0.0ms
(fma x.re y.re (* y.im x.im))
5.0ms
(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
2.0ms
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

series279.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma x.re y.re (* y.im x.im))
119.0ms
(/ (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
123.0ms
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

simplify1.3s

Counts
120 → 120
Iterations

Useful iterations: 3 (501.0ms)

IterNodesCost
01602484
13282423
28642246
327482192
done50002192

prune520.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* y.im x.im))
0.1b
(/ (/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
8.2b
(/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
8.5b
(/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
1644×times-frac
785×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
624×sqrt-prod
161×associate-/l*
38×div-inv
20×add-exp-log add-cbrt-cube
15×associate-/r*
10×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×fma-udef
Counts
4 → 794
Calls
4 calls:
0.0ms
(fma x.re y.re (* y.im x.im))
38.0ms
(/ (/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
12.0ms
(/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
3.0ms
(/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma x.re y.re (* y.im x.im))
122.0ms
(/ (/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
124.0ms
(/ (/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
252.0ms
(/ (fma x.re y.re (* y.im x.im)) (sqrt (hypot y.re y.im)))

simplify1.1s

Counts
806 → 806
Iterations

Useful iterations: done (1.1s)

IterNodesCost
082930021
1192027014
done500126738

prune1.8s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.2b

regimes226.0ms

Accuracy

36.1% (7.3b remaining)

Error of 12.9b against oracle of 5.6b and baseline of 17.0b

bsearch75.0ms

Steps
ItersRangePoint
8
7.599228493726907e+133
3.825156670365702e+136
1.3841272509628985e+136
6
-1.1032309685048642e+159
-2.4649475886005464e+158
-3.819667997978458e+158

simplify6.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02557
13251
23351
33651
44051
done4051

end0.0ms

sample514.0ms

Algorithm
intervals
Results
304.0ms8482×body80valid