Details

Time bar (total: 13.8s)

sample20.0ms

Algorithm
intervals
Results
10.0ms272×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
27.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(+ (* x.re y.re) (* x.im y.im))
12.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series145.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
34.0ms
(+ (* x.re y.re) (* x.im y.im))
84.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
70 → 70
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
01051154
1288969
21018867
33742867
done5000867

prune236.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
0.3b
(fma y.re x.re (* y.im x.im))
16.8b
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite23.0ms

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:
2.0ms
(/ 1 (hypot y.re y.im))
14.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
0.0ms
(fma y.re x.re (* y.im x.im))
2.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series381.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (hypot y.re y.im))
183.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
40.0ms
(fma y.re x.re (* y.im x.im))
104.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify3.8s

Counts
142 → 142
Iterations

Useful iterations: 2 (244.0ms)

IterNodesCost
01522192
13722031
211981759
345731759
done50011759

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b
(fma y.re x.re (* y.im x.im))
16.8b
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite13.0ms

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:
6.0ms
(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma y.re x.re (* y.im x.im))
2.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series274.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
39.0ms
(fma y.re x.re (* y.im x.im))
107.0ms
(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify2.2s

Counts
120 → 120
Iterations

Useful iterations: 3 (773.0ms)

IterNodesCost
01592484
13272423
27892246
323052192
done50002192

prune371.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
0.3b
(fma y.re x.re (* y.im x.im))
16.9b
(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 319
Calls
4 calls:
20.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
5.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
0.0ms
(fma y.re x.re (* y.im x.im))
2.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
125.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
39.0ms
(fma y.re x.re (* y.im x.im))
97.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

simplify2.3s

Counts
331 → 331
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04578797
110747956
226947150
done50007078

prune586.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

regimes220.0ms

Accuracy

30.1% (7.9b remaining)

Error of 13.7b against oracle of 5.9b and baseline of 17.1b

bsearch83.0ms

Steps
ItersRangePoint
8
2.7287424349260767e+55
7.2976976434618665e+59
7.1823270231744765e+59
10
-6.208573332862927e+135
-3.0985365288236678e+125
-2.065894531772732e+130

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02035
12435
done2435

end0.0ms

sample517.0ms

Algorithm
intervals
Results
308.0ms8471×body80valid