Details

Time bar (total: 3.4s)

sample22.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217
done217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize10.0ms

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))
25.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

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:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
7.0ms
(+ (* x.re y.re) (* x.im y.im))
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ (* y.re y.re) (* y.im y.im))
33.0ms
(+ (* x.re y.re) (* x.im y.im))
87.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify134.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0290532
11199475
24872462
35001462
done5001462

prune205.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.5b
(fma x.re y.re (* x.im y.im))
17.9b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
154×add-exp-log
86×prod-exp
57×div-exp
44×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×rec-exp
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity times-frac
7×associate-*r* associate-*l*
5×pow1
3×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
3 → 112
Calls
3 calls:
49.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms
(fma x.re y.re (* x.im y.im))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series359.0ms

Counts
3 → 9
Calls
3 calls:
190.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
41.0ms
(fma x.re y.re (* x.im y.im))
127.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify42.0ms

Counts
121 → 121
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
04721079
11607796
25001794
done5001794

prune213.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b
(fma x.re y.re (* x.im y.im))
17.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×fma-udef associate-/l/
Counts
3 → 89
Calls
3 calls:
16.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series288.0ms

Counts
3 → 9
Calls
3 calls:
126.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
39.0ms
(fma x.re y.re (* x.im y.im))
123.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify74.0ms

Counts
98 → 98
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0297767
11133677
23251677
35001670
done5001670

prune261.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.5b
(fma x.re y.re (* x.im y.im))
18.0b
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
29×add-cbrt-cube
26×prod-exp
23×div-exp
18×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac
11×add-cube-cbrt
9×cbrt-undiv 1-exp cbrt-unprod
5×pow1
4×rec-exp
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ un-div-inv div-inv associate-/l/
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative fma-udef associate-/l*
Counts
3 → 86
Calls
3 calls:
16.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
14.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series288.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
43.0ms
(fma x.re y.re (* x.im y.im))
123.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify41.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0385730
11623579
25001550
done5001550

prune170.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.5b

regimes202.0ms

Accuracy

24.7% (8.2b remaining)

Error of 13.6b against oracle of 5.5b and baseline of 16.3b

bsearch86.0ms

Steps
ItersRangePoint
7
1.3381238936583669e+69
2.3069922374741435e+70
2.2847758660481544e+70
6
-7.922501144416864e+66
-5.906598016548616e+65
-7.723814496095852e+66

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014
done3014

end0.0ms

sample581.0ms

Algorithm
intervals
Results
290.0ms8463×body80valid