Details

Time bar (total: 7.7s)

sample21.0ms

Algorithm
intervals
Results
11.0ms264×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
0.5b
(fma x.re y.re (* x.im y.im))
26.5b
(/ (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 y.re y.re (* y.im y.im))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma y.re y.re (* y.im y.im))
36.0ms
(fma x.re y.re (* x.im y.im))
86.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify699.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
074833
1116819
2389707
31479707
done5001707

prune175.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)))
0.5b
(fma x.re y.re (* x.im y.im))
17.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(hypot y.re y.im)
13.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series366.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(hypot y.re y.im)
174.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
38.0ms
(fma x.re y.re (* x.im y.im))
110.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify785.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
01471955
13701833
214121579
done50001579

prune313.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b
(fma x.re y.re (* x.im y.im))
17.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.re y.im)
5.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series300.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(hypot y.re y.im)
112.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
35.0ms
(fma x.re y.re (* x.im y.im))
110.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.2s

Counts
133 → 133
Iterations

Useful iterations: 3 (598.0ms)

IterNodesCost
01682544
13462481
211412298
335742244
done50002244

prune370.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)))
0.5b
(fma x.re y.re (* y.im x.im))
17.5b
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(hypot y.re y.im)
16.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)))
0.0ms
(fma x.re y.re (* y.im x.im))
2.0ms
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

series381.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot y.re y.im)
175.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im)))
39.0ms
(fma x.re y.re (* y.im x.im))
123.0ms
(/ (fma x.re y.re (* y.im x.im)) (hypot y.re y.im))

simplify787.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
01461955
13701833
214111579
done50001579

prune291.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.8b

regimes200.0ms

Accuracy

37.8% (7.2b remaining)

Error of 13.1b against oracle of 5.9b and baseline of 17.4b

bsearch90.0ms

Steps
ItersRangePoint
11
5.286434132095145e+107
2.6900018818139096e+129
1.8955542797321017e+121
10
-3.4896836630642546e+148
-1.4395777107888637e+138
-6.751507617690198e+142

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02035
12535
done2535

end0.0ms

sample489.0ms

Algorithm
intervals
Results
282.0ms8511×body80valid