Details

Time bar (total: 8.2s)

sample34.0ms

Algorithm
intervals
Results
22.0ms274×body80valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
25.0b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
4.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series144.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(fma x.re y.re (* x.im y.im))
100.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify563.0ms

Counts
47 → 47
Iterations
IterNodes
done2002
3936
2296
1106
067

prune263.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma x.re y.re (* x.im y.im))
15.6b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
5.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma x.re y.re (* x.im y.im))
120.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
52.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
66.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify536.0ms

Counts
99 → 99
Iterations
IterNodes
done2003
3857
2304
1143
093

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma y.re x.re (* y.im x.im))
15.6b
(/ (fma y.re x.re (* y.im x.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
0.0ms
(fma y.re x.re (* y.im x.im))
7.0ms
(/ (fma y.re x.re (* y.im x.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma y.re x.re (* y.im x.im))
129.0ms
(/ (fma y.re x.re (* y.im x.im)) (sqrt (fma y.im y.im (* y.re y.re))))
69.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
57.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify556.0ms

Counts
99 → 99
Iterations
IterNodes
done2002
3868
2301
1142
091

prune496.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
15.6b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))
31.7b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp fma-udef hypot-def
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 162
Calls
4 calls:
29.0ms
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
127.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
64.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts
174 → 174
Iterations
IterNodes
done2001
21359
1444
0171

prune839.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.7b

regimes314.0ms

Accuracy

0% (1.6b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 16.0b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
115
011

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8466×body80valid