Average Error: 0.0 → 0
Time: 904.0ms
Precision: binary64
\[x \cdot \left(x - 1\right) \]
↓
\[\mathsf{fma}\left(x, x, -x\right) \]
(FPCore (x) :precision binary64 (* x (- x 1.0)))
↓
(FPCore (x) :precision binary64 (fma x x (- x)))
double code(double x) {
	return x * (x - 1.0);
}
↓
double code(double x) {
	return fma(x, x, -x);
}

function code(x)
	return Float64(x * Float64(x - 1.0))
end
↓
function code(x)
	return fma(x, x, Float64(-x))
end

code[x_] := N[(x * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(x * x + (-x)), $MachinePrecision]

x \cdot \left(x - 1\right)
↓
\mathsf{fma}\left(x, x, -x\right)

Error

Target

Original0.0
Target0.0
Herbie0
\[x \cdot x - x \]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x - 1\right) \]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x - x} \]

  3. Applied egg-rr0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -x\right)} \]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, -x\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (* x x) x)

  (* x (- x 1.0)))