Average Error: 0.0 → 0.0

Time: 1.0s

Precision: binary64

Cost: 320

\[x \cdot \left(y + 1\right) \]

↓

\[x + y \cdot x \]

(FPCore (x y) :precision binary64 (* x (+ y 1.0)))

↓

(FPCore (x y) :precision binary64 (+ x (* y x)))

double code(double x, double y) {
	return x * (y + 1.0);
}

↓

double code(double x, double y) {
	return x + (y * x);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y + 1.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * x)
end function

public static double code(double x, double y) {
	return x * (y + 1.0);
}

↓

public static double code(double x, double y) {
	return x + (y * x);
}

def code(x, y):
	return x * (y + 1.0)

↓

def code(x, y):
	return x + (y * x)

function code(x, y)
	return Float64(x * Float64(y + 1.0))
end

↓

function code(x, y)
	return Float64(x + Float64(y * x))
end

function tmp = code(x, y)
	tmp = x * (y + 1.0);
end

↓

function tmp = code(x, y)
	tmp = x + (y * x);
end

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

↓

code[x_, y_] := N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]

x \cdot \left(y + 1\right)

↓

x + y \cdot x

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

\[x + x \cdot y \]

Derivation

Initial program 0.0
\[x \cdot \left(y + 1\right) \]
Taylor expanded in y around 0 0.0
\[\leadsto \color{blue}{y \cdot x + x} \]
Final simplification0.0
\[\leadsto x + y \cdot x \]

Alternatives

Alternative 1
Error	1.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

\[x \cdot \left(y + 1\right) \]

Alternative 3
Error	27.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022340 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

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

  (* x (+ y 1.0)))