Average Error: 6.0 → 0.2
Time: 2.6s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
↓
\[\left(1 - x\right) \cdot \left(\frac{1}{y} + \frac{x}{y} \cdot -0.3333333333333333\right) \]
(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))
↓
(FPCore (x y)
 :precision binary64
 (* (- 1.0 x) (+ (/ 1.0 y) (* (/ x y) -0.3333333333333333))))
double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}
↓
double code(double x, double y) {
	return (1.0 - x) * ((1.0 / y) + ((x / y) * -0.3333333333333333));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * ((1.0d0 / y) + ((x / y) * (-0.3333333333333333d0)))
end function

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}
↓
public static double code(double x, double y) {
	return (1.0 - x) * ((1.0 / y) + ((x / y) * -0.3333333333333333));
}

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)
↓
def code(x, y):
	return (1.0 - x) * ((1.0 / y) + ((x / y) * -0.3333333333333333))

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end
↓
function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(1.0 / y) + Float64(Float64(x / y) * -0.3333333333333333)))
end

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end
↓
function tmp = code(x, y)
	tmp = (1.0 - x) * ((1.0 / y) + ((x / y) * -0.3333333333333333));
end

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \left(\frac{1}{y} + \frac{x}{y} \cdot -0.3333333333333333\right)

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.0
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3} \]

Derivation

  1. Initial program 6.0

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]

  2. Simplified0.4

    \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]

  3. Taylor expanded in x around 0 0.2

    \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{1}{y} - 0.3333333333333333 \cdot \frac{x}{y}\right)} \]

  4. Final simplification0.2

    \[\leadsto \left(1 - x\right) \cdot \left(\frac{1}{y} + \frac{x}{y} \cdot -0.3333333333333333\right) \]

Reproduce

herbie shell --seed 2022156 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))