Average Error: 5.1 → 0.1
Time: 1.8s
Precision: binary64
\[\frac{x}{y \cdot y} - 3 \]
↓
\[\frac{\frac{x}{y}}{y} + -3 \]
(FPCore (x y) :precision binary64 (- (/ x (* y y)) 3.0))
↓
(FPCore (x y) :precision binary64 (+ (/ (/ x y) y) -3.0))
double code(double x, double y) {
	return (x / (y * y)) - 3.0;
}
↓
double code(double x, double y) {
	return ((x / y) / y) + -3.0;
}

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

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

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

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

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

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

\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} + -3

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.1
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3 \]

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3 \]

  2. Taylor expanded in x around 0 5.1

    \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} - 3 \]

  3. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]

  4. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} + -3 \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

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

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