Quotient of products

Percentage Accurate: 99.6% → 99.6%
Time: 742.0ms
Alternatives: 1
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]
(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))
double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 * a2) / (b1 * b2)
end function

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

def code(a1, a2, b1, b2):
	return (a1 * a2) / (b1 * b2)

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 * a2) / (b1 * b2);
end

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{a1 \cdot a2}{b1 \cdot b2}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 1 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 99.6% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]
(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))
double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 * a2) / (b1 * b2)
end function

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

def code(a1, a2, b1, b2):
	return (a1 * a2) / (b1 * b2)

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 * a2) / (b1 * b2);
end

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{a1 \cdot a2}{b1 \cdot b2}
\end{array}

Alternative 1: 99.6% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{a2 \cdot a1}{b2 \cdot b1} \end{array} \]
(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a2 a1) (* b2 b1)))
double code(double a1, double a2, double b1, double b2) {
	return (a2 * a1) / (b2 * b1);
}

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a2 * a1) / (b2 * b1)
end function

public static double code(double a1, double a2, double b1, double b2) {
	return (a2 * a1) / (b2 * b1);
}

def code(a1, a2, b1, b2):
	return (a2 * a1) / (b2 * b1)

function code(a1, a2, b1, b2)
	return Float64(Float64(a2 * a1) / Float64(b2 * b1))
end

function tmp = code(a1, a2, b1, b2)
	tmp = (a2 * a1) / (b2 * b1);
end

code[a1_, a2_, b1_, b2_] := N[(N[(a2 * a1), $MachinePrecision] / N[(b2 * b1), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{a2 \cdot a1}{b2 \cdot b1}
\end{array}
Derivation

  1. Initial program 85.8%

    \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
  2. Add Preprocessing

  3. Final simplification85.8%

    \[\leadsto \frac{a2 \cdot a1}{b2 \cdot b1} \]
  4. Add Preprocessing

Developer Target 1: 75.8% accurate, 0.8× speedup?

\[\begin{array}{l} \\ \frac{a1}{b1} \cdot \frac{a2}{b2} \end{array} \]
(FPCore (a1 a2 b1 b2) :precision binary64 (* (/ a1 b1) (/ a2 b2)))
double code(double a1, double a2, double b1, double b2) {
	return (a1 / b1) * (a2 / b2);
}

real(8) function code(a1, a2, b1, b2)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: b1
    real(8), intent (in) :: b2
    code = (a1 / b1) * (a2 / b2)
end function

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 / b1) * (a2 / b2);
}

def code(a1, a2, b1, b2):
	return (a1 / b1) * (a2 / b2)

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 / b1) * Float64(a2 / b2))
end

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 / b1) * (a2 / b2);
end

code[a1_, a2_, b1_, b2_] := N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\frac{a1}{b1} \cdot \frac{a2}{b2}
\end{array}

Reproduce

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herbie shell --seed 2024343 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ a1 b1) (/ a2 b2)))

  (/ (* a1 a2) (* b1 b2)))