Quotient of products

Percentage Accurate: 85.8% → 89.8%

Time: 3.1s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a1 \cdot a2}{b1 \cdot b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \leq -4 \cdot 10^{+184} \lor \neg \left(a1 \cdot a2 \leq -2 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{a1}{\frac{b2}{a2} \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (or (<= (* a1 a2) -4e+184) (not (<= (* a1 a2) -2e-168)))
   (/ a1 (* (/ b2 a2) b1))
   (/ (* a1 a2) (* b2 b1))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((a1 * a2) <= -4e+184) || !((a1 * a2) <= -2e-168)) {
		tmp = a1 / ((b2 / a2) * b1);
	} else {
		tmp = (a1 * a2) / (b2 * b1);
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (((a1 * a2) <= (-4d+184)) .or. (.not. ((a1 * a2) <= (-2d-168)))) then
        tmp = a1 / ((b2 / a2) * b1)
    else
        tmp = (a1 * a2) / (b2 * b1)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (((a1 * a2) <= -4e+184) || !((a1 * a2) <= -2e-168)) {
		tmp = a1 / ((b2 / a2) * b1);
	} else {
		tmp = (a1 * a2) / (b2 * b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if ((a1 * a2) <= -4e+184) or not ((a1 * a2) <= -2e-168):
		tmp = a1 / ((b2 / a2) * b1)
	else:
		tmp = (a1 * a2) / (b2 * b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if ((Float64(a1 * a2) <= -4e+184) || !(Float64(a1 * a2) <= -2e-168))
		tmp = Float64(a1 / Float64(Float64(b2 / a2) * b1));
	else
		tmp = Float64(Float64(a1 * a2) / Float64(b2 * b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (((a1 * a2) <= -4e+184) || ~(((a1 * a2) <= -2e-168)))
		tmp = a1 / ((b2 / a2) * b1);
	else
		tmp = (a1 * a2) / (b2 * b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[Or[LessEqual[N[(a1 * a2), $MachinePrecision], -4e+184], N[Not[LessEqual[N[(a1 * a2), $MachinePrecision], -2e-168]], $MachinePrecision]], N[(a1 / N[(N[(b2 / a2), $MachinePrecision] * b1), $MachinePrecision]), $MachinePrecision], N[(N[(a1 * a2), $MachinePrecision] / N[(b2 * b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a1 a2) < -4.00000000000000007e184 or -2.0000000000000001e-168 < (*.f64 a1 a2)

   1. Initial program 81.4%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 92.0%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

      2. *-commutative 92.0%

         \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]
   4. Step-by-step derivation

      1. clear-num 92.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{b2}{a2}}} \cdot \frac{a1}{b1} \]

      2. frac-times 95.3%

         \[\leadsto \color{blue}{\frac{1 \cdot a1}{\frac{b2}{a2} \cdot b1}} \]

      3. *-un-lft-identity 95.3%

         \[\leadsto \frac{\color{blue}{a1}}{\frac{b2}{a2} \cdot b1} \]

   5. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\frac{a1}{\frac{b2}{a2} \cdot b1}} \]

   if -4.00000000000000007e184 < (*.f64 a1 a2) < -2.0000000000000001e-168

   1. Initial program 99.5%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \leq -4 \cdot 10^{+184} \lor \neg \left(a1 \cdot a2 \leq -2 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{a1}{\frac{b2}{a2} \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \end{array} \]

Alternative 2: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a2 \leq -5 \cdot 10^{-297}:\\ \;\;\;\;a1 \cdot \frac{a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (if (<= a2 -5e-297) (* a1 (/ a2 (* b2 b1))) (* (/ a2 b2) (/ a1 b1))))

C

double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= -5e-297) {
		tmp = a1 * (a2 / (b2 * b1));
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (a2 <= (-5d-297)) then
        tmp = a1 * (a2 / (b2 * b1))
    else
        tmp = (a2 / b2) * (a1 / b1)
    end if
    code = tmp
end function

Java

public static double code(double a1, double a2, double b1, double b2) {
	double tmp;
	if (a2 <= -5e-297) {
		tmp = a1 * (a2 / (b2 * b1));
	} else {
		tmp = (a2 / b2) * (a1 / b1);
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	tmp = 0
	if a2 <= -5e-297:
		tmp = a1 * (a2 / (b2 * b1))
	else:
		tmp = (a2 / b2) * (a1 / b1)
	return tmp

Julia

function code(a1, a2, b1, b2)
	tmp = 0.0
	if (a2 <= -5e-297)
		tmp = Float64(a1 * Float64(a2 / Float64(b2 * b1)));
	else
		tmp = Float64(Float64(a2 / b2) * Float64(a1 / b1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a1, a2, b1, b2)
	tmp = 0.0;
	if (a2 <= -5e-297)
		tmp = a1 * (a2 / (b2 * b1));
	else
		tmp = (a2 / b2) * (a1 / b1);
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := If[LessEqual[a2, -5e-297], N[(a1 * N[(a2 / N[(b2 * b1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a2 / b2), $MachinePrecision] * N[(a1 / b1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a2 < -5e-297

   1. Initial program 91.4%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 85.8%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

      2. *-commutative 85.8%

         \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

   4. Taylor expanded in a2 around 0 91.4%

      \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}} \]
   5. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \frac{a1 \cdot a2}{\color{blue}{b2 \cdot b1}} \]

      2. associate-*r/ 92.8%

         \[\leadsto \color{blue}{a1 \cdot \frac{a2}{b2 \cdot b1}} \]

      3. *-commutative 92.8%

         \[\leadsto a1 \cdot \frac{a2}{\color{blue}{b1 \cdot b2}} \]

   6. Simplified 92.8%

      \[\leadsto \color{blue}{a1 \cdot \frac{a2}{b1 \cdot b2}} \]

   if -5e-297 < a2

   1. Initial program 81.1%

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
   2. Step-by-step derivation

      1. times-frac 94.7%

         \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

      2. *-commutative 94.7%

         \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a2 \leq -5 \cdot 10^{-297}:\\ \;\;\;\;a1 \cdot \frac{a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 3: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a1 \cdot \frac{a2}{b2 \cdot b1} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (* a1 (/ a2 (* b2 b1))))

C

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

Fortran

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 / (b2 * b1))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

   \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
2. Step-by-step derivation

   1. times-frac 90.3%

      \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]

   2. *-commutative 90.3%

      \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

3. Simplified 90.3%

   \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

4. Taylor expanded in a2 around 0 86.2%

   \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}} \]
5. Step-by-step derivation

   1. *-commutative 86.2%

      \[\leadsto \frac{a1 \cdot a2}{\color{blue}{b2 \cdot b1}} \]

   2. associate-*r/ 89.0%

      \[\leadsto \color{blue}{a1 \cdot \frac{a2}{b2 \cdot b1}} \]

   3. *-commutative 89.0%

      \[\leadsto a1 \cdot \frac{a2}{\color{blue}{b1 \cdot b2}} \]

6. Simplified 89.0%

   \[\leadsto \color{blue}{a1 \cdot \frac{a2}{b1 \cdot b2}} \]

7. Final simplification 89.0%

   \[\leadsto a1 \cdot \frac{a2}{b2 \cdot b1} \]

Developer target: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a1}{b1} \cdot \frac{a2}{b2} \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (* (/ a1 b1) (/ a2 b2)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023272 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

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