Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.4% → 99.7%

Time: 4.0s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ 100.0 (+ x y))))

C

double code(double x, double y) {
	return x * (100.0 / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (100.0d0 / (x + y))
end function

Java

public static double code(double x, double y) {
	return x * (100.0 / (x + y));
}

Python

def code(x, y):
	return x * (100.0 / (x + y))

Julia

function code(x, y)
	return Float64(x * Float64(100.0 / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (100.0 / (x + y));
end

Wolfram

code[x_, y_] := N[(x * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

4. Final simplification 99.7%

   \[\leadsto x \cdot \frac{100}{x + y} \]

Alternative 2: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-63} \lor \neg \left(y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 6.5 \cdot 10^{-87}\right) \land y \leq 2.25 \cdot 10^{+78}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.7e-63)
         (not (or (<= y 1.6e-160) (and (not (<= y 6.5e-87)) (<= y 2.25e+78)))))
   (* 100.0 (/ x y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.7e-63) || !((y <= 1.6e-160) || (!(y <= 6.5e-87) && (y <= 2.25e+78)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.7d-63)) .or. (.not. (y <= 1.6d-160) .or. (.not. (y <= 6.5d-87)) .and. (y <= 2.25d+78))) then
        tmp = 100.0d0 * (x / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.7e-63) || !((y <= 1.6e-160) || (!(y <= 6.5e-87) && (y <= 2.25e+78)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.7e-63) or not ((y <= 1.6e-160) or (not (y <= 6.5e-87) and (y <= 2.25e+78))):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.7e-63) || !((y <= 1.6e-160) || (!(y <= 6.5e-87) && (y <= 2.25e+78))))
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.7e-63) || ~(((y <= 1.6e-160) || (~((y <= 6.5e-87)) && (y <= 2.25e+78)))))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.7e-63], N[Not[Or[LessEqual[y, 1.6e-160], And[N[Not[LessEqual[y, 6.5e-87]], $MachinePrecision], LessEqual[y, 2.25e+78]]]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000012e-63 or 1.60000000000000004e-160 < y < 6.5000000000000003e-87 or 2.25e78 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around 0 79.3%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]

   if -3.70000000000000012e-63 < y < 1.60000000000000004e-160 or 6.5000000000000003e-87 < y < 2.25e78

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-63} \lor \neg \left(y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 6.5 \cdot 10^{-87}\right) \land y \leq 2.25 \cdot 10^{+78}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-63} \lor \neg \left(y \leq 1.45 \cdot 10^{-160} \lor \neg \left(y \leq 7.6 \cdot 10^{-88}\right) \land y \leq 2.25 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4e-63)
         (not
          (or (<= y 1.45e-160) (and (not (<= y 7.6e-88)) (<= y 2.25e+78)))))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4e-63) || !((y <= 1.45e-160) || (!(y <= 7.6e-88) && (y <= 2.25e+78)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4d-63)) .or. (.not. (y <= 1.45d-160) .or. (.not. (y <= 7.6d-88)) .and. (y <= 2.25d+78))) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4e-63) || !((y <= 1.45e-160) || (!(y <= 7.6e-88) && (y <= 2.25e+78)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4e-63) or not ((y <= 1.45e-160) or (not (y <= 7.6e-88) and (y <= 2.25e+78))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4e-63) || !((y <= 1.45e-160) || (!(y <= 7.6e-88) && (y <= 2.25e+78))))
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4e-63) || ~(((y <= 1.45e-160) || (~((y <= 7.6e-88)) && (y <= 2.25e+78)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4e-63], N[Not[Or[LessEqual[y, 1.45e-160], And[N[Not[LessEqual[y, 7.6e-88]], $MachinePrecision], LessEqual[y, 2.25e+78]]]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000027e-63 or 1.45e-160 < y < 7.60000000000000022e-88 or 2.25e78 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around 0 79.4%

      \[\leadsto x \cdot \color{blue}{\frac{100}{y}} \]

   if -4.00000000000000027e-63 < y < 1.45e-160 or 7.60000000000000022e-88 < y < 2.25e78

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-63} \lor \neg \left(y \leq 1.45 \cdot 10^{-160} \lor \neg \left(y \leq 7.6 \cdot 10^{-88}\right) \land y \leq 2.25 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -3.3e-63)
     t_0
     (if (<= y 1.6e-160)
       100.0
       (if (<= y 7.6e-88) t_0 (if (<= y 5.8e+78) 100.0 (/ x (* y 0.01))))))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -3.3e-63) {
		tmp = t_0;
	} else if (y <= 1.6e-160) {
		tmp = 100.0;
	} else if (y <= 7.6e-88) {
		tmp = t_0;
	} else if (y <= 5.8e+78) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (100.0d0 / y)
    if (y <= (-3.3d-63)) then
        tmp = t_0
    else if (y <= 1.6d-160) then
        tmp = 100.0d0
    else if (y <= 7.6d-88) then
        tmp = t_0
    else if (y <= 5.8d+78) then
        tmp = 100.0d0
    else
        tmp = x / (y * 0.01d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -3.3e-63) {
		tmp = t_0;
	} else if (y <= 1.6e-160) {
		tmp = 100.0;
	} else if (y <= 7.6e-88) {
		tmp = t_0;
	} else if (y <= 5.8e+78) {
		tmp = 100.0;
	} else {
		tmp = x / (y * 0.01);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -3.3e-63:
		tmp = t_0
	elif y <= 1.6e-160:
		tmp = 100.0
	elif y <= 7.6e-88:
		tmp = t_0
	elif y <= 5.8e+78:
		tmp = 100.0
	else:
		tmp = x / (y * 0.01)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -3.3e-63)
		tmp = t_0;
	elseif (y <= 1.6e-160)
		tmp = 100.0;
	elseif (y <= 7.6e-88)
		tmp = t_0;
	elseif (y <= 5.8e+78)
		tmp = 100.0;
	else
		tmp = Float64(x / Float64(y * 0.01));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -3.3e-63)
		tmp = t_0;
	elseif (y <= 1.6e-160)
		tmp = 100.0;
	elseif (y <= 7.6e-88)
		tmp = t_0;
	elseif (y <= 5.8e+78)
		tmp = 100.0;
	else
		tmp = x / (y * 0.01);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-63], t$95$0, If[LessEqual[y, 1.6e-160], 100.0, If[LessEqual[y, 7.6e-88], t$95$0, If[LessEqual[y, 5.8e+78], 100.0, N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999994e-63 or 1.60000000000000004e-160 < y < 7.60000000000000022e-88

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around 0 71.8%

      \[\leadsto x \cdot \color{blue}{\frac{100}{y}} \]

   if -3.29999999999999994e-63 < y < 1.60000000000000004e-160 or 7.60000000000000022e-88 < y < 5.80000000000000034e78

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{100} \]

   if 5.80000000000000034e78 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}} \]

      2. remove-double-neg 99.8%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(-\left(-x\right)\right)} + y}{100}} \]

      3. sub0-neg 99.8%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(0 - \left(-x\right)\right)} + y}{100}} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x}{\frac{\color{blue}{0 - \left(\left(-x\right) - y\right)}}{100}} \]

      5. neg-sub0 99.8%

         \[\leadsto \frac{x}{\frac{\color{blue}{-\left(\left(-x\right) - y\right)}}{100}} \]

      6. distribute-frac-neg 99.8%

         \[\leadsto \frac{x}{\color{blue}{-\frac{\left(-x\right) - y}{100}}} \]

      7. div-sub 99.8%

         \[\leadsto \frac{x}{-\color{blue}{\left(\frac{-x}{100} - \frac{y}{100}\right)}} \]

      8. sub-neg 99.8%

         \[\leadsto \frac{x}{-\color{blue}{\left(\frac{-x}{100} + \left(-\frac{y}{100}\right)\right)}} \]

      9. distribute-neg-frac 99.8%

         \[\leadsto \frac{x}{-\left(\frac{-x}{100} + \color{blue}{\frac{-y}{100}}\right)} \]

      10. distribute-neg-out 99.8%

          \[\leadsto \frac{x}{\color{blue}{\left(-\frac{-x}{100}\right) + \left(-\frac{-y}{100}\right)}} \]

      11. neg-mul-1 99.8%

          \[\leadsto \frac{x}{\left(-\frac{\color{blue}{-1 \cdot x}}{100}\right) + \left(-\frac{-y}{100}\right)} \]

      12. associate-/l* 99.8%

          \[\leadsto \frac{x}{\left(-\color{blue}{\frac{-1}{\frac{100}{x}}}\right) + \left(-\frac{-y}{100}\right)} \]

      13. associate-/r/ 99.8%

          \[\leadsto \frac{x}{\left(-\color{blue}{\frac{-1}{100} \cdot x}\right) + \left(-\frac{-y}{100}\right)} \]

      14. metadata-eval 99.8%

          \[\leadsto \frac{x}{\left(-\frac{\color{blue}{-1}}{100} \cdot x\right) + \left(-\frac{-y}{100}\right)} \]

      15. *-inverses 99.8%

          \[\leadsto \frac{x}{\left(-\frac{-\color{blue}{\frac{x}{x}}}{100} \cdot x\right) + \left(-\frac{-y}{100}\right)} \]

      16. distribute-frac-neg 99.8%

          \[\leadsto \frac{x}{\left(-\frac{\color{blue}{\frac{-x}{x}}}{100} \cdot x\right) + \left(-\frac{-y}{100}\right)} \]

      17. associate-/r* 99.8%

          \[\leadsto \frac{x}{\left(-\color{blue}{\frac{-x}{x \cdot 100}} \cdot x\right) + \left(-\frac{-y}{100}\right)} \]

      18. distribute-rgt-neg-in 99.8%

          \[\leadsto \frac{x}{\color{blue}{\frac{-x}{x \cdot 100} \cdot \left(-x\right)} + \left(-\frac{-y}{100}\right)} \]

      19. neg-mul-1 99.8%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\frac{\color{blue}{-1 \cdot y}}{100}\right)} \]

      20. associate-/l* 99.7%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\color{blue}{\frac{-1}{\frac{100}{y}}}\right)} \]

      21. associate-/r/ 99.8%

          \[\leadsto \frac{x}{\frac{-x}{x \cdot 100} \cdot \left(-x\right) + \left(-\color{blue}{\frac{-1}{100} \cdot y}\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

   4. Taylor expanded in x around 0 91.9%

      \[\leadsto \frac{x}{\color{blue}{0.01 \cdot y}} \]
   5. Step-by-step derivation

      1. *-commutative 91.9%

         \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]

   6. Simplified 91.9%

      \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 5: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -2.2e-63)
     t_0
     (if (<= y 1.6e-160)
       100.0
       (if (<= y 2.05e-87) t_0 (if (<= y 6.5e+78) 100.0 (/ (* x 100.0) y)))))))

C

double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -2.2e-63) {
		tmp = t_0;
	} else if (y <= 1.6e-160) {
		tmp = 100.0;
	} else if (y <= 2.05e-87) {
		tmp = t_0;
	} else if (y <= 6.5e+78) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (100.0d0 / y)
    if (y <= (-2.2d-63)) then
        tmp = t_0
    else if (y <= 1.6d-160) then
        tmp = 100.0d0
    else if (y <= 2.05d-87) then
        tmp = t_0
    else if (y <= 6.5d+78) then
        tmp = 100.0d0
    else
        tmp = (x * 100.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -2.2e-63) {
		tmp = t_0;
	} else if (y <= 1.6e-160) {
		tmp = 100.0;
	} else if (y <= 2.05e-87) {
		tmp = t_0;
	} else if (y <= 6.5e+78) {
		tmp = 100.0;
	} else {
		tmp = (x * 100.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -2.2e-63:
		tmp = t_0
	elif y <= 1.6e-160:
		tmp = 100.0
	elif y <= 2.05e-87:
		tmp = t_0
	elif y <= 6.5e+78:
		tmp = 100.0
	else:
		tmp = (x * 100.0) / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -2.2e-63)
		tmp = t_0;
	elseif (y <= 1.6e-160)
		tmp = 100.0;
	elseif (y <= 2.05e-87)
		tmp = t_0;
	elseif (y <= 6.5e+78)
		tmp = 100.0;
	else
		tmp = Float64(Float64(x * 100.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -2.2e-63)
		tmp = t_0;
	elseif (y <= 1.6e-160)
		tmp = 100.0;
	elseif (y <= 2.05e-87)
		tmp = t_0;
	elseif (y <= 6.5e+78)
		tmp = 100.0;
	else
		tmp = (x * 100.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-63], t$95$0, If[LessEqual[y, 1.6e-160], 100.0, If[LessEqual[y, 2.05e-87], t$95$0, If[LessEqual[y, 6.5e+78], 100.0, N[(N[(x * 100.0), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e-63 or 1.60000000000000004e-160 < y < 2.05000000000000016e-87

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around 0 71.8%

      \[\leadsto x \cdot \color{blue}{\frac{100}{y}} \]

   if -2.2e-63 < y < 1.60000000000000004e-160 or 2.05000000000000016e-87 < y < 6.50000000000000036e78

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{100} \]

   if 6.50000000000000036e78 < y

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.6%

         \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

   4. Taylor expanded in x around 0 91.7%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 92.0%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

   6. Applied egg-rr 92.0%

      \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \end{array} \]

Alternative 6: 50.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 100 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 100.0)

C

double code(double x, double y) {
	return 100.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0
end function

Java

public static double code(double x, double y) {
	return 100.0;
}

Python

def code(x, y):
	return 100.0

Julia

function code(x, y)
	return 100.0
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0;
end

Wolfram

code[x_, y_] := 100.0

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]

4. Taylor expanded in x around inf 48.8%

   \[\leadsto \color{blue}{100} \]

5. Final simplification 48.8%

   \[\leadsto 100 \]

Developer target: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1} \cdot \frac{100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ 100.0 (+ x y))))

C

double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / 1.0d0) * (100.0d0 / (x + y))
end function

Java

public static double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Python

def code(x, y):
	return (x / 1.0) * (100.0 / (x + y))

Julia

function code(x, y)
	return Float64(Float64(x / 1.0) * Float64(100.0 / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / 1.0) * (100.0 / (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))