Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.7% → 98.5%

Time: 6.3s

Alternatives: 10

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-208} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-208) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-208) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-208)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-208) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-208) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-208) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-208) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-208], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.0000000000000001e-208 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -1.0000000000000001e-208 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 13.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 94.8%

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

      2. associate-/l* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. +-commutative 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-z}{\frac{y}{y + x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-208} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+144}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= y -3.6e+43)
     (- z)
     (if (<= y 2.1e-199)
       t_1
       (if (<= y 2.6e-65)
         (+ x y)
         (if (<= y 4e+88)
           t_1
           (if (<= y 1.32e+144)
             (/ y t_0)
             (if (<= y 1.35e+144) (/ (- x) (/ y z)) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (y <= -3.6e+43) {
		tmp = -z;
	} else if (y <= 2.1e-199) {
		tmp = t_1;
	} else if (y <= 2.6e-65) {
		tmp = x + y;
	} else if (y <= 4e+88) {
		tmp = t_1;
	} else if (y <= 1.32e+144) {
		tmp = y / t_0;
	} else if (y <= 1.35e+144) {
		tmp = -x / (y / z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (y <= (-3.6d+43)) then
        tmp = -z
    else if (y <= 2.1d-199) then
        tmp = t_1
    else if (y <= 2.6d-65) then
        tmp = x + y
    else if (y <= 4d+88) then
        tmp = t_1
    else if (y <= 1.32d+144) then
        tmp = y / t_0
    else if (y <= 1.35d+144) then
        tmp = -x / (y / z)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (y <= -3.6e+43) {
		tmp = -z;
	} else if (y <= 2.1e-199) {
		tmp = t_1;
	} else if (y <= 2.6e-65) {
		tmp = x + y;
	} else if (y <= 4e+88) {
		tmp = t_1;
	} else if (y <= 1.32e+144) {
		tmp = y / t_0;
	} else if (y <= 1.35e+144) {
		tmp = -x / (y / z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if y <= -3.6e+43:
		tmp = -z
	elif y <= 2.1e-199:
		tmp = t_1
	elif y <= 2.6e-65:
		tmp = x + y
	elif y <= 4e+88:
		tmp = t_1
	elif y <= 1.32e+144:
		tmp = y / t_0
	elif y <= 1.35e+144:
		tmp = -x / (y / z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -3.6e+43)
		tmp = Float64(-z);
	elseif (y <= 2.1e-199)
		tmp = t_1;
	elseif (y <= 2.6e-65)
		tmp = Float64(x + y);
	elseif (y <= 4e+88)
		tmp = t_1;
	elseif (y <= 1.32e+144)
		tmp = Float64(y / t_0);
	elseif (y <= 1.35e+144)
		tmp = Float64(Float64(-x) / Float64(y / z));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (y <= -3.6e+43)
		tmp = -z;
	elseif (y <= 2.1e-199)
		tmp = t_1;
	elseif (y <= 2.6e-65)
		tmp = x + y;
	elseif (y <= 4e+88)
		tmp = t_1;
	elseif (y <= 1.32e+144)
		tmp = y / t_0;
	elseif (y <= 1.35e+144)
		tmp = -x / (y / z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -3.6e+43], (-z), If[LessEqual[y, 2.1e-199], t$95$1, If[LessEqual[y, 2.6e-65], N[(x + y), $MachinePrecision], If[LessEqual[y, 4e+88], t$95$1, If[LessEqual[y, 1.32e+144], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 1.35e+144], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], (-z)]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.6000000000000001e43 or 1.35000000000000008e144 < y

   1. Initial program 68.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.6%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.6%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{-z} \]

   if -3.6000000000000001e43 < y < 2.10000000000000002e-199 or 2.6000000000000001e-65 < y < 3.99999999999999984e88

   1. Initial program 99.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.0%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   if 2.10000000000000002e-199 < y < 2.6000000000000001e-65

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

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

   5. Simplified 79.7%

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

   if 3.99999999999999984e88 < y < 1.32e144

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.9%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   if 1.32e144 < y < 1.35000000000000008e144

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around inf 98.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.4%

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

      2. associate-/l* 100.0%

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

   6. Simplified 100.0%

      \[\leadsto \color{blue}{-\frac{x}{\frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+144}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-64}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -2.5e+43)
     (- z)
     (if (<= y 6.6e-206)
       t_0
       (if (<= y 8.6e-64) (+ x y) (if (<= y 4.2e+94) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.5e+43) {
		tmp = -z;
	} else if (y <= 6.6e-206) {
		tmp = t_0;
	} else if (y <= 8.6e-64) {
		tmp = x + y;
	} else if (y <= 4.2e+94) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-2.5d+43)) then
        tmp = -z
    else if (y <= 6.6d-206) then
        tmp = t_0
    else if (y <= 8.6d-64) then
        tmp = x + y
    else if (y <= 4.2d+94) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.5e+43) {
		tmp = -z;
	} else if (y <= 6.6e-206) {
		tmp = t_0;
	} else if (y <= 8.6e-64) {
		tmp = x + y;
	} else if (y <= 4.2e+94) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -2.5e+43:
		tmp = -z
	elif y <= 6.6e-206:
		tmp = t_0
	elif y <= 8.6e-64:
		tmp = x + y
	elif y <= 4.2e+94:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -2.5e+43)
		tmp = Float64(-z);
	elseif (y <= 6.6e-206)
		tmp = t_0;
	elseif (y <= 8.6e-64)
		tmp = Float64(x + y);
	elseif (y <= 4.2e+94)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -2.5e+43)
		tmp = -z;
	elseif (y <= 6.6e-206)
		tmp = t_0;
	elseif (y <= 8.6e-64)
		tmp = x + y;
	elseif (y <= 4.2e+94)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+43], (-z), If[LessEqual[y, 6.6e-206], t$95$0, If[LessEqual[y, 8.6e-64], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.2e+94], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000002e43 or 4.19999999999999979e94 < y

   1. Initial program 70.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{-z} \]

   if -2.5000000000000002e43 < y < 6.59999999999999961e-206 or 8.59999999999999947e-64 < y < 4.19999999999999979e94

   1. Initial program 99.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.7%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   if 6.59999999999999961e-206 < y < 8.59999999999999947e-64

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-64}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e+26)
   (- z)
   (if (<= y 2.4e+30)
     (+ x y)
     (if (<= y 2.25e+89)
       (/ (- x) (/ y z))
       (if (<= y 3.5e+133) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+26) {
		tmp = -z;
	} else if (y <= 2.4e+30) {
		tmp = x + y;
	} else if (y <= 2.25e+89) {
		tmp = -x / (y / z);
	} else if (y <= 3.5e+133) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.5d+26)) then
        tmp = -z
    else if (y <= 2.4d+30) then
        tmp = x + y
    else if (y <= 2.25d+89) then
        tmp = -x / (y / z)
    else if (y <= 3.5d+133) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+26) {
		tmp = -z;
	} else if (y <= 2.4e+30) {
		tmp = x + y;
	} else if (y <= 2.25e+89) {
		tmp = -x / (y / z);
	} else if (y <= 3.5e+133) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e+26:
		tmp = -z
	elif y <= 2.4e+30:
		tmp = x + y
	elif y <= 2.25e+89:
		tmp = -x / (y / z)
	elif y <= 3.5e+133:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e+26)
		tmp = Float64(-z);
	elseif (y <= 2.4e+30)
		tmp = Float64(x + y);
	elseif (y <= 2.25e+89)
		tmp = Float64(Float64(-x) / Float64(y / z));
	elseif (y <= 3.5e+133)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e+26)
		tmp = -z;
	elseif (y <= 2.4e+30)
		tmp = x + y;
	elseif (y <= 2.25e+89)
		tmp = -x / (y / z);
	elseif (y <= 3.5e+133)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e+26], (-z), If[LessEqual[y, 2.4e+30], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.25e+89], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+133], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000054e26 or 3.4999999999999998e133 < y

   1. Initial program 69.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.7%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{-z} \]

   if -9.50000000000000054e26 < y < 2.3999999999999999e30 or 2.25e89 < y < 3.4999999999999998e133

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 2.3999999999999999e30 < y < 2.25e89

   1. Initial program 93.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around inf 49.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.5%

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

      2. associate-/l* 57.0%

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

   6. Simplified 57.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.4e+27)
   (- z)
   (if (<= y 2.4e+30)
     (+ x y)
     (if (<= y 4.1e+88)
       (* x (/ (- z) y))
       (if (<= y 3.5e+133) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.4e+27) {
		tmp = -z;
	} else if (y <= 2.4e+30) {
		tmp = x + y;
	} else if (y <= 4.1e+88) {
		tmp = x * (-z / y);
	} else if (y <= 3.5e+133) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.4d+27)) then
        tmp = -z
    else if (y <= 2.4d+30) then
        tmp = x + y
    else if (y <= 4.1d+88) then
        tmp = x * (-z / y)
    else if (y <= 3.5d+133) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.4e+27) {
		tmp = -z;
	} else if (y <= 2.4e+30) {
		tmp = x + y;
	} else if (y <= 4.1e+88) {
		tmp = x * (-z / y);
	} else if (y <= 3.5e+133) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.4e+27:
		tmp = -z
	elif y <= 2.4e+30:
		tmp = x + y
	elif y <= 4.1e+88:
		tmp = x * (-z / y)
	elif y <= 3.5e+133:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.4e+27)
		tmp = Float64(-z);
	elseif (y <= 2.4e+30)
		tmp = Float64(x + y);
	elseif (y <= 4.1e+88)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (y <= 3.5e+133)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.4e+27)
		tmp = -z;
	elseif (y <= 2.4e+30)
		tmp = x + y;
	elseif (y <= 4.1e+88)
		tmp = x * (-z / y);
	elseif (y <= 3.5e+133)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.4e+27], (-z), If[LessEqual[y, 2.4e+30], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.1e+88], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+133], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.39999999999999952e27 or 3.4999999999999998e133 < y

   1. Initial program 69.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.7%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{-z} \]

   if -9.39999999999999952e27 < y < 2.3999999999999999e30 or 4.10000000000000028e88 < y < 3.4999999999999998e133

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 2.3999999999999999e30 < y < 4.10000000000000028e88

   1. Initial program 93.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around inf 49.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.5%

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

      2. distribute-neg-frac 49.5%

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

      3. distribute-lft-neg-out 49.5%

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

      4. associate-*r/ 57.1%

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

      5. distribute-lft-neg-out 57.1%

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

      6. distribute-rgt-neg-in 57.1%

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

      7. distribute-frac-neg 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+27}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+133}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-36} \lor \neg \left(y \leq 1.18 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e-36) (not (<= y 1.18e+36)))
   (/ (- z) (/ y (+ x y)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e-36) || !(y <= 1.18e+36)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.2d-36)) .or. (.not. (y <= 1.18d+36))) then
        tmp = -z / (y / (x + y))
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e-36) || !(y <= 1.18e+36)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e-36) or not (y <= 1.18e+36):
		tmp = -z / (y / (x + y))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e-36) || !(y <= 1.18e+36))
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.2e-36) || ~((y <= 1.18e+36)))
		tmp = -z / (y / (x + y));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e-36], N[Not[LessEqual[y, 1.18e+36]], $MachinePrecision]], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e-36 or 1.17999999999999997e36 < y

   1. Initial program 74.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 67.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 67.4%

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

      2. associate-/l* 80.3%

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

      3. distribute-neg-frac 80.3%

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

      4. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -2.1999999999999999e-36 < y < 1.17999999999999997e36

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.1%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-36} \lor \neg \left(y \leq 1.18 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+29} \lor \neg \left(y \leq 3.3 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e+29) (not (<= y 3.3e+133))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+29) || !(y <= 3.3e+133)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.5d+29)) .or. (.not. (y <= 3.3d+133))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+29) || !(y <= 3.3e+133)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e+29) or not (y <= 3.3e+133):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e+29) || !(y <= 3.3e+133))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e+29) || ~((y <= 3.3e+133)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e+29], N[Not[LessEqual[y, 3.3e+133]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e29 or 3.3e133 < y

   1. Initial program 69.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.7%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{-z} \]

   if -2.5e29 < y < 3.3e133

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+29} \lor \neg \left(y \leq 3.3 \cdot 10^{+133}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-38} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.85e-38) (not (<= y 1.2e+37))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.85e-38) || !(y <= 1.2e+37)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.85d-38)) .or. (.not. (y <= 1.2d+37))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.85e-38) || !(y <= 1.2e+37)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.85e-38) or not (y <= 1.2e+37):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.85e-38) || !(y <= 1.2e+37))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.85e-38) || ~((y <= 1.2e+37)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.85e-38], N[Not[LessEqual[y, 1.2e+37]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.84999999999999997e-38 or 1.2e37 < y

   1. Initial program 74.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 65.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{-z} \]

   if -2.84999999999999997e-38 < y < 1.2e37

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-38} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-67) x (if (<= x 1.2e-128) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-67) {
		tmp = x;
	} else if (x <= 1.2e-128) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.2d-67)) then
        tmp = x
    else if (x <= 1.2d-128) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-67) {
		tmp = x;
	} else if (x <= 1.2e-128) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-67:
		tmp = x
	elif x <= 1.2e-128:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-67)
		tmp = x;
	elseif (x <= 1.2e-128)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-67)
		tmp = x;
	elseif (x <= 1.2e-128)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-67], x, If[LessEqual[x, 1.2e-128], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999998e-67 or 1.1999999999999999e-128 < x

   1. Initial program 88.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 45.9%

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

   if -7.19999999999999998e-67 < x < 1.1999999999999999e-128

   1. Initial program 83.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.2%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around 0 31.0%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.5% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.6%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 34.4%

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

4. Final simplification 34.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))