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

Percentage Accurate: 88.6% → 99.4%

Time: 8.1s

Alternatives: 9

Speedup: 0.3×

• could not determine a ground truth

  1. x = -3.9631657107079307e-265
  2. y = 1.7016949393964617e-266
  3. z = -1.7431768469964255e+96

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: 88.6% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-251} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-251) (not (<= t_0 0.0))) t_0 (- (- z) (* z (/ 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-251) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (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-251)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - (z * (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-251) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-251) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - (z * (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-251) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z * 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-251) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - (z * (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-251], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000002e-251 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -1.00000000000000002e-251 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 8.2%

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

   3. Taylor expanded in y around inf 8.2%

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

      1. neg-mul-1 8.2%

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

      2. distribute-neg-frac2 8.2%

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

   5. Simplified 8.2%

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

   6. Taylor expanded in x around 0 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

      3. mul-1-neg 97.5%

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

      4. *-commutative 97.5%

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

      5. associate-/l* 99.9%

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

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\left(-z\right) - z \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-251} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t\_0}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)))
   (if (<= y -3e+56)
     (- z)
     (if (<= y -2e+22)
       (/ x t_0)
       (if (<= y -3.4e-5)
         t_1
         (if (<= y 4e-33)
           (+ x y)
           (if (<= y 1.8e+36)
             t_1
             (if (<= y 1.75e+93) (/ (* x z) (- y)) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double tmp;
	if (y <= -3e+56) {
		tmp = -z;
	} else if (y <= -2e+22) {
		tmp = x / t_0;
	} else if (y <= -3.4e-5) {
		tmp = t_1;
	} else if (y <= 4e-33) {
		tmp = x + y;
	} else if (y <= 1.8e+36) {
		tmp = t_1;
	} else if (y <= 1.75e+93) {
		tmp = (x * z) / -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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    if (y <= (-3d+56)) then
        tmp = -z
    else if (y <= (-2d+22)) then
        tmp = x / t_0
    else if (y <= (-3.4d-5)) then
        tmp = t_1
    else if (y <= 4d-33) then
        tmp = x + y
    else if (y <= 1.8d+36) then
        tmp = t_1
    else if (y <= 1.75d+93) then
        tmp = (x * z) / -y
    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 = y / t_0;
	double tmp;
	if (y <= -3e+56) {
		tmp = -z;
	} else if (y <= -2e+22) {
		tmp = x / t_0;
	} else if (y <= -3.4e-5) {
		tmp = t_1;
	} else if (y <= 4e-33) {
		tmp = x + y;
	} else if (y <= 1.8e+36) {
		tmp = t_1;
	} else if (y <= 1.75e+93) {
		tmp = (x * z) / -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	tmp = 0
	if y <= -3e+56:
		tmp = -z
	elif y <= -2e+22:
		tmp = x / t_0
	elif y <= -3.4e-5:
		tmp = t_1
	elif y <= 4e-33:
		tmp = x + y
	elif y <= 1.8e+36:
		tmp = t_1
	elif y <= 1.75e+93:
		tmp = (x * z) / -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -3e+56)
		tmp = Float64(-z);
	elseif (y <= -2e+22)
		tmp = Float64(x / t_0);
	elseif (y <= -3.4e-5)
		tmp = t_1;
	elseif (y <= 4e-33)
		tmp = Float64(x + y);
	elseif (y <= 1.8e+36)
		tmp = t_1;
	elseif (y <= 1.75e+93)
		tmp = Float64(Float64(x * z) / Float64(-y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	tmp = 0.0;
	if (y <= -3e+56)
		tmp = -z;
	elseif (y <= -2e+22)
		tmp = x / t_0;
	elseif (y <= -3.4e-5)
		tmp = t_1;
	elseif (y <= 4e-33)
		tmp = x + y;
	elseif (y <= 1.8e+36)
		tmp = t_1;
	elseif (y <= 1.75e+93)
		tmp = (x * z) / -y;
	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[(y / t$95$0), $MachinePrecision]}, If[LessEqual[y, -3e+56], (-z), If[LessEqual[y, -2e+22], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, -3.4e-5], t$95$1, If[LessEqual[y, 4e-33], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.8e+36], t$95$1, If[LessEqual[y, 1.75e+93], N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision], (-z)]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.00000000000000006e56 or 1.74999999999999999e93 < y

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. mul-1-neg 73.8%

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

   5. Simplified 73.8%

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

   if -3.00000000000000006e56 < y < -2e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.3%

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

   if -2e22 < y < -3.4e-5 or 4.0000000000000002e-33 < y < 1.7999999999999999e36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 75.2%

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

   if -3.4e-5 < y < 4.0000000000000002e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. +-commutative 81.0%

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

   5. Simplified 81.0%

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

   if 1.7999999999999999e36 < y < 1.74999999999999999e93

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. neg-mul-1 70.5%

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

      2. distribute-neg-frac2 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in x around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

   8. Simplified 70.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e+51)
   (- z)
   (if (<= y 4.5e-33) (+ x y) (if (<= y 1.5e+93) (* z (/ (- x) y)) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+51) {
		tmp = -z;
	} else if (y <= 4.5e-33) {
		tmp = x + y;
	} else if (y <= 1.5e+93) {
		tmp = z * (-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 <= (-2.05d+51)) then
        tmp = -z
    else if (y <= 4.5d-33) then
        tmp = x + y
    else if (y <= 1.5d+93) then
        tmp = z * (-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 <= -2.05e+51) {
		tmp = -z;
	} else if (y <= 4.5e-33) {
		tmp = x + y;
	} else if (y <= 1.5e+93) {
		tmp = z * (-x / y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e+51:
		tmp = -z
	elif y <= 4.5e-33:
		tmp = x + y
	elif y <= 1.5e+93:
		tmp = z * (-x / y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e+51)
		tmp = Float64(-z);
	elseif (y <= 4.5e-33)
		tmp = Float64(x + y);
	elseif (y <= 1.5e+93)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.05e+51)
		tmp = -z;
	elseif (y <= 4.5e-33)
		tmp = x + y;
	elseif (y <= 1.5e+93)
		tmp = z * (-x / y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e+51], (-z), If[LessEqual[y, 4.5e-33], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.5e+93], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000005e51 or 1.49999999999999989e93 < y

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. mul-1-neg 73.3%

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

   5. Simplified 73.3%

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

   if -2.05000000000000005e51 < y < 4.49999999999999991e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if 4.49999999999999991e-33 < y < 1.49999999999999989e93

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-neg-frac2 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-/l* 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

      4. distribute-neg-frac2 46.7%

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

   8. Simplified 46.7%

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

   9. Taylor expanded in x around 0 52.8%

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

       1. associate-*r/ 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-*r* 52.8%

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

       4. associate-*r/ 52.5%

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

       5. neg-mul-1 52.5%

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

   11. Simplified 52.5%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+51)
   (- z)
   (if (<= y 5.7e-33) (+ x y) (if (<= y 2.8e+93) (/ (* x z) (- y)) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+51) {
		tmp = -z;
	} else if (y <= 5.7e-33) {
		tmp = x + y;
	} else if (y <= 2.8e+93) {
		tmp = (x * z) / -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 <= (-1.55d+51)) then
        tmp = -z
    else if (y <= 5.7d-33) then
        tmp = x + y
    else if (y <= 2.8d+93) then
        tmp = (x * z) / -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 <= -1.55e+51) {
		tmp = -z;
	} else if (y <= 5.7e-33) {
		tmp = x + y;
	} else if (y <= 2.8e+93) {
		tmp = (x * z) / -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+51:
		tmp = -z
	elif y <= 5.7e-33:
		tmp = x + y
	elif y <= 2.8e+93:
		tmp = (x * z) / -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+51)
		tmp = Float64(-z);
	elseif (y <= 5.7e-33)
		tmp = Float64(x + y);
	elseif (y <= 2.8e+93)
		tmp = Float64(Float64(x * z) / Float64(-y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+51)
		tmp = -z;
	elseif (y <= 5.7e-33)
		tmp = x + y;
	elseif (y <= 2.8e+93)
		tmp = (x * z) / -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+51], (-z), If[LessEqual[y, 5.7e-33], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.8e+93], N[(N[(x * z), $MachinePrecision] / (-y)), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000006e51 or 2.79999999999999989e93 < y

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. mul-1-neg 73.3%

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

   5. Simplified 73.3%

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

   if -1.55000000000000006e51 < y < 5.70000000000000025e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if 5.70000000000000025e-33 < y < 2.79999999999999989e93

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-neg-frac2 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. mul-1-neg 52.8%

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

   8. Simplified 52.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+51}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot z}{-y}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-16} \lor \neg \left(y \leq 3.5 \cdot 10^{-33}\right):\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e-16) (not (<= y 3.5e-33)))
   (* z (/ (+ x y) (- y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e-16) || !(y <= 3.5e-33)) {
		tmp = z * ((x + y) / -y);
	} 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 <= (-6.8d-16)) .or. (.not. (y <= 3.5d-33))) then
        tmp = z * ((x + y) / -y)
    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 <= -6.8e-16) || !(y <= 3.5e-33)) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.8e-16) or not (y <= 3.5e-33):
		tmp = z * ((x + y) / -y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e-16) || !(y <= 3.5e-33))
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.8e-16) || ~((y <= 3.5e-33)))
		tmp = z * ((x + y) / -y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e-16], N[Not[LessEqual[y, 3.5e-33]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e-16 or 3.4999999999999999e-33 < y

   1. Initial program 75.8%

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

   3. Taylor expanded in z around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-/l* 84.2%

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

      3. distribute-lft-neg-in 84.2%

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

      4. +-commutative 84.2%

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

   5. Simplified 84.2%

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

   if -6.8e-16 < y < 3.4999999999999999e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. +-commutative 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-16} \lor \neg \left(y \leq 3.5 \cdot 10^{-33}\right):\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-10)
   (- z)
   (if (<= y -5.8e-140) y (if (<= y 4.5e-33) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-10) {
		tmp = -z;
	} else if (y <= -5.8e-140) {
		tmp = y;
	} else if (y <= 4.5e-33) {
		tmp = x;
	} 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-10)) then
        tmp = -z
    else if (y <= (-5.8d-140)) then
        tmp = y
    else if (y <= 4.5d-33) then
        tmp = x
    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-10) {
		tmp = -z;
	} else if (y <= -5.8e-140) {
		tmp = y;
	} else if (y <= 4.5e-33) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e-10:
		tmp = -z
	elif y <= -5.8e-140:
		tmp = y
	elif y <= 4.5e-33:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e-10)
		tmp = Float64(-z);
	elseif (y <= -5.8e-140)
		tmp = y;
	elseif (y <= 4.5e-33)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e-10)
		tmp = -z;
	elseif (y <= -5.8e-140)
		tmp = y;
	elseif (y <= 4.5e-33)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e-10], (-z), If[LessEqual[y, -5.8e-140], y, If[LessEqual[y, 4.5e-33], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000028e-10 or 4.49999999999999991e-33 < y

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. mul-1-neg 60.9%

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

   5. Simplified 60.9%

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

   if -9.50000000000000028e-10 < y < -5.79999999999999995e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 56.8%

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

   4. Taylor expanded in y around 0 48.1%

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

   if -5.79999999999999995e-140 < y < 4.49999999999999991e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.7%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 5.7 \cdot 10^{-33}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.15e+51) (not (<= y 5.7e-33))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e+51) || !(y <= 5.7e-33)) {
		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 <= (-2.15d+51)) .or. (.not. (y <= 5.7d-33))) 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 <= -2.15e+51) || !(y <= 5.7e-33)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.15e+51) or not (y <= 5.7e-33):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.15e+51) || !(y <= 5.7e-33))
		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 <= -2.15e+51) || ~((y <= 5.7e-33)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.15e+51], N[Not[LessEqual[y, 5.7e-33]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e51 or 5.70000000000000025e-33 < y

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 63.5%

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

      1. mul-1-neg 63.5%

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

   5. Simplified 63.5%

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

   if -2.1499999999999999e51 < y < 5.70000000000000025e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 5.7 \cdot 10^{-33}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-163}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5e-126) x (if (<= x 9.4e-163) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e-126) {
		tmp = x;
	} else if (x <= 9.4e-163) {
		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 <= (-5d-126)) then
        tmp = x
    else if (x <= 9.4d-163) 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 <= -5e-126) {
		tmp = x;
	} else if (x <= 9.4e-163) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5e-126:
		tmp = x
	elif x <= 9.4e-163:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5e-126)
		tmp = x;
	elseif (x <= 9.4e-163)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5e-126)
		tmp = x;
	elseif (x <= 9.4e-163)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5e-126], x, If[LessEqual[x, 9.4e-163], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000006e-126 or 9.4e-163 < x

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 40.3%

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

   if -5.00000000000000006e-126 < x < 9.4e-163

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 78.9%

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

   4. Taylor expanded in y around 0 46.5%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-163}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 87.7%

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

3. Taylor expanded in y around 0 32.8%

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

4. Final simplification 32.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.3% 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 2024062 
(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))))