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

Percentage Accurate: 87.8% → 99.8%

Time: 6.1s

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: 87.8% 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: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-305} \lor \neg \left(t\_0 \leq 2 \cdot 10^{-287}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-305) (not (<= t_0 2e-287)))
     t_0
     (- (- z) (/ (* z (+ x z)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-305) || !(t_0 <= 2e-287)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / 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 <= (-5d-305)) .or. (.not. (t_0 <= 2d-287))) then
        tmp = t_0
    else
        tmp = -z - ((z * (x + z)) / 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 <= -5e-305) || !(t_0 <= 2e-287)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-305) or not (t_0 <= 2e-287):
		tmp = t_0
	else:
		tmp = -z - ((z * (x + z)) / 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 <= -5e-305) || !(t_0 <= 2e-287))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(z * Float64(x + z)) / 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 <= -5e-305) || ~((t_0 <= 2e-287)))
		tmp = t_0;
	else
		tmp = -z - ((z * (x + z)) / 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, -5e-305], N[Not[LessEqual[t$95$0, 2e-287]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999985e-305 or 2.00000000000000004e-287 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.99999999999999985e-305 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 2.00000000000000004e-287

   1. Initial program 8.6%

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

   3. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}\right) - \frac{{z}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate--l+ 99.9%

         \[\leadsto \color{blue}{-1 \cdot z + \left(-1 \cdot \frac{x \cdot z}{y} - \frac{{z}^{2}}{y}\right)} \]

      2. associate-*r/ 99.9%

         \[\leadsto -1 \cdot z + \left(\color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} - \frac{{z}^{2}}{y}\right) \]

      3. div-sub 99.9%

         \[\leadsto -1 \cdot z + \color{blue}{\frac{-1 \cdot \left(x \cdot z\right) - {z}^{2}}{y}} \]

      4. remove-double-neg 99.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{\left(-\left(-{z}^{2}\right)\right)}}{y} \]

      5. mul-1-neg 99.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \left(-\color{blue}{-1 \cdot {z}^{2}}\right)}{y} \]

      6. neg-mul-1 99.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{-1 \cdot \left(-1 \cdot {z}^{2}\right)}}{y} \]

      7. distribute-lft-out-- 99.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-1 \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      8. mul-1-neg 99.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-\left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      9. distribute-neg-frac 99.9%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)} \]

      10. unsub-neg 99.9%

          \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      11. mul-1-neg 99.9%

          \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z - -1 \cdot {z}^{2}}{y} \]

      12. cancel-sign-sub-inv 99.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{x \cdot z + \left(--1\right) \cdot {z}^{2}}}{y} \]

      13. metadata-eval 99.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      14. *-lft-identity 99.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      15. +-commutative 99.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      16. unpow2 99.9%

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

      17. distribute-rgt-out 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-305} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-287}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-305} \lor \neg \left(t\_0 \leq 2 \cdot 10^{-287}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-305) (not (<= t_0 2e-287)))
     t_0
     (- (- z) (/ (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-305) || !(t_0 <= 2e-287)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / 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 <= (-5d-305)) .or. (.not. (t_0 <= 2d-287))) then
        tmp = t_0
    else
        tmp = -z - ((x * z) / 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 <= -5e-305) || !(t_0 <= 2e-287)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-305) or not (t_0 <= 2e-287):
		tmp = t_0
	else:
		tmp = -z - ((x * z) / 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 <= -5e-305) || !(t_0 <= 2e-287))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / 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 <= -5e-305) || ~((t_0 <= 2e-287)))
		tmp = t_0;
	else
		tmp = -z - ((x * z) / 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, -5e-305], N[Not[LessEqual[t$95$0, 2e-287]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999985e-305 or 2.00000000000000004e-287 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -4.99999999999999985e-305 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 2.00000000000000004e-287

   1. Initial program 8.6%

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

   3. Taylor expanded in z around 0 97.0%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto -1 \cdot \color{blue}{\left(z + \frac{x \cdot z}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-305} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 2 \cdot 10^{-287}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t\_0}\\ t_2 := \frac{x}{t\_0}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-262}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-183}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (/ x t_0)))
   (if (<= y -1.75e+15)
     t_1
     (if (<= y -7.5e-262)
       t_2
       (if (<= y 7.5e-183)
         (+ x y)
         (if (<= y 4.5e-8) t_2 (if (<= y 1.9e+219) t_1 (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -1.75e+15) {
		tmp = t_1;
	} else if (y <= -7.5e-262) {
		tmp = t_2;
	} else if (y <= 7.5e-183) {
		tmp = x + y;
	} else if (y <= 4.5e-8) {
		tmp = t_2;
	} else if (y <= 1.9e+219) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = x / t_0
    if (y <= (-1.75d+15)) then
        tmp = t_1
    else if (y <= (-7.5d-262)) then
        tmp = t_2
    else if (y <= 7.5d-183) then
        tmp = x + y
    else if (y <= 4.5d-8) then
        tmp = t_2
    else if (y <= 1.9d+219) then
        tmp = t_1
    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 t_2 = x / t_0;
	double tmp;
	if (y <= -1.75e+15) {
		tmp = t_1;
	} else if (y <= -7.5e-262) {
		tmp = t_2;
	} else if (y <= 7.5e-183) {
		tmp = x + y;
	} else if (y <= 4.5e-8) {
		tmp = t_2;
	} else if (y <= 1.9e+219) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = x / t_0
	tmp = 0
	if y <= -1.75e+15:
		tmp = t_1
	elif y <= -7.5e-262:
		tmp = t_2
	elif y <= 7.5e-183:
		tmp = x + y
	elif y <= 4.5e-8:
		tmp = t_2
	elif y <= 1.9e+219:
		tmp = t_1
	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)
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -1.75e+15)
		tmp = t_1;
	elseif (y <= -7.5e-262)
		tmp = t_2;
	elseif (y <= 7.5e-183)
		tmp = Float64(x + y);
	elseif (y <= 4.5e-8)
		tmp = t_2;
	elseif (y <= 1.9e+219)
		tmp = t_1;
	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;
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -1.75e+15)
		tmp = t_1;
	elseif (y <= -7.5e-262)
		tmp = t_2;
	elseif (y <= 7.5e-183)
		tmp = x + y;
	elseif (y <= 4.5e-8)
		tmp = t_2;
	elseif (y <= 1.9e+219)
		tmp = t_1;
	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]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.75e+15], t$95$1, If[LessEqual[y, -7.5e-262], t$95$2, If[LessEqual[y, 7.5e-183], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.5e-8], t$95$2, If[LessEqual[y, 1.9e+219], t$95$1, (-z)]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.75e15 or 4.49999999999999993e-8 < y < 1.89999999999999998e219

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0 64.7%

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

   if -1.75e15 < y < -7.5000000000000002e-262 or 7.5000000000000004e-183 < y < 4.49999999999999993e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.2%

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

   if -7.5000000000000002e-262 < y < 7.5000000000000004e-183

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if 1.89999999999999998e219 < y

   1. Initial program 47.3%

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

   3. Taylor expanded in y around inf 94.5%

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

      1. mul-1-neg 94.5%

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

   5. Simplified 94.5%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-183}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+219}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-262}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-183}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 0.00015:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -1.02e+71)
     (- z)
     (if (<= y -2.5e-262)
       t_0
       (if (<= y 1.85e-183) (+ x y) (if (<= y 0.00015) t_0 (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -1.02e+71) {
		tmp = -z;
	} else if (y <= -2.5e-262) {
		tmp = t_0;
	} else if (y <= 1.85e-183) {
		tmp = x + y;
	} else if (y <= 0.00015) {
		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 <= (-1.02d+71)) then
        tmp = -z
    else if (y <= (-2.5d-262)) then
        tmp = t_0
    else if (y <= 1.85d-183) then
        tmp = x + y
    else if (y <= 0.00015d0) 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 <= -1.02e+71) {
		tmp = -z;
	} else if (y <= -2.5e-262) {
		tmp = t_0;
	} else if (y <= 1.85e-183) {
		tmp = x + y;
	} else if (y <= 0.00015) {
		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 <= -1.02e+71:
		tmp = -z
	elif y <= -2.5e-262:
		tmp = t_0
	elif y <= 1.85e-183:
		tmp = x + y
	elif y <= 0.00015:
		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 <= -1.02e+71)
		tmp = Float64(-z);
	elseif (y <= -2.5e-262)
		tmp = t_0;
	elseif (y <= 1.85e-183)
		tmp = Float64(x + y);
	elseif (y <= 0.00015)
		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 <= -1.02e+71)
		tmp = -z;
	elseif (y <= -2.5e-262)
		tmp = t_0;
	elseif (y <= 1.85e-183)
		tmp = x + y;
	elseif (y <= 0.00015)
		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, -1.02e+71], (-z), If[LessEqual[y, -2.5e-262], t$95$0, If[LessEqual[y, 1.85e-183], N[(x + y), $MachinePrecision], If[LessEqual[y, 0.00015], t$95$0, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02000000000000003e71 or 1.49999999999999987e-4 < y

   1. Initial program 71.2%

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

   3. Taylor expanded in y around inf 65.0%

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

      1. mul-1-neg 65.0%

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

   5. Simplified 65.0%

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

   if -1.02000000000000003e71 < y < -2.49999999999999996e-262 or 1.8499999999999999e-183 < y < 1.49999999999999987e-4

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 66.6%

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

   if -2.49999999999999996e-262 < y < 1.8499999999999999e-183

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-183}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 0.00015:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-20}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-66}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.12e-20)
   (- z)
   (if (<= y 1.35e-119) x (if (<= y 2.2e-66) y (if (<= y 1.5e-11) x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e-20) {
		tmp = -z;
	} else if (y <= 1.35e-119) {
		tmp = x;
	} else if (y <= 2.2e-66) {
		tmp = y;
	} else if (y <= 1.5e-11) {
		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 <= (-1.12d-20)) then
        tmp = -z
    else if (y <= 1.35d-119) then
        tmp = x
    else if (y <= 2.2d-66) then
        tmp = y
    else if (y <= 1.5d-11) 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 <= -1.12e-20) {
		tmp = -z;
	} else if (y <= 1.35e-119) {
		tmp = x;
	} else if (y <= 2.2e-66) {
		tmp = y;
	} else if (y <= 1.5e-11) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.12e-20:
		tmp = -z
	elif y <= 1.35e-119:
		tmp = x
	elif y <= 2.2e-66:
		tmp = y
	elif y <= 1.5e-11:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.12e-20)
		tmp = Float64(-z);
	elseif (y <= 1.35e-119)
		tmp = x;
	elseif (y <= 2.2e-66)
		tmp = y;
	elseif (y <= 1.5e-11)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.12e-20)
		tmp = -z;
	elseif (y <= 1.35e-119)
		tmp = x;
	elseif (y <= 2.2e-66)
		tmp = y;
	elseif (y <= 1.5e-11)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.12e-20], (-z), If[LessEqual[y, 1.35e-119], x, If[LessEqual[y, 2.2e-66], y, If[LessEqual[y, 1.5e-11], x, (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12000000000000002e-20 or 1.5e-11 < y

   1. Initial program 75.3%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. mul-1-neg 59.2%

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

   5. Simplified 59.2%

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

   if -1.12000000000000002e-20 < y < 1.35000000000000013e-119 or 2.2000000000000001e-66 < y < 1.5e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.6%

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

   if 1.35000000000000013e-119 < y < 2.2000000000000001e-66

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 59.9%

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

   4. Taylor expanded in y around 0 38.1%

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

Alternative 6: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+25} \lor \neg \left(z \leq 1.2 \cdot 10^{-52}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e+25) (not (<= z 1.2e-52)))
   (+ x y)
   (- (- z) (/ (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e+25) || !(z <= 1.2e-52)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / 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 ((z <= (-2.3d+25)) .or. (.not. (z <= 1.2d-52))) then
        tmp = x + y
    else
        tmp = -z - ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e+25) || !(z <= 1.2e-52)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e+25) or not (z <= 1.2e-52):
		tmp = x + y
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e+25) || !(z <= 1.2e-52))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e+25) || ~((z <= 1.2e-52)))
		tmp = x + y;
	else
		tmp = -z - ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e+25], N[Not[LessEqual[z, 1.2e-52]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e25 or 1.2000000000000001e-52 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.7%

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

      1. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if -2.2999999999999998e25 < z < 1.2000000000000001e-52

   1. Initial program 74.9%

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

   3. Taylor expanded in z around 0 76.0%

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

   4. Taylor expanded in x around 0 83.6%

      \[\leadsto -1 \cdot \color{blue}{\left(z + \frac{x \cdot z}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+25} \lor \neg \left(z \leq 1.2 \cdot 10^{-52}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-51}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+25) (not (<= z 2.15e-51)))
   (+ x y)
   (* z (/ (+ x y) (- y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+25) || !(z <= 2.15e-51)) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -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 ((z <= (-2.5d+25)) .or. (.not. (z <= 2.15d-51))) then
        tmp = x + y
    else
        tmp = z * ((x + y) / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+25) || !(z <= 2.15e-51)) {
		tmp = x + y;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+25) or not (z <= 2.15e-51):
		tmp = x + y
	else:
		tmp = z * ((x + y) / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+25) || !(z <= 2.15e-51))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e+25) || ~((z <= 2.15e-51)))
		tmp = x + y;
	else
		tmp = z * ((x + y) / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+25], N[Not[LessEqual[z, 2.15e-51]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000012e25 or 2.1499999999999999e-51 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.7%

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

      1. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if -2.50000000000000012e25 < z < 2.1499999999999999e-51

   1. Initial program 74.9%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-/l* 83.0%

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

      3. associate-*r* 83.0%

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

      4. associate-*l/ 83.0%

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

      5. *-commutative 83.0%

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

      6. neg-mul-1 83.0%

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

      7. distribute-neg-in 83.0%

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

      8. unsub-neg 83.0%

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

   5. Simplified 83.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+25} \lor \neg \left(z \leq 2.15 \cdot 10^{-51}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+73} \lor \neg \left(y \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.2e+73) (not (<= y 2.1e+28))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+73) || !(y <= 2.1e+28)) {
		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 <= (-8.2d+73)) .or. (.not. (y <= 2.1d+28))) 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 <= -8.2e+73) || !(y <= 2.1e+28)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.2e+73) or not (y <= 2.1e+28):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.2e+73) || !(y <= 2.1e+28))
		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 <= -8.2e+73) || ~((y <= 2.1e+28)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.2e+73], N[Not[LessEqual[y, 2.1e+28]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e73 or 2.09999999999999989e28 < y

   1. Initial program 68.7%

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

   3. Taylor expanded in y around inf 66.9%

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

      1. mul-1-neg 66.9%

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

   5. Simplified 66.9%

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

   if -8.1999999999999996e73 < y < 2.09999999999999989e28

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 67.7%

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

      1. +-commutative 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+73} \lor \neg \left(y \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-159}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-165) x (if (<= x 7.5e-159) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-165) {
		tmp = x;
	} else if (x <= 7.5e-159) {
		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 <= (-1.6d-165)) then
        tmp = x
    else if (x <= 7.5d-159) 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 <= -1.6e-165) {
		tmp = x;
	} else if (x <= 7.5e-159) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-165:
		tmp = x
	elif x <= 7.5e-159:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-165)
		tmp = x;
	elseif (x <= 7.5e-159)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e-165)
		tmp = x;
	elseif (x <= 7.5e-159)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-165], x, If[LessEqual[x, 7.5e-159], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000006e-165 or 7.5e-159 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 40.2%

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

   if -1.60000000000000006e-165 < x < 7.5e-159

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in y around 0 36.0%

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

Alternative 10: 35.2% 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 88.1%

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

3. Taylor expanded in y around 0 34.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 93.9% 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 2024103 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (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))))