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

Percentage Accurate: 87.7% → 99.7%

Time: 13.8s

Alternatives: 7

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: 87.7% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-268}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -4e-268)
     t_0
     (if (<= t_0 0.0) (* z (- -1.0 (/ x y))) (/ (+ x y) (/ (- z y) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -4e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (x + y) / ((z - 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-4d-268)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = (x + y) / ((z - y) / z)
    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 <= -4e-268) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = (x + y) / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -4e-268:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = (x + y) / ((z - y) / z)
	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 <= -4e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x + y) / Float64(Float64(z - y) / z));
	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 <= -4e-268)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = (x + y) / ((z - y) / z);
	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[LessEqual[t$95$0, -4e-268], t$95$0, If[LessEqual[t$95$0, 0.0], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999983e-268

   1. Initial program 99.9%

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

   if -3.99999999999999983e-268 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 10.2%

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

   3. Taylor expanded in z around 0 10.2%

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

      1. *-un-lft-identity 10.2%

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

      2. div-inv 10.2%

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

      3. times-frac 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in y around inf 97.3%

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

   7. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. metadata-eval 99.9%

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

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

   if -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.9%

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

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-268} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-268) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ 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 <= -4e-268) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (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 <= (-4d-268)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (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 <= -4e-268) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-268) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (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 <= -4e-268) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - 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 <= -4e-268) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (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, -4e-268], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999983e-268 or -0.0 < (/.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 -3.99999999999999983e-268 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 10.2%

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

   3. Taylor expanded in z around 0 10.2%

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

      1. *-un-lft-identity 10.2%

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

      2. div-inv 10.2%

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

      3. times-frac 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in y around inf 97.3%

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

   7. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. metadata-eval 99.9%

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

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-268} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-43} \lor \neg \left(z \leq 1.8 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e-43) (not (<= z 1.8e+23))) (+ x y) (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-43) || !(z <= 1.8e+23)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (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 ((z <= (-3.3d-43)) .or. (.not. (z <= 1.8d+23))) then
        tmp = x + y
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-43) || !(z <= 1.8e+23)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e-43) or not (z <= 1.8e+23):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e-43) || !(z <= 1.8e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e-43) || ~((z <= 1.8e+23)))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e-43], N[Not[LessEqual[z, 1.8e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000016e-43 or 1.7999999999999999e23 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. +-commutative 79.5%

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

   5. Simplified 79.5%

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

   if -3.30000000000000016e-43 < z < 1.7999999999999999e23

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. *-un-lft-identity 71.1%

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

      2. div-inv 70.9%

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

      3. times-frac 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in y around inf 86.9%

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

   7. Taylor expanded in z around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-rgt-neg-in 74.4%

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

      3. mul-1-neg 74.4%

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

      4. distribute-lft-in 74.4%

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

      5. metadata-eval 74.4%

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

      6. mul-1-neg 74.4%

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

      7. unsub-neg 74.4%

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

   9. Simplified 74.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-43} \lor \neg \left(z \leq 1.8 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+48} \lor \neg \left(y \leq 2.9 \cdot 10^{+100}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e+48) (not (<= y 2.9e+100))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+48) || !(y <= 2.9e+100)) {
		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 <= (-6d+48)) .or. (.not. (y <= 2.9d+100))) 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 <= -6e+48) || !(y <= 2.9e+100)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e+48) or not (y <= 2.9e+100):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e+48) || !(y <= 2.9e+100))
		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 <= -6e+48) || ~((y <= 2.9e+100)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e+48], N[Not[LessEqual[y, 2.9e+100]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9999999999999999e48 or 2.9e100 < y

   1. Initial program 60.2%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. neg-mul-1 70.5%

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

   5. Simplified 70.5%

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

   if -5.9999999999999999e48 < y < 2.9e100

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. +-commutative 72.4%

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

   5. Simplified 72.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+48} \lor \neg \left(y \leq 2.9 \cdot 10^{+100}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+47} \lor \neg \left(y \leq 4.5 \cdot 10^{-41}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+47) (not (<= y 4.5e-41))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+47) || !(y <= 4.5e-41)) {
		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 <= (-1.8d+47)) .or. (.not. (y <= 4.5d-41))) 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 <= -1.8e+47) || !(y <= 4.5e-41)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+47) or not (y <= 4.5e-41):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+47) || !(y <= 4.5e-41))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+47) || ~((y <= 4.5e-41)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+47], N[Not[LessEqual[y, 4.5e-41]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000004e47 or 4.5e-41 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. neg-mul-1 59.5%

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

   5. Simplified 59.5%

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

   if -1.80000000000000004e47 < y < 4.5e-41

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 61.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+47} \lor \neg \left(y \leq 4.5 \cdot 10^{-41}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-136}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-88) x (if (<= x 2.9e-136) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-88) {
		tmp = x;
	} else if (x <= 2.9e-136) {
		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 <= (-1.8d-88)) then
        tmp = x
    else if (x <= 2.9d-136) 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 <= -1.8e-88) {
		tmp = x;
	} else if (x <= 2.9e-136) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e-88:
		tmp = x
	elif x <= 2.9e-136:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-88)
		tmp = x;
	elseif (x <= 2.9e-136)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e-88)
		tmp = x;
	elseif (x <= 2.9e-136)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-88], x, If[LessEqual[x, 2.9e-136], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-88 or 2.89999999999999995e-136 < x

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 47.1%

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

   if -1.8e-88 < x < 2.89999999999999995e-136

   1. Initial program 81.4%

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

   3. Taylor expanded in z around inf 52.0%

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

      1. +-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around inf 39.6%

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

Alternative 7: 34.8% 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 85.2%

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

3. Taylor expanded in y around 0 37.3%

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

Developer Target 1: 93.5% 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 2024143 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

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