Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.6% → 97.0%

Time: 17.2s

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (y - z)) / (t - z);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (y - z)) / (t - z);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x * ((y - z) / (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y - z) / (t - z))
end function

Java

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

Python

def code(x, y, z, t):
	return x * ((y - z) / (t - z))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y - z) / Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y - z) / (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.2%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 86.2%

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

   2. associate-*l/ 97.5%

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

   3. *-commutative 97.5%

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

3. Simplified 97.5%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Final simplification 97.5%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 2: 70.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -5.8e+72)
     t_2
     (if (<= t -3.8e-18)
       t_1
       (if (<= t -6.4e-81)
         t_2
         (if (<= t -3.5e-107)
           t_1
           (if (<= t -1.15e-144)
             (* x (/ y (- t z)))
             (if (<= t 6.2) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -5.8e+72) {
		tmp = t_2;
	} else if (t <= -3.8e-18) {
		tmp = t_1;
	} else if (t <= -6.4e-81) {
		tmp = t_2;
	} else if (t <= -3.5e-107) {
		tmp = t_1;
	} else if (t <= -1.15e-144) {
		tmp = x * (y / (t - z));
	} else if (t <= 6.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    t_2 = x * ((y - z) / t)
    if (t <= (-5.8d+72)) then
        tmp = t_2
    else if (t <= (-3.8d-18)) then
        tmp = t_1
    else if (t <= (-6.4d-81)) then
        tmp = t_2
    else if (t <= (-3.5d-107)) then
        tmp = t_1
    else if (t <= (-1.15d-144)) then
        tmp = x * (y / (t - z))
    else if (t <= 6.2d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -5.8e+72) {
		tmp = t_2;
	} else if (t <= -3.8e-18) {
		tmp = t_1;
	} else if (t <= -6.4e-81) {
		tmp = t_2;
	} else if (t <= -3.5e-107) {
		tmp = t_1;
	} else if (t <= -1.15e-144) {
		tmp = x * (y / (t - z));
	} else if (t <= 6.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	t_2 = x * ((y - z) / t)
	tmp = 0
	if t <= -5.8e+72:
		tmp = t_2
	elif t <= -3.8e-18:
		tmp = t_1
	elif t <= -6.4e-81:
		tmp = t_2
	elif t <= -3.5e-107:
		tmp = t_1
	elif t <= -1.15e-144:
		tmp = x * (y / (t - z))
	elif t <= 6.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	t_2 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -5.8e+72)
		tmp = t_2;
	elseif (t <= -3.8e-18)
		tmp = t_1;
	elseif (t <= -6.4e-81)
		tmp = t_2;
	elseif (t <= -3.5e-107)
		tmp = t_1;
	elseif (t <= -1.15e-144)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 6.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	t_2 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -5.8e+72)
		tmp = t_2;
	elseif (t <= -3.8e-18)
		tmp = t_1;
	elseif (t <= -6.4e-81)
		tmp = t_2;
	elseif (t <= -3.5e-107)
		tmp = t_1;
	elseif (t <= -1.15e-144)
		tmp = x * (y / (t - z));
	elseif (t <= 6.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+72], t$95$2, If[LessEqual[t, -3.8e-18], t$95$1, If[LessEqual[t, -6.4e-81], t$95$2, If[LessEqual[t, -3.5e-107], t$95$1, If[LessEqual[t, -1.15e-144], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.80000000000000034e72 or -3.7999999999999998e-18 < t < -6.4e-81 or 6.20000000000000018 < t

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 85.7%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.3%

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

   if -5.80000000000000034e72 < t < -3.7999999999999998e-18 or -6.4e-81 < t < -3.49999999999999985e-107 or -1.15e-144 < t < 6.20000000000000018

   1. Initial program 85.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

      2. associate-*l/ 96.8%

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

      3. *-commutative 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 83.2%

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

      3. distribute-neg-frac 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

      3. associate-*l/ 83.5%

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

      4. *-commutative 83.5%

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

   10. Simplified 83.5%

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

   if -3.49999999999999985e-107 < t < -1.15e-144

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 94.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 3.7:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -2.65e+73)
     t_2
     (if (<= t -2.4e-18)
       t_1
       (if (<= t -5.8e-81)
         (/ x (/ t (- y z)))
         (if (<= t -2.6e-107)
           t_1
           (if (<= t -7.4e-147)
             (* x (/ y (- t z)))
             (if (<= t 3.7) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -2.65e+73) {
		tmp = t_2;
	} else if (t <= -2.4e-18) {
		tmp = t_1;
	} else if (t <= -5.8e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -2.6e-107) {
		tmp = t_1;
	} else if (t <= -7.4e-147) {
		tmp = x * (y / (t - z));
	} else if (t <= 3.7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    t_2 = x * ((y - z) / t)
    if (t <= (-2.65d+73)) then
        tmp = t_2
    else if (t <= (-2.4d-18)) then
        tmp = t_1
    else if (t <= (-5.8d-81)) then
        tmp = x / (t / (y - z))
    else if (t <= (-2.6d-107)) then
        tmp = t_1
    else if (t <= (-7.4d-147)) then
        tmp = x * (y / (t - z))
    else if (t <= 3.7d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -2.65e+73) {
		tmp = t_2;
	} else if (t <= -2.4e-18) {
		tmp = t_1;
	} else if (t <= -5.8e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -2.6e-107) {
		tmp = t_1;
	} else if (t <= -7.4e-147) {
		tmp = x * (y / (t - z));
	} else if (t <= 3.7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	t_2 = x * ((y - z) / t)
	tmp = 0
	if t <= -2.65e+73:
		tmp = t_2
	elif t <= -2.4e-18:
		tmp = t_1
	elif t <= -5.8e-81:
		tmp = x / (t / (y - z))
	elif t <= -2.6e-107:
		tmp = t_1
	elif t <= -7.4e-147:
		tmp = x * (y / (t - z))
	elif t <= 3.7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	t_2 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -2.65e+73)
		tmp = t_2;
	elseif (t <= -2.4e-18)
		tmp = t_1;
	elseif (t <= -5.8e-81)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= -2.6e-107)
		tmp = t_1;
	elseif (t <= -7.4e-147)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 3.7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	t_2 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -2.65e+73)
		tmp = t_2;
	elseif (t <= -2.4e-18)
		tmp = t_1;
	elseif (t <= -5.8e-81)
		tmp = x / (t / (y - z));
	elseif (t <= -2.6e-107)
		tmp = t_1;
	elseif (t <= -7.4e-147)
		tmp = x * (y / (t - z));
	elseif (t <= 3.7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e+73], t$95$2, If[LessEqual[t, -2.4e-18], t$95$1, If[LessEqual[t, -5.8e-81], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-107], t$95$1, If[LessEqual[t, -7.4e-147], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.64999999999999998e73 or 3.7000000000000002 < t

   1. Initial program 84.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 84.2%

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

      2. associate-*l/ 97.9%

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

      3. *-commutative 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.3%

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

   if -2.64999999999999998e73 < t < -2.39999999999999994e-18 or -5.79999999999999978e-81 < t < -2.6000000000000001e-107 or -7.40000000000000039e-147 < t < 3.7000000000000002

   1. Initial program 85.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

      2. associate-*l/ 96.8%

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

      3. *-commutative 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 83.2%

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

      3. distribute-neg-frac 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

      3. associate-*l/ 83.5%

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

      4. *-commutative 83.5%

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

   10. Simplified 83.5%

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

   if -2.39999999999999994e-18 < t < -5.79999999999999978e-81

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.0%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

   if -2.6000000000000001e-107 < t < -7.40000000000000039e-147

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 94.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-107}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 3.7:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 1.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -5.5e+72)
     t_2
     (if (<= t -1.06e-17)
       t_1
       (if (<= t -6.4e-81)
         (/ x (/ t (- y z)))
         (if (<= t -4.1e-107)
           t_1
           (if (<= t -1.18e-144)
             (/ x (/ (- t z) y))
             (if (<= t 1.2) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -5.5e+72) {
		tmp = t_2;
	} else if (t <= -1.06e-17) {
		tmp = t_1;
	} else if (t <= -6.4e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -4.1e-107) {
		tmp = t_1;
	} else if (t <= -1.18e-144) {
		tmp = x / ((t - z) / y);
	} else if (t <= 1.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    t_2 = x * ((y - z) / t)
    if (t <= (-5.5d+72)) then
        tmp = t_2
    else if (t <= (-1.06d-17)) then
        tmp = t_1
    else if (t <= (-6.4d-81)) then
        tmp = x / (t / (y - z))
    else if (t <= (-4.1d-107)) then
        tmp = t_1
    else if (t <= (-1.18d-144)) then
        tmp = x / ((t - z) / y)
    else if (t <= 1.2d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -5.5e+72) {
		tmp = t_2;
	} else if (t <= -1.06e-17) {
		tmp = t_1;
	} else if (t <= -6.4e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -4.1e-107) {
		tmp = t_1;
	} else if (t <= -1.18e-144) {
		tmp = x / ((t - z) / y);
	} else if (t <= 1.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	t_2 = x * ((y - z) / t)
	tmp = 0
	if t <= -5.5e+72:
		tmp = t_2
	elif t <= -1.06e-17:
		tmp = t_1
	elif t <= -6.4e-81:
		tmp = x / (t / (y - z))
	elif t <= -4.1e-107:
		tmp = t_1
	elif t <= -1.18e-144:
		tmp = x / ((t - z) / y)
	elif t <= 1.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	t_2 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -5.5e+72)
		tmp = t_2;
	elseif (t <= -1.06e-17)
		tmp = t_1;
	elseif (t <= -6.4e-81)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= -4.1e-107)
		tmp = t_1;
	elseif (t <= -1.18e-144)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (t <= 1.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	t_2 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -5.5e+72)
		tmp = t_2;
	elseif (t <= -1.06e-17)
		tmp = t_1;
	elseif (t <= -6.4e-81)
		tmp = x / (t / (y - z));
	elseif (t <= -4.1e-107)
		tmp = t_1;
	elseif (t <= -1.18e-144)
		tmp = x / ((t - z) / y);
	elseif (t <= 1.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+72], t$95$2, If[LessEqual[t, -1.06e-17], t$95$1, If[LessEqual[t, -6.4e-81], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-107], t$95$1, If[LessEqual[t, -1.18e-144], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5e72 or 1.19999999999999996 < t

   1. Initial program 84.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 84.2%

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

      2. associate-*l/ 97.9%

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

      3. *-commutative 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.3%

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

   if -5.5e72 < t < -1.06000000000000006e-17 or -6.4e-81 < t < -4.0999999999999999e-107 or -1.18e-144 < t < 1.19999999999999996

   1. Initial program 85.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

      2. associate-*l/ 96.8%

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

      3. *-commutative 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 83.2%

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

      3. distribute-neg-frac 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

      3. associate-*l/ 83.5%

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

      4. *-commutative 83.5%

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

   10. Simplified 83.5%

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

   if -1.06000000000000006e-17 < t < -6.4e-81

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.0%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

   if -4.0999999999999999e-107 < t < -1.18e-144

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 94.2%

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

      1. associate-/l* 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-107}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 1.2:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x - \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (- x (/ x (/ z y)))))
   (if (<= t -5.8e+72)
     t_1
     (if (<= t -1.35e-17)
       (- x (* y (/ x z)))
       (if (<= t -5.2e-81)
         (/ x (/ t (- y z)))
         (if (<= t -2.75e-110)
           t_2
           (if (<= t -1.35e-161)
             (/ (* x y) (- t z))
             (if (<= t 4.6e-5) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x - (x / (z / y));
	double tmp;
	if (t <= -5.8e+72) {
		tmp = t_1;
	} else if (t <= -1.35e-17) {
		tmp = x - (y * (x / z));
	} else if (t <= -5.2e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -2.75e-110) {
		tmp = t_2;
	} else if (t <= -1.35e-161) {
		tmp = (x * y) / (t - z);
	} else if (t <= 4.6e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x - (x / (z / y))
    if (t <= (-5.8d+72)) then
        tmp = t_1
    else if (t <= (-1.35d-17)) then
        tmp = x - (y * (x / z))
    else if (t <= (-5.2d-81)) then
        tmp = x / (t / (y - z))
    else if (t <= (-2.75d-110)) then
        tmp = t_2
    else if (t <= (-1.35d-161)) then
        tmp = (x * y) / (t - z)
    else if (t <= 4.6d-5) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x - (x / (z / y));
	double tmp;
	if (t <= -5.8e+72) {
		tmp = t_1;
	} else if (t <= -1.35e-17) {
		tmp = x - (y * (x / z));
	} else if (t <= -5.2e-81) {
		tmp = x / (t / (y - z));
	} else if (t <= -2.75e-110) {
		tmp = t_2;
	} else if (t <= -1.35e-161) {
		tmp = (x * y) / (t - z);
	} else if (t <= 4.6e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x - (x / (z / y))
	tmp = 0
	if t <= -5.8e+72:
		tmp = t_1
	elif t <= -1.35e-17:
		tmp = x - (y * (x / z))
	elif t <= -5.2e-81:
		tmp = x / (t / (y - z))
	elif t <= -2.75e-110:
		tmp = t_2
	elif t <= -1.35e-161:
		tmp = (x * y) / (t - z)
	elif t <= 4.6e-5:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x - Float64(x / Float64(z / y)))
	tmp = 0.0
	if (t <= -5.8e+72)
		tmp = t_1;
	elseif (t <= -1.35e-17)
		tmp = Float64(x - Float64(y * Float64(x / z)));
	elseif (t <= -5.2e-81)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= -2.75e-110)
		tmp = t_2;
	elseif (t <= -1.35e-161)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (t <= 4.6e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x - (x / (z / y));
	tmp = 0.0;
	if (t <= -5.8e+72)
		tmp = t_1;
	elseif (t <= -1.35e-17)
		tmp = x - (y * (x / z));
	elseif (t <= -5.2e-81)
		tmp = x / (t / (y - z));
	elseif (t <= -2.75e-110)
		tmp = t_2;
	elseif (t <= -1.35e-161)
		tmp = (x * y) / (t - z);
	elseif (t <= 4.6e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+72], t$95$1, If[LessEqual[t, -1.35e-17], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-81], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-110], t$95$2, If[LessEqual[t, -1.35e-161], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-5], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.80000000000000034e72 or 4.6e-5 < t

   1. Initial program 84.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 84.2%

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

      2. associate-*l/ 97.9%

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

      3. *-commutative 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.3%

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

   if -5.80000000000000034e72 < t < -1.3500000000000001e-17

   1. Initial program 76.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 76.4%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 75.8%

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

      3. distribute-neg-frac 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in z around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. associate-*l/ 75.8%

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

      4. *-commutative 75.8%

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

   10. Simplified 75.8%

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

   if -1.3500000000000001e-17 < t < -5.1999999999999998e-81

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.0%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

   if -5.1999999999999998e-81 < t < -2.7499999999999999e-110 or -1.35e-161 < t < 4.6e-5

   1. Initial program 87.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

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

      2. associate-*l/ 97.1%

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

      3. *-commutative 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. associate-/l* 86.3%

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

      3. distribute-neg-frac 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in z around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

      3. associate-*l/ 84.8%

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

      4. *-commutative 84.8%

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

   10. Simplified 84.8%

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

       1. associate-*r/ 84.1%

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

       2. *-commutative 84.1%

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

       3. associate-/l* 86.3%

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

   12. Applied egg-rr 86.3%

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

   if -2.7499999999999999e-110 < t < -1.35e-161

   1. Initial program 100.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-110}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 850000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+143)
   x
   (if (<= z -2.1e+95)
     (* x (- (/ y z)))
     (if (<= z -1.7e+46) x (if (<= z 850000000.0) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+143) {
		tmp = x;
	} else if (z <= -2.1e+95) {
		tmp = x * -(y / z);
	} else if (z <= -1.7e+46) {
		tmp = x;
	} else if (z <= 850000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.85d+143)) then
        tmp = x
    else if (z <= (-2.1d+95)) then
        tmp = x * -(y / z)
    else if (z <= (-1.7d+46)) then
        tmp = x
    else if (z <= 850000000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+143) {
		tmp = x;
	} else if (z <= -2.1e+95) {
		tmp = x * -(y / z);
	} else if (z <= -1.7e+46) {
		tmp = x;
	} else if (z <= 850000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+143:
		tmp = x
	elif z <= -2.1e+95:
		tmp = x * -(y / z)
	elif z <= -1.7e+46:
		tmp = x
	elif z <= 850000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+143)
		tmp = x;
	elseif (z <= -2.1e+95)
		tmp = Float64(x * Float64(-Float64(y / z)));
	elseif (z <= -1.7e+46)
		tmp = x;
	elseif (z <= 850000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85e+143)
		tmp = x;
	elseif (z <= -2.1e+95)
		tmp = x * -(y / z);
	elseif (z <= -1.7e+46)
		tmp = x;
	elseif (z <= 850000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+143], x, If[LessEqual[z, -2.1e+95], N[(x * (-N[(y / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -1.7e+46], x, If[LessEqual[z, 850000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001e143 or -2.1e95 < z < -1.6999999999999999e46 or 8.5e8 < z

   1. Initial program 75.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 75.4%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 64.0%

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

   if -1.8500000000000001e143 < z < -2.1e95

   1. Initial program 89.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 89.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 67.9%

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

   6. Taylor expanded in t around 0 57.5%

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

      1. associate-*r/ 57.5%

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

      2. neg-mul-1 57.5%

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

   8. Simplified 57.5%

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

   if -1.6999999999999999e46 < z < 8.5e8

   1. Initial program 93.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 93.9%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 58.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 850000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+24} \lor \neg \left(y \leq 0.0275\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e+24) (not (<= y 0.0275)))
   (/ x (/ (- t z) y))
   (* x (/ (- z) (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e+24) || !(y <= 0.0275)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (-z / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d+24)) .or. (.not. (y <= 0.0275d0))) then
        tmp = x / ((t - z) / y)
    else
        tmp = x * (-z / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e+24) || !(y <= 0.0275)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (-z / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e+24) or not (y <= 0.0275):
		tmp = x / ((t - z) / y)
	else:
		tmp = x * (-z / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e+24) || !(y <= 0.0275))
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x * Float64(Float64(-z) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e+24) || ~((y <= 0.0275)))
		tmp = x / ((t - z) / y);
	else
		tmp = x * (-z / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e+24], N[Not[LessEqual[y, 0.0275]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000019e24 or 0.0275000000000000001 < y

   1. Initial program 83.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 83.6%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.2%

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

      1. associate-/l* 83.3%

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

   7. Simplified 83.3%

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

   if -4.50000000000000019e24 < y < 0.0275000000000000001

   1. Initial program 88.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 88.6%

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

      2. associate-*l/ 98.2%

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

      3. *-commutative 98.2%

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

   3. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

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

      1. neg-mul-1 80.6%

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

      2. distribute-neg-frac 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+24} \lor \neg \left(y \leq 0.0275\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+165) x (if (<= z 8.2e+65) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+165) {
		tmp = x;
	} else if (z <= 8.2e+65) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.5d+165)) then
        tmp = x
    else if (z <= 8.2d+65) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+165) {
		tmp = x;
	} else if (z <= 8.2e+65) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+165:
		tmp = x
	elif z <= 8.2e+65:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+165)
		tmp = x;
	elseif (z <= 8.2e+65)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+165)
		tmp = x;
	elseif (z <= 8.2e+65)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+165], x, If[LessEqual[z, 8.2e+65], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e165 or 8.2000000000000003e65 < z

   1. Initial program 70.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 70.5%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 69.9%

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

   if -8.5000000000000001e165 < z < 8.2000000000000003e65

   1. Initial program 92.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 92.6%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4800000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+46) x (if (<= z 4800000000.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+46) {
		tmp = x;
	} else if (z <= 4800000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.5d+46)) then
        tmp = x
    else if (z <= 4800000000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+46) {
		tmp = x;
	} else if (z <= 4800000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+46:
		tmp = x
	elif z <= 4800000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+46)
		tmp = x;
	elseif (z <= 4800000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e+46)
		tmp = x;
	elseif (z <= 4800000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+46], x, If[LessEqual[z, 4800000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000001e46 or 4.8e9 < z

   1. Initial program 76.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 76.5%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.3%

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

   if -4.5000000000000001e46 < z < 4.8e9

   1. Initial program 93.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-commutative 93.9%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 58.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4800000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 86.2%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 86.2%

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

   2. associate-*l/ 97.5%

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

   3. *-commutative 97.5%

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

3. Simplified 97.5%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 31.7%

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

6. Final simplification 31.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))