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

Percentage Accurate: 83.9% → 97.4%

Time: 11.3s

Alternatives: 8

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: 83.9% 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: 97.4% 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 80.7%

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

   1. *-commutative 80.7%

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

   2. associate-*l/ 96.3%

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

   3. *-commutative 96.3%

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

3. Simplified 96.3%

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

5. Final simplification 96.3%

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

Alternative 2: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 520:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.6e+57)
     (* x (/ (- z y) z))
     (if (<= z -7.6e-34)
       (* x (/ y (- t z)))
       (if (<= z -5.8e-45)
         t_1
         (if (<= z 7.6e-232)
           (/ (* x (- y z)) t)
           (if (<= z 520.0) (/ x (/ (- t z) y)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.6e+57) {
		tmp = x * ((z - y) / z);
	} else if (z <= -7.6e-34) {
		tmp = x * (y / (t - z));
	} else if (z <= -5.8e-45) {
		tmp = t_1;
	} else if (z <= 7.6e-232) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 520.0) {
		tmp = x / ((t - z) / y);
	} 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) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.6d+57)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-7.6d-34)) then
        tmp = x * (y / (t - z))
    else if (z <= (-5.8d-45)) then
        tmp = t_1
    else if (z <= 7.6d-232) then
        tmp = (x * (y - z)) / t
    else if (z <= 520.0d0) then
        tmp = x / ((t - z) / y)
    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 * (z / (z - t));
	double tmp;
	if (z <= -1.6e+57) {
		tmp = x * ((z - y) / z);
	} else if (z <= -7.6e-34) {
		tmp = x * (y / (t - z));
	} else if (z <= -5.8e-45) {
		tmp = t_1;
	} else if (z <= 7.6e-232) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 520.0) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.6e+57:
		tmp = x * ((z - y) / z)
	elif z <= -7.6e-34:
		tmp = x * (y / (t - z))
	elif z <= -5.8e-45:
		tmp = t_1
	elif z <= 7.6e-232:
		tmp = (x * (y - z)) / t
	elif z <= 520.0:
		tmp = x / ((t - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.6e+57)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -7.6e-34)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= -5.8e-45)
		tmp = t_1;
	elseif (z <= 7.6e-232)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 520.0)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.6e+57)
		tmp = x * ((z - y) / z);
	elseif (z <= -7.6e-34)
		tmp = x * (y / (t - z));
	elseif (z <= -5.8e-45)
		tmp = t_1;
	elseif (z <= 7.6e-232)
		tmp = (x * (y - z)) / t;
	elseif (z <= 520.0)
		tmp = x / ((t - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+57], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-34], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-45], t$95$1, If[LessEqual[z, 7.6e-232], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 520.0], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.60000000000000015e57

   1. Initial program 56.5%

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

      1. *-commutative 56.5%

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

      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 t around 0 89.9%

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

      1. associate-*r/ 89.9%

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

      2. neg-mul-1 89.9%

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

   7. Simplified 89.9%

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

   if -1.60000000000000015e57 < z < -7.6000000000000002e-34

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

      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 66.7%

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

   if -7.6000000000000002e-34 < z < -5.8e-45 or 520 < z

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      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 y around 0 86.5%

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

      1. neg-mul-1 86.5%

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

      2. distribute-neg-frac 86.5%

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

   7. Simplified 86.5%

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

      1. frac-2neg 86.5%

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

      2. div-inv 86.4%

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

      3. remove-double-neg 86.4%

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

      4. sub-neg 86.4%

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

      5. distribute-neg-in 86.4%

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

      6. remove-double-neg 86.4%

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

   9. Applied egg-rr 86.4%

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

       1. associate-*r/ 86.5%

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

       2. *-rgt-identity 86.5%

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

       3. +-commutative 86.5%

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

       4. unsub-neg 86.5%

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

   11. Simplified 86.5%

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

   if -5.8e-45 < z < 7.6000000000000003e-232

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 85.6%

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

   if 7.6000000000000003e-232 < z < 520

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 520:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-290}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 235000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (* x (/ z (- z t)))))
   (if (<= z -1.45e+78)
     t_2
     (if (<= z -4.1e-189)
       t_1
       (if (<= z -4.2e-290)
         (* (- y z) (/ x t))
         (if (<= z 235000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -1.45e+78) {
		tmp = t_2;
	} else if (z <= -4.1e-189) {
		tmp = t_1;
	} else if (z <= -4.2e-290) {
		tmp = (y - z) * (x / t);
	} else if (z <= 235000.0) {
		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 / (t - z))
    t_2 = x * (z / (z - t))
    if (z <= (-1.45d+78)) then
        tmp = t_2
    else if (z <= (-4.1d-189)) then
        tmp = t_1
    else if (z <= (-4.2d-290)) then
        tmp = (y - z) * (x / t)
    else if (z <= 235000.0d0) 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 / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -1.45e+78) {
		tmp = t_2;
	} else if (z <= -4.1e-189) {
		tmp = t_1;
	} else if (z <= -4.2e-290) {
		tmp = (y - z) * (x / t);
	} else if (z <= 235000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x * (z / (z - t))
	tmp = 0
	if z <= -1.45e+78:
		tmp = t_2
	elif z <= -4.1e-189:
		tmp = t_1
	elif z <= -4.2e-290:
		tmp = (y - z) * (x / t)
	elif z <= 235000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.45e+78)
		tmp = t_2;
	elseif (z <= -4.1e-189)
		tmp = t_1;
	elseif (z <= -4.2e-290)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 235000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.45e+78)
		tmp = t_2;
	elseif (z <= -4.1e-189)
		tmp = t_1;
	elseif (z <= -4.2e-290)
		tmp = (y - z) * (x / t);
	elseif (z <= 235000.0)
		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[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+78], t$95$2, If[LessEqual[z, -4.1e-189], t$95$1, If[LessEqual[z, -4.2e-290], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 235000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000008e78 or 235000 < z

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      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 y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   7. Simplified 86.4%

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

      1. frac-2neg 86.4%

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

      2. div-inv 86.2%

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

      3. remove-double-neg 86.2%

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

      4. sub-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. remove-double-neg 86.2%

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

   9. Applied egg-rr 86.2%

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

       1. associate-*r/ 86.4%

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

       2. *-rgt-identity 86.4%

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

       3. +-commutative 86.4%

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

       4. unsub-neg 86.4%

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

   11. Simplified 86.4%

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

   if -1.45000000000000008e78 < z < -4.1000000000000003e-189 or -4.2000000000000002e-290 < z < 235000

   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/ 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 y around inf 74.6%

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

   if -4.1000000000000003e-189 < z < -4.2000000000000002e-290

   1. Initial program 92.1%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 88.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-290}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 235000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 22000000:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1e+78)
     t_1
     (if (<= z -1.12e-189)
       (* x (/ y (- t z)))
       (if (<= z 1.05e-229)
         (/ (* x (- y z)) t)
         (if (<= z 22000000.0) (/ x (/ (- t z) y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1e+78) {
		tmp = t_1;
	} else if (z <= -1.12e-189) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.05e-229) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 22000000.0) {
		tmp = x / ((t - z) / y);
	} 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) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1d+78)) then
        tmp = t_1
    else if (z <= (-1.12d-189)) then
        tmp = x * (y / (t - z))
    else if (z <= 1.05d-229) then
        tmp = (x * (y - z)) / t
    else if (z <= 22000000.0d0) then
        tmp = x / ((t - z) / y)
    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 * (z / (z - t));
	double tmp;
	if (z <= -1e+78) {
		tmp = t_1;
	} else if (z <= -1.12e-189) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.05e-229) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 22000000.0) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1e+78:
		tmp = t_1
	elif z <= -1.12e-189:
		tmp = x * (y / (t - z))
	elif z <= 1.05e-229:
		tmp = (x * (y - z)) / t
	elif z <= 22000000.0:
		tmp = x / ((t - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1e+78)
		tmp = t_1;
	elseif (z <= -1.12e-189)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.05e-229)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 22000000.0)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1e+78)
		tmp = t_1;
	elseif (z <= -1.12e-189)
		tmp = x * (y / (t - z));
	elseif (z <= 1.05e-229)
		tmp = (x * (y - z)) / t;
	elseif (z <= 22000000.0)
		tmp = x / ((t - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+78], t$95$1, If[LessEqual[z, -1.12e-189], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-229], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 22000000.0], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000001e78 or 2.2e7 < z

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      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 y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   7. Simplified 86.4%

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

      1. frac-2neg 86.4%

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

      2. div-inv 86.2%

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

      3. remove-double-neg 86.2%

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

      4. sub-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. remove-double-neg 86.2%

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

   9. Applied egg-rr 86.2%

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

       1. associate-*r/ 86.4%

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

       2. *-rgt-identity 86.4%

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

       3. +-commutative 86.4%

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

       4. unsub-neg 86.4%

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

   11. Simplified 86.4%

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

   if -1.00000000000000001e78 < z < -1.12000000000000002e-189

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      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 y around inf 69.6%

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

   if -1.12000000000000002e-189 < z < 1.04999999999999992e-229

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*l/ 86.2%

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

      3. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 90.2%

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

   if 1.04999999999999992e-229 < z < 2.2e7

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 22000000:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78} \lor \neg \left(z \leq 90\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+78) (not (<= z 90.0)))
   (* x (/ z (- z t)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+78) || !(z <= 90.0)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (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 ((z <= (-1d+78)) .or. (.not. (z <= 90.0d0))) then
        tmp = x * (z / (z - t))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+78) || !(z <= 90.0)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+78) or not (z <= 90.0):
		tmp = x * (z / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+78) || !(z <= 90.0))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e+78) || ~((z <= 90.0)))
		tmp = x * (z / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+78], N[Not[LessEqual[z, 90.0]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000001e78 or 90 < z

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      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 y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   7. Simplified 86.4%

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

      1. frac-2neg 86.4%

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

      2. div-inv 86.2%

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

      3. remove-double-neg 86.2%

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

      4. sub-neg 86.2%

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

      5. distribute-neg-in 86.2%

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

      6. remove-double-neg 86.2%

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

   9. Applied egg-rr 86.2%

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

       1. associate-*r/ 86.4%

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

       2. *-rgt-identity 86.4%

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

       3. +-commutative 86.4%

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

       4. unsub-neg 86.4%

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

   11. Simplified 86.4%

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

   if -1.00000000000000001e78 < z < 90

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*l/ 93.8%

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

      3. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 73.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78} \lor \neg \left(z \leq 90\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+121) x (if (<= z 6.4e+18) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+121) {
		tmp = x;
	} else if (z <= 6.4e+18) {
		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 <= (-1.8d+121)) then
        tmp = x
    else if (z <= 6.4d+18) 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 <= -1.8e+121) {
		tmp = x;
	} else if (z <= 6.4e+18) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+121:
		tmp = x
	elif z <= 6.4e+18:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+121)
		tmp = x;
	elseif (z <= 6.4e+18)
		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 <= -1.8e+121)
		tmp = x;
	elseif (z <= 6.4e+18)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+121], x, If[LessEqual[z, 6.4e+18], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999991e121 or 6.4e18 < z

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

      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 79.5%

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

   if -1.79999999999999991e121 < z < 6.4e18

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 72.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+58) x (if (<= z 6.5e+18) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+58) {
		tmp = x;
	} else if (z <= 6.5e+18) {
		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 <= (-3.8d+58)) then
        tmp = x
    else if (z <= 6.5d+18) 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 <= -3.8e+58) {
		tmp = x;
	} else if (z <= 6.5e+18) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+58:
		tmp = x
	elif z <= 6.5e+18:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+58)
		tmp = x;
	elseif (z <= 6.5e+18)
		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 <= -3.8e+58)
		tmp = x;
	elseif (z <= 6.5e+18)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+58], x, If[LessEqual[z, 6.5e+18], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999999e58 or 6.5e18 < z

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      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 75.7%

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

   if -3.7999999999999999e58 < z < 6.5e18

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 93.8%

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

      3. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 61.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.7% 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 80.7%

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

   1. *-commutative 80.7%

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

   2. associate-*l/ 96.3%

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

   3. *-commutative 96.3%

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

3. Simplified 96.3%

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

5. Taylor expanded in z around inf 38.8%

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

6. Final simplification 38.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.3% 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 2024019 
(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)))