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

Percentage Accurate: 84.3% → 97.3%

Time: 9.8s

Alternatives: 9

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: 84.3% 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: 97.3% 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 87.9%

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

   1. *-commutative 87.9%

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

   2. associate-*l/ 97.6%

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

   3. *-commutative 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 2: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(\frac{t}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -7.2e+211)
     x
     (if (<= z -4.8e+172)
       (* x (/ (- z) t))
       (if (<= z -7.8e+39)
         x
         (if (<= z 6.5e+73)
           t_1
           (if (<= z 7.2e+99)
             x
             (if (<= z 1.7e+146)
               t_1
               (if (<= z 5e+241) (* x (+ (/ t z) 1.0)) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4.8e+172) {
		tmp = x * (-z / t);
	} else if (z <= -7.8e+39) {
		tmp = x;
	} else if (z <= 6.5e+73) {
		tmp = t_1;
	} else if (z <= 7.2e+99) {
		tmp = x;
	} else if (z <= 1.7e+146) {
		tmp = t_1;
	} else if (z <= 5e+241) {
		tmp = x * ((t / z) + 1.0);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-7.2d+211)) then
        tmp = x
    else if (z <= (-4.8d+172)) then
        tmp = x * (-z / t)
    else if (z <= (-7.8d+39)) then
        tmp = x
    else if (z <= 6.5d+73) then
        tmp = t_1
    else if (z <= 7.2d+99) then
        tmp = x
    else if (z <= 1.7d+146) then
        tmp = t_1
    else if (z <= 5d+241) then
        tmp = x * ((t / z) + 1.0d0)
    else
        tmp = x
    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 tmp;
	if (z <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4.8e+172) {
		tmp = x * (-z / t);
	} else if (z <= -7.8e+39) {
		tmp = x;
	} else if (z <= 6.5e+73) {
		tmp = t_1;
	} else if (z <= 7.2e+99) {
		tmp = x;
	} else if (z <= 1.7e+146) {
		tmp = t_1;
	} else if (z <= 5e+241) {
		tmp = x * ((t / z) + 1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -7.2e+211:
		tmp = x
	elif z <= -4.8e+172:
		tmp = x * (-z / t)
	elif z <= -7.8e+39:
		tmp = x
	elif z <= 6.5e+73:
		tmp = t_1
	elif z <= 7.2e+99:
		tmp = x
	elif z <= 1.7e+146:
		tmp = t_1
	elif z <= 5e+241:
		tmp = x * ((t / z) + 1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -7.2e+211)
		tmp = x;
	elseif (z <= -4.8e+172)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -7.8e+39)
		tmp = x;
	elseif (z <= 6.5e+73)
		tmp = t_1;
	elseif (z <= 7.2e+99)
		tmp = x;
	elseif (z <= 1.7e+146)
		tmp = t_1;
	elseif (z <= 5e+241)
		tmp = Float64(x * Float64(Float64(t / z) + 1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -7.2e+211)
		tmp = x;
	elseif (z <= -4.8e+172)
		tmp = x * (-z / t);
	elseif (z <= -7.8e+39)
		tmp = x;
	elseif (z <= 6.5e+73)
		tmp = t_1;
	elseif (z <= 7.2e+99)
		tmp = x;
	elseif (z <= 1.7e+146)
		tmp = t_1;
	elseif (z <= 5e+241)
		tmp = x * ((t / z) + 1.0);
	else
		tmp = x;
	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]}, If[LessEqual[z, -7.2e+211], x, If[LessEqual[z, -4.8e+172], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e+39], x, If[LessEqual[z, 6.5e+73], t$95$1, If[LessEqual[z, 7.2e+99], x, If[LessEqual[z, 1.7e+146], t$95$1, If[LessEqual[z, 5e+241], N[(x * N[(N[(t / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000006e211 or -4.8000000000000001e172 < z < -7.8000000000000002e39 or 6.5000000000000001e73 < z < 7.2000000000000003e99 or 5.00000000000000025e241 < z

   1. Initial program 79.9%

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

      1. *-commutative 79.9%

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

      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 69.6%

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

   if -7.20000000000000006e211 < z < -4.8000000000000001e172

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      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 inf 100.0%

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

   6. Taylor expanded in y around 0 84.3%

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

      1. neg-mul-1 84.3%

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

      2. distribute-neg-frac 84.3%

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

   8. Simplified 84.3%

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

   if -7.8000000000000002e39 < z < 6.5000000000000001e73 or 7.2000000000000003e99 < z < 1.69999999999999995e146

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l/ 96.1%

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

      3. *-commutative 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 73.8%

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

   if 1.69999999999999995e146 < z < 5.00000000000000025e241

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      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 73.3%

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

      1. mul-1-neg 73.3%

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

      2. associate-/l* 98.0%

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

      3. distribute-neg-frac 98.0%

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

      4. div-sub 98.0%

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

      5. *-inverses 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in t around 0 62.5%

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

      1. *-lft-identity 62.5%

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

      2. associate-/l* 73.1%

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

      3. associate-/r/ 72.6%

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

      4. distribute-rgt-in 72.6%

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

      5. +-commutative 72.6%

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

   10. Simplified 72.6%

       \[\leadsto \color{blue}{x \cdot \left(\frac{t}{z} + 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(\frac{t}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -215000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) t))))
   (if (<= z -7.2e+211)
     x
     (if (<= z -4.8e+172)
       t_1
       (if (<= z -215000000000.0)
         x
         (if (<= z -1.5e-26)
           t_1
           (if (<= z -2.5e-51)
             x
             (if (<= z -5.6e-285)
               (* y (/ x t))
               (if (<= z 3.3e+14) (* x (/ y t)) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double tmp;
	if (z <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4.8e+172) {
		tmp = t_1;
	} else if (z <= -215000000000.0) {
		tmp = x;
	} else if (z <= -1.5e-26) {
		tmp = t_1;
	} else if (z <= -2.5e-51) {
		tmp = x;
	} else if (z <= -5.6e-285) {
		tmp = y * (x / t);
	} else if (z <= 3.3e+14) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (-z / t)
    if (z <= (-7.2d+211)) then
        tmp = x
    else if (z <= (-4.8d+172)) then
        tmp = t_1
    else if (z <= (-215000000000.0d0)) then
        tmp = x
    else if (z <= (-1.5d-26)) then
        tmp = t_1
    else if (z <= (-2.5d-51)) then
        tmp = x
    else if (z <= (-5.6d-285)) then
        tmp = y * (x / t)
    else if (z <= 3.3d+14) 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 t_1 = x * (-z / t);
	double tmp;
	if (z <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4.8e+172) {
		tmp = t_1;
	} else if (z <= -215000000000.0) {
		tmp = x;
	} else if (z <= -1.5e-26) {
		tmp = t_1;
	} else if (z <= -2.5e-51) {
		tmp = x;
	} else if (z <= -5.6e-285) {
		tmp = y * (x / t);
	} else if (z <= 3.3e+14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / t)
	tmp = 0
	if z <= -7.2e+211:
		tmp = x
	elif z <= -4.8e+172:
		tmp = t_1
	elif z <= -215000000000.0:
		tmp = x
	elif z <= -1.5e-26:
		tmp = t_1
	elif z <= -2.5e-51:
		tmp = x
	elif z <= -5.6e-285:
		tmp = y * (x / t)
	elif z <= 3.3e+14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -7.2e+211)
		tmp = x;
	elseif (z <= -4.8e+172)
		tmp = t_1;
	elseif (z <= -215000000000.0)
		tmp = x;
	elseif (z <= -1.5e-26)
		tmp = t_1;
	elseif (z <= -2.5e-51)
		tmp = x;
	elseif (z <= -5.6e-285)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 3.3e+14)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / t);
	tmp = 0.0;
	if (z <= -7.2e+211)
		tmp = x;
	elseif (z <= -4.8e+172)
		tmp = t_1;
	elseif (z <= -215000000000.0)
		tmp = x;
	elseif (z <= -1.5e-26)
		tmp = t_1;
	elseif (z <= -2.5e-51)
		tmp = x;
	elseif (z <= -5.6e-285)
		tmp = y * (x / t);
	elseif (z <= 3.3e+14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+211], x, If[LessEqual[z, -4.8e+172], t$95$1, If[LessEqual[z, -215000000000.0], x, If[LessEqual[z, -1.5e-26], t$95$1, If[LessEqual[z, -2.5e-51], x, If[LessEqual[z, -5.6e-285], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000006e211 or -4.8000000000000001e172 < z < -2.15e11 or -1.50000000000000006e-26 < z < -2.50000000000000002e-51 or 3.3e14 < z

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      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 61.5%

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

   if -7.20000000000000006e211 < z < -4.8000000000000001e172 or -2.15e11 < z < -1.50000000000000006e-26

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 t around inf 92.6%

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

   6. Taylor expanded in y around 0 73.2%

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

      1. neg-mul-1 73.2%

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

      2. distribute-neg-frac 73.2%

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

   8. Simplified 73.2%

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

   if -2.50000000000000002e-51 < z < -5.59999999999999982e-285

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 74.0%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

      1. associate-/r/ 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -5.59999999999999982e-285 < z < 3.3e14

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l/ 95.4%

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

      3. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around 0 66.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -215000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3450000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-283}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e+211)
   x
   (if (<= z -4e+172)
     (* x (/ (- z) t))
     (if (<= z -3450000000000.0)
       x
       (if (<= z -5e-25)
         (/ (- x) (/ t z))
         (if (<= z -2.3e-51)
           x
           (if (<= z -1.15e-283)
             (* y (/ x t))
             (if (<= z 3.3e+14) (* x (/ y t)) x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4e+172) {
		tmp = x * (-z / t);
	} else if (z <= -3450000000000.0) {
		tmp = x;
	} else if (z <= -5e-25) {
		tmp = -x / (t / z);
	} else if (z <= -2.3e-51) {
		tmp = x;
	} else if (z <= -1.15e-283) {
		tmp = y * (x / t);
	} else if (z <= 3.3e+14) {
		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 <= (-7.2d+211)) then
        tmp = x
    else if (z <= (-4d+172)) then
        tmp = x * (-z / t)
    else if (z <= (-3450000000000.0d0)) then
        tmp = x
    else if (z <= (-5d-25)) then
        tmp = -x / (t / z)
    else if (z <= (-2.3d-51)) then
        tmp = x
    else if (z <= (-1.15d-283)) then
        tmp = y * (x / t)
    else if (z <= 3.3d+14) 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 <= -7.2e+211) {
		tmp = x;
	} else if (z <= -4e+172) {
		tmp = x * (-z / t);
	} else if (z <= -3450000000000.0) {
		tmp = x;
	} else if (z <= -5e-25) {
		tmp = -x / (t / z);
	} else if (z <= -2.3e-51) {
		tmp = x;
	} else if (z <= -1.15e-283) {
		tmp = y * (x / t);
	} else if (z <= 3.3e+14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e+211:
		tmp = x
	elif z <= -4e+172:
		tmp = x * (-z / t)
	elif z <= -3450000000000.0:
		tmp = x
	elif z <= -5e-25:
		tmp = -x / (t / z)
	elif z <= -2.3e-51:
		tmp = x
	elif z <= -1.15e-283:
		tmp = y * (x / t)
	elif z <= 3.3e+14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e+211)
		tmp = x;
	elseif (z <= -4e+172)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -3450000000000.0)
		tmp = x;
	elseif (z <= -5e-25)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -2.3e-51)
		tmp = x;
	elseif (z <= -1.15e-283)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 3.3e+14)
		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 <= -7.2e+211)
		tmp = x;
	elseif (z <= -4e+172)
		tmp = x * (-z / t);
	elseif (z <= -3450000000000.0)
		tmp = x;
	elseif (z <= -5e-25)
		tmp = -x / (t / z);
	elseif (z <= -2.3e-51)
		tmp = x;
	elseif (z <= -1.15e-283)
		tmp = y * (x / t);
	elseif (z <= 3.3e+14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e+211], x, If[LessEqual[z, -4e+172], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3450000000000.0], x, If[LessEqual[z, -5e-25], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-51], x, If[LessEqual[z, -1.15e-283], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.20000000000000006e211 or -4.0000000000000003e172 < z < -3.45e12 or -4.99999999999999962e-25 < z < -2.30000000000000002e-51 or 3.3e14 < z

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      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 61.5%

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

   if -7.20000000000000006e211 < z < -4.0000000000000003e172

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      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 inf 100.0%

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

   6. Taylor expanded in y around 0 84.3%

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

      1. neg-mul-1 84.3%

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

      2. distribute-neg-frac 84.3%

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

   8. Simplified 84.3%

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

   if -3.45e12 < z < -4.99999999999999962e-25

   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/ 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around inf 87.0%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. associate-/l* 65.1%

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

      3. distribute-neg-frac 65.1%

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

   8. Simplified 65.1%

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

   if -2.30000000000000002e-51 < z < -1.1499999999999999e-283

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 74.0%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

      1. associate-/r/ 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -1.1499999999999999e-283 < z < 3.3e14

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l/ 95.4%

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

      3. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around 0 66.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3450000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-283}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+36} \lor \neg \left(y \leq 3 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.8e+36) (not (<= y 3e+37)))
   (* x (/ y (- t z)))
   (/ (- x) (+ (/ t z) -1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.8e+36) || !(y <= 3e+37)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	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 <= (-7.8d+36)) .or. (.not. (y <= 3d+37))) then
        tmp = x * (y / (t - z))
    else
        tmp = -x / ((t / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.8e+36) || !(y <= 3e+37)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.8e+36) or not (y <= 3e+37):
		tmp = x * (y / (t - z))
	else:
		tmp = -x / ((t / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.8e+36) || !(y <= 3e+37))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.8e+36) || ~((y <= 3e+37)))
		tmp = x * (y / (t - z));
	else
		tmp = -x / ((t / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.8e+36], N[Not[LessEqual[y, 3e+37]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.80000000000000042e36 or 3.00000000000000022e37 < y

   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/ 98.9%

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

      3. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 76.7%

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

   if -7.80000000000000042e36 < y < 3.00000000000000022e37

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      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 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-/l* 84.6%

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

      3. distribute-neg-frac 84.6%

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

      4. div-sub 84.7%

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

      5. *-inverses 84.7%

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

   7. Simplified 84.7%

      \[\leadsto \color{blue}{\frac{-x}{\frac{t}{z} - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+36} \lor \neg \left(y \leq 3 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+37} \lor \neg \left(y \leq 1.4 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.05e+37) (not (<= y 1.4e+40)))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e+37) || !(y <= 1.4e+40)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	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 <= (-2.05d+37)) .or. (.not. (y <= 1.4d+40))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.05e+37) || !(y <= 1.4e+40)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.05e+37) or not (y <= 1.4e+40):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.05e+37) || !(y <= 1.4e+40))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.05e+37) || ~((y <= 1.4e+40)))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.05e+37], N[Not[LessEqual[y, 1.4e+40]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e37 or 1.4000000000000001e40 < y

   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/ 98.9%

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

      3. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around inf 76.7%

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

   if -2.0499999999999999e37 < y < 1.4000000000000001e40

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      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 0 84.6%

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

      1. neg-mul-1 84.6%

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

      2. distribute-neg-frac 84.6%

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

   7. Simplified 84.6%

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

      1. frac-2neg 84.6%

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

      2. div-inv 84.5%

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

      3. remove-double-neg 84.5%

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

      4. sub-neg 84.5%

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

      5. distribute-neg-in 84.5%

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

      6. remove-double-neg 84.5%

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

   9. Applied egg-rr 84.5%

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

       1. associate-*r/ 84.6%

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

       2. *-rgt-identity 84.6%

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

       3. +-commutative 84.6%

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

       4. unsub-neg 84.6%

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

   11. Simplified 84.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+37} \lor \neg \left(y \leq 1.4 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.15e+38) x (if (<= z 3e+14) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e+38) {
		tmp = x;
	} else if (z <= 3e+14) {
		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 <= (-2.15d+38)) then
        tmp = x
    else if (z <= 3d+14) 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 <= -2.15e+38) {
		tmp = x;
	} else if (z <= 3e+14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.15e+38:
		tmp = x
	elif z <= 3e+14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.15e+38)
		tmp = x;
	elseif (z <= 3e+14)
		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 <= -2.15e+38)
		tmp = x;
	elseif (z <= 3e+14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.15e+38], x, If[LessEqual[z, 3e+14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999998e38 or 3e14 < z

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

      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 59.5%

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

   if -2.1499999999999998e38 < z < 3e14

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*l/ 95.3%

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

      3. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around 0 66.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+37) x (if (<= z 3.3e+14) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+37) {
		tmp = x;
	} else if (z <= 3.3e+14) {
		tmp = x / (t / y);
	} 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 <= (-3.6d+37)) then
        tmp = x
    else if (z <= 3.3d+14) then
        tmp = x / (t / y)
    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 <= -3.6e+37) {
		tmp = x;
	} else if (z <= 3.3e+14) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+37:
		tmp = x
	elif z <= 3.3e+14:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+37)
		tmp = x;
	elseif (z <= 3.3e+14)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e+37)
		tmp = x;
	elseif (z <= 3.3e+14)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+37], x, If[LessEqual[z, 3.3e+14], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999998e37 or 3.3e14 < z

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

      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 59.5%

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

   if -3.59999999999999998e37 < z < 3.3e14

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*l/ 95.3%

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

      3. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.8% 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 87.9%

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

   1. *-commutative 87.9%

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

   2. associate-*l/ 97.6%

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

   3. *-commutative 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in z around inf 35.1%

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

6. Final simplification 35.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.2% 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 2024013 
(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)))