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

Percentage Accurate: 83.9% → 96.9%

Time: 9.0s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 96.9% 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 85.9%

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

   1. associate-*r/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-113}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\frac{y}{t} - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+56)
   (* x (/ z (- z t)))
   (if (<= z 1.4e-229)
     (/ x (/ (- t z) y))
     (if (<= z 1.7e-113)
       (* (- y z) (/ x t))
       (if (<= z 4.9e+72) (* x (- (/ y t) (/ z t))) (* x (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+56) {
		tmp = x * (z / (z - t));
	} else if (z <= 1.4e-229) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.7e-113) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4.9e+72) {
		tmp = x * ((y / t) - (z / t));
	} else {
		tmp = x * (1.0 - (y / 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 <= (-2.8d+56)) then
        tmp = x * (z / (z - t))
    else if (z <= 1.4d-229) then
        tmp = x / ((t - z) / y)
    else if (z <= 1.7d-113) then
        tmp = (y - z) * (x / t)
    else if (z <= 4.9d+72) then
        tmp = x * ((y / t) - (z / t))
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+56) {
		tmp = x * (z / (z - t));
	} else if (z <= 1.4e-229) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.7e-113) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4.9e+72) {
		tmp = x * ((y / t) - (z / t));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+56:
		tmp = x * (z / (z - t))
	elif z <= 1.4e-229:
		tmp = x / ((t - z) / y)
	elif z <= 1.7e-113:
		tmp = (y - z) * (x / t)
	elif z <= 4.9e+72:
		tmp = x * ((y / t) - (z / t))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+56)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 1.4e-229)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (z <= 1.7e-113)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 4.9e+72)
		tmp = Float64(x * Float64(Float64(y / t) - Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+56)
		tmp = x * (z / (z - t));
	elseif (z <= 1.4e-229)
		tmp = x / ((t - z) / y);
	elseif (z <= 1.7e-113)
		tmp = (y - z) * (x / t);
	elseif (z <= 4.9e+72)
		tmp = x * ((y / t) - (z / t));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+56], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-229], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-113], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+72], N[(x * N[(N[(y / t), $MachinePrecision] - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.80000000000000008e56

   1. Initial program 75.0%

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

      1. associate-*r/ 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. Taylor expanded in y around 0 89.6%

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

      1. neg-mul-1 89.6%

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

      2. distribute-neg-frac 89.6%

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

   6. Simplified 89.6%

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

      1. frac-2neg 89.6%

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

      2. div-inv 89.6%

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

      3. remove-double-neg 89.6%

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

      4. sub-neg 89.6%

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

      5. distribute-neg-in 89.6%

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

      6. remove-double-neg 89.6%

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

   8. Applied egg-rr 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-rgt-identity 89.6%

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

      3. +-commutative 89.6%

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

      4. unsub-neg 89.6%

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

   10. Simplified 89.6%

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

   if -2.80000000000000008e56 < z < 1.39999999999999995e-229

   1. Initial program 93.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 81.9%

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

   if 1.39999999999999995e-229 < z < 1.7000000000000001e-113

   1. Initial program 99.8%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 87.1%

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

   if 1.7000000000000001e-113 < z < 4.90000000000000006e72

   1. Initial program 88.7%

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

      1. associate-*r/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around inf 72.9%

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

   5. Taylor expanded in y around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. neg-mul-1 72.9%

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

      3. sub-neg 72.9%

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

   7. Simplified 72.9%

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

   if 4.90000000000000006e72 < z

   1. Initial program 75.2%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   8. Simplified 83.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-113}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\frac{y}{t} - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.62e+59)
   (* x (/ z (- z t)))
   (if (<= z 4.7e-228)
     (/ x (/ (- t z) y))
     (if (<= z 1.5e-113)
       (* (- y z) (/ x t))
       (if (<= z 4.5e+71) (* x (/ (- y z) t)) (* x (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.62e+59) {
		tmp = x * (z / (z - t));
	} else if (z <= 4.7e-228) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.5e-113) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4.5e+71) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / 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 <= (-1.62d+59)) then
        tmp = x * (z / (z - t))
    else if (z <= 4.7d-228) then
        tmp = x / ((t - z) / y)
    else if (z <= 1.5d-113) then
        tmp = (y - z) * (x / t)
    else if (z <= 4.5d+71) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.62e+59) {
		tmp = x * (z / (z - t));
	} else if (z <= 4.7e-228) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.5e-113) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4.5e+71) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.62e+59:
		tmp = x * (z / (z - t))
	elif z <= 4.7e-228:
		tmp = x / ((t - z) / y)
	elif z <= 1.5e-113:
		tmp = (y - z) * (x / t)
	elif z <= 4.5e+71:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.62e+59)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 4.7e-228)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (z <= 1.5e-113)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 4.5e+71)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.62e+59)
		tmp = x * (z / (z - t));
	elseif (z <= 4.7e-228)
		tmp = x / ((t - z) / y);
	elseif (z <= 1.5e-113)
		tmp = (y - z) * (x / t);
	elseif (z <= 4.5e+71)
		tmp = x * ((y - z) / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.62e+59], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-228], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-113], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+71], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6200000000000001e59

   1. Initial program 75.0%

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

      1. associate-*r/ 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. Taylor expanded in y around 0 89.6%

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

      1. neg-mul-1 89.6%

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

      2. distribute-neg-frac 89.6%

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

   6. Simplified 89.6%

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

      1. frac-2neg 89.6%

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

      2. div-inv 89.6%

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

      3. remove-double-neg 89.6%

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

      4. sub-neg 89.6%

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

      5. distribute-neg-in 89.6%

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

      6. remove-double-neg 89.6%

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

   8. Applied egg-rr 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-rgt-identity 89.6%

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

      3. +-commutative 89.6%

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

      4. unsub-neg 89.6%

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

   10. Simplified 89.6%

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

   if -1.6200000000000001e59 < z < 4.7000000000000002e-228

   1. Initial program 93.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 81.9%

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

   if 4.7000000000000002e-228 < z < 1.5e-113

   1. Initial program 99.8%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 87.1%

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

   if 1.5e-113 < z < 4.50000000000000043e71

   1. Initial program 88.7%

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

      1. associate-*r/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around inf 72.9%

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

   if 4.50000000000000043e71 < z

   1. Initial program 75.2%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   8. Simplified 83.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 4: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+83)
   x
   (if (<= z -4.6e-8) (* x (/ (- z) t)) (if (<= z 2.05e+71) (* x (/ y t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+83) {
		tmp = x;
	} else if (z <= -4.6e-8) {
		tmp = x * (-z / t);
	} else if (z <= 2.05e+71) {
		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 <= (-9.5d+83)) then
        tmp = x
    else if (z <= (-4.6d-8)) then
        tmp = x * (-z / t)
    else if (z <= 2.05d+71) 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 <= -9.5e+83) {
		tmp = x;
	} else if (z <= -4.6e-8) {
		tmp = x * (-z / t);
	} else if (z <= 2.05e+71) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+83:
		tmp = x
	elif z <= -4.6e-8:
		tmp = x * (-z / t)
	elif z <= 2.05e+71:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+83)
		tmp = x;
	elseif (z <= -4.6e-8)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 2.05e+71)
		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 <= -9.5e+83)
		tmp = x;
	elseif (z <= -4.6e-8)
		tmp = x * (-z / t);
	elseif (z <= 2.05e+71)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+83], x, If[LessEqual[z, -4.6e-8], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+71], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000002e83 or 2.0500000000000001e71 < z

   1. Initial program 73.9%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 75.3%

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

   if -9.5000000000000002e83 < z < -4.6000000000000002e-8

   1. Initial program 90.0%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 60.3%

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

   5. Taylor expanded in y around 0 47.4%

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

      1. neg-mul-1 47.4%

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

      2. distribute-neg-frac 47.4%

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

   7. Simplified 47.4%

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

   if -4.6000000000000002e-8 < z < 2.0500000000000001e71

   1. Initial program 93.8%

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

      1. associate-*r/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 66.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.35:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+101)
   x
   (if (<= z -1.35) (/ (- x) (/ t z)) (if (<= z 1.6e+72) (* x (/ y t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+101) {
		tmp = x;
	} else if (z <= -1.35) {
		tmp = -x / (t / z);
	} else if (z <= 1.6e+72) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.05d+101)) then
        tmp = x
    else if (z <= (-1.35d0)) then
        tmp = -x / (t / z)
    else if (z <= 1.6d+72) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+101) {
		tmp = x;
	} else if (z <= -1.35) {
		tmp = -x / (t / z);
	} else if (z <= 1.6e+72) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+101:
		tmp = x
	elif z <= -1.35:
		tmp = -x / (t / z)
	elif z <= 1.6e+72:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+101)
		tmp = x;
	elseif (z <= -1.35)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= 1.6e+72)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+101)
		tmp = x;
	elseif (z <= -1.35)
		tmp = -x / (t / z);
	elseif (z <= 1.6e+72)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+101], x, If[LessEqual[z, -1.35], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+72], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e101 or 1.6000000000000001e72 < z

   1. Initial program 73.3%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 75.8%

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

   if -1.05e101 < z < -1.3500000000000001

   1. Initial program 90.9%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 59.5%

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

   5. Taylor expanded in y around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/l* 48.0%

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

      3. distribute-neg-frac 48.0%

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

   7. Simplified 48.0%

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

   if -1.3500000000000001 < z < 1.6000000000000001e72

   1. Initial program 93.8%

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

      1. associate-*r/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 66.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.35:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-21} \lor \neg \left(z \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-21) (not (<= z 5.5e+32)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-21) || !(z <= 5.5e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / 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 ((z <= (-9d-21)) .or. (.not. (z <= 5.5d+32))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-21) || !(z <= 5.5e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-21) or not (z <= 5.5e+32):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-21) || !(z <= 5.5e+32))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-21) || ~((z <= 5.5e+32)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-21], N[Not[LessEqual[z, 5.5e+32]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999936e-21 or 5.49999999999999984e32 < z

   1. Initial program 78.4%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

   8. Simplified 74.3%

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

   if -8.99999999999999936e-21 < z < 5.49999999999999984e32

   1. Initial program 93.8%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 68.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-21} \lor \neg \left(z \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-10)
   (* x (/ z (- z t)))
   (if (<= z 5e+33) (* x (/ y t)) (* x (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-10) {
		tmp = x * (z / (z - t));
	} else if (z <= 5e+33) {
		tmp = x * (y / t);
	} else {
		tmp = x * (1.0 - (y / 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 <= (-1.8d-10)) then
        tmp = x * (z / (z - t))
    else if (z <= 5d+33) then
        tmp = x * (y / t)
    else
        tmp = x * (1.0d0 - (y / z))
    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-10) {
		tmp = x * (z / (z - t));
	} else if (z <= 5e+33) {
		tmp = x * (y / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-10:
		tmp = x * (z / (z - t))
	elif z <= 5e+33:
		tmp = x * (y / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-10)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 5e+33)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-10)
		tmp = x * (z / (z - t));
	elseif (z <= 5e+33)
		tmp = x * (y / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-10], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+33], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e-10

   1. Initial program 77.5%

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

      1. associate-*r/ 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. Taylor expanded in y around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. distribute-neg-frac 80.7%

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

   6. Simplified 80.7%

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

      1. frac-2neg 80.7%

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

      2. div-inv 80.7%

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

      3. remove-double-neg 80.7%

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

      4. sub-neg 80.7%

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

      5. distribute-neg-in 80.7%

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

      6. remove-double-neg 80.7%

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

   8. Applied egg-rr 80.7%

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

      1. associate-*r/ 80.7%

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

      2. *-rgt-identity 80.7%

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

      3. +-commutative 80.7%

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

      4. unsub-neg 80.7%

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

   10. Simplified 80.7%

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

   if -1.8e-10 < z < 4.99999999999999973e33

   1. Initial program 94.0%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 67.9%

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

   if 4.99999999999999973e33 < z

   1. Initial program 78.0%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   8. Simplified 79.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 8: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.7e+79)
   (* x (/ z (- z t)))
   (if (<= z 2.05e+77) (* x (/ (- y z) t)) (* x (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+79) {
		tmp = x * (z / (z - t));
	} else if (z <= 2.05e+77) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / 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 <= (-5.7d+79)) then
        tmp = x * (z / (z - t))
    else if (z <= 2.05d+77) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+79) {
		tmp = x * (z / (z - t));
	} else if (z <= 2.05e+77) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.7e+79:
		tmp = x * (z / (z - t))
	elif z <= 2.05e+77:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.7e+79)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 2.05e+77)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.7e+79)
		tmp = x * (z / (z - t));
	elseif (z <= 2.05e+77)
		tmp = x * ((y - z) / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.7e+79], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+77], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999997e79

   1. Initial program 72.7%

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

      1. associate-*r/ 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. Taylor expanded in y around 0 91.6%

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

      1. neg-mul-1 91.6%

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

      2. distribute-neg-frac 91.6%

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

   6. Simplified 91.6%

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

      1. frac-2neg 91.6%

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

      2. div-inv 91.5%

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

      3. remove-double-neg 91.5%

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

      4. sub-neg 91.5%

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

      5. distribute-neg-in 91.5%

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

      6. remove-double-neg 91.5%

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

   8. Applied egg-rr 91.5%

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

      1. associate-*r/ 91.6%

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

      2. *-rgt-identity 91.6%

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

      3. +-commutative 91.6%

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

      4. unsub-neg 91.6%

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

   10. Simplified 91.6%

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

   if -5.6999999999999997e79 < z < 2.05e77

   1. Initial program 93.3%

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

      1. associate-*r/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 77.1%

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

   if 2.05e77 < z

   1. Initial program 75.2%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+49) x (if (<= z 4.5e+74) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+49) {
		tmp = x;
	} else if (z <= 4.5e+74) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d+49)) then
        tmp = x
    else if (z <= 4.5d+74) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+49) {
		tmp = x;
	} else if (z <= 4.5e+74) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+49:
		tmp = x
	elif z <= 4.5e+74:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+49)
		tmp = x;
	elseif (z <= 4.5e+74)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e+49)
		tmp = x;
	elseif (z <= 4.5e+74)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+49], x, If[LessEqual[z, 4.5e+74], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e49 or 4.5e74 < z

   1. Initial program 75.4%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 71.4%

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

   if -1.45e49 < z < 4.5e74

   1. Initial program 93.0%

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

      1. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 63.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 34.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. associate-*r/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in z around inf 35.0%

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

5. Final simplification 35.0%

   \[\leadsto x \]

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(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)))