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

Percentage Accurate: 84.1% → 98.6%

Time: 7.0s

Alternatives: 9

Speedup: 0.7×

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: 84.1% 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: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t - z}\\ t_2 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-315}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x (- t z)))) (t_2 (/ (* x (- y z)) (- t z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-315)
       t_2
       (if (<= t_2 0.0) (/ y (/ t x)) (if (<= t_2 5e+290) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / (t - z));
	double t_2 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-315) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y / (t / x);
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / (t - z));
	double t_2 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-315) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y / (t / x);
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / (t - z))
	t_2 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-315:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y / (t / x)
	elif t_2 <= 5e+290:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / Float64(t - z)))
	t_2 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-315)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y / Float64(t / x));
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / (t - z));
	t_2 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-315)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y / (t / x);
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-315], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+290], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -inf.0 or 4.9999999999999998e290 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 36.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2.0000000019e-315 or -0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.9999999999999998e290

   1. Initial program 99.7%

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

   if -2.0000000019e-315 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -0.0

   1. Initial program 83.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -2 \cdot 10^{-315}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 0:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 2: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e+80)
   x
   (if (<= z 2.6e-89)
     (* (- y z) (/ x t))
     (if (<= z 5e+27)
       (* x (/ y (- t z)))
       (if (<= z 1.25e+85) (/ (- x) (/ t z)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+80) {
		tmp = x;
	} else if (z <= 2.6e-89) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5e+27) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.25e+85) {
		tmp = -x / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d+80)) then
        tmp = x
    else if (z <= 2.6d-89) then
        tmp = (y - z) * (x / t)
    else if (z <= 5d+27) then
        tmp = x * (y / (t - z))
    else if (z <= 1.25d+85) then
        tmp = -x / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+80) {
		tmp = x;
	} else if (z <= 2.6e-89) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5e+27) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.25e+85) {
		tmp = -x / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e+80:
		tmp = x
	elif z <= 2.6e-89:
		tmp = (y - z) * (x / t)
	elif z <= 5e+27:
		tmp = x * (y / (t - z))
	elif z <= 1.25e+85:
		tmp = -x / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e+80)
		tmp = x;
	elseif (z <= 2.6e-89)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 5e+27)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.25e+85)
		tmp = Float64(Float64(-x) / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e+80)
		tmp = x;
	elseif (z <= 2.6e-89)
		tmp = (y - z) * (x / t);
	elseif (z <= 5e+27)
		tmp = x * (y / (t - z));
	elseif (z <= 1.25e+85)
		tmp = -x / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e+80], x, If[LessEqual[z, 2.6e-89], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+27], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+85], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000008e80 or 1.25e85 < z

   1. Initial program 68.7%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -4.60000000000000008e80 < z < 2.5999999999999999e-89

   1. Initial program 91.5%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 73.7%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 77.9%

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

   6. Simplified 77.9%

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

   if 2.5999999999999999e-89 < z < 4.99999999999999979e27

   1. Initial program 96.0%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/l* 69.5%

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

      3. associate-/r/ 67.6%

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

   6. Simplified 67.6%

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

   if 4.99999999999999979e27 < z < 1.25e85

   1. Initial program 67.9%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around inf 52.0%

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

      1. associate-/l* 84.1%

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

      2. associate-/r/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. associate-/l* 84.1%

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

   9. Simplified 84.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+199}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+87)
   (* x (/ z (- z t)))
   (if (<= z 1.85e+199) (* (- y z) (/ x (- t z))) (/ (- x) (/ z (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+87) {
		tmp = x * (z / (z - t));
	} else if (z <= 1.85e+199) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = -x / (z / (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 <= (-1.2d+87)) then
        tmp = x * (z / (z - t))
    else if (z <= 1.85d+199) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = -x / (z / (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 <= -1.2e+87) {
		tmp = x * (z / (z - t));
	} else if (z <= 1.85e+199) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = -x / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+87:
		tmp = x * (z / (z - t))
	elif z <= 1.85e+199:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = -x / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+87)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 1.85e+199)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(Float64(-x) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+87)
		tmp = x * (z / (z - t));
	elseif (z <= 1.85e+199)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = -x / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+87], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+199], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999991e87

   1. Initial program 68.3%

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

      1. associate-*l/ 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-*l/ 56.7%

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

      3. distribute-rgt-neg-out 56.7%

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

   6. Simplified 56.7%

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

      1. *-commutative 56.7%

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

      2. frac-2neg 56.7%

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

      3. associate-*r/ 54.9%

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

      4. add-sqr-sqrt 54.6%

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

      5. sqrt-unprod 25.2%

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

      6. sqr-neg 25.2%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 7.9%

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

      9. add-sqr-sqrt 5.0%

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

      10. sqrt-unprod 21.4%

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

      11. sqr-neg 21.4%

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

      12. sqrt-unprod 22.9%

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

      13. add-sqr-sqrt 54.9%

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

      14. sub-neg 54.9%

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

      15. distribute-neg-in 54.9%

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

      16. add-sqr-sqrt 54.6%

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

      17. sqrt-unprod 24.1%

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

      18. sqr-neg 24.1%

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

      19. sqrt-unprod 0.0%

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

      20. add-sqr-sqrt 15.1%

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

      21. add-sqr-sqrt 15.1%

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

      22. sqrt-unprod 9.8%

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

      23. sqr-neg 9.8%

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

      24. sqrt-unprod 0.0%

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

      25. add-sqr-sqrt 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. associate-/l* 56.5%

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

      2. associate-/r/ 79.9%

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

      3. +-commutative 79.9%

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

      4. unsub-neg 79.9%

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

   10. Simplified 79.9%

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

   if -1.19999999999999991e87 < z < 1.85000000000000011e199

   1. Initial program 90.1%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   if 1.85000000000000011e199 < z

   1. Initial program 58.9%

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

      1. associate-*l/ 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in t around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-/l* 88.5%

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

      3. distribute-neg-frac 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+199}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-28} \lor \neg \left(y \leq 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.4e-28) (not (<= y 1e+51)))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.4e-28) || !(y <= 1e+51)) {
		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 <= (-7.4d-28)) .or. (.not. (y <= 1d+51))) 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 <= -7.4e-28) || !(y <= 1e+51)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.4e-28) or not (y <= 1e+51):
		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 <= -7.4e-28) || !(y <= 1e+51))
		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 <= -7.4e-28) || ~((y <= 1e+51)))
		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, -7.4e-28], N[Not[LessEqual[y, 1e+51]], $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 < -7.40000000000000039e-28 or 1e51 < y

   1. Initial program 82.6%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 72.9%

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

      3. associate-/r/ 77.2%

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

   6. Simplified 77.2%

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

   if -7.40000000000000039e-28 < y < 1e51

   1. Initial program 84.0%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*l/ 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

   6. Simplified 66.4%

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

      1. *-commutative 66.4%

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

      2. frac-2neg 66.4%

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

      3. associate-*r/ 67.8%

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

      4. add-sqr-sqrt 34.4%

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

      5. sqrt-unprod 36.8%

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

      6. sqr-neg 36.8%

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

      7. sqrt-unprod 10.8%

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

      8. add-sqr-sqrt 17.5%

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

      9. add-sqr-sqrt 8.0%

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

      10. sqrt-unprod 30.9%

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

      11. sqr-neg 30.9%

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

      12. sqrt-unprod 32.5%

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

      13. add-sqr-sqrt 67.8%

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

      14. sub-neg 67.8%

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

      15. distribute-neg-in 67.8%

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

      16. add-sqr-sqrt 34.4%

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

      17. sqrt-unprod 45.3%

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

      18. sqr-neg 45.3%

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

      19. sqrt-unprod 18.5%

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

      20. add-sqr-sqrt 35.3%

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

      21. add-sqr-sqrt 16.8%

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

      22. sqrt-unprod 42.8%

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

      23. sqr-neg 42.8%

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

      24. sqrt-unprod 33.2%

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

      25. add-sqr-sqrt 67.8%

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

   8. Applied egg-rr 67.8%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 78.6%

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

      3. +-commutative 78.6%

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

      4. unsub-neg 78.6%

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

   10. Simplified 78.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-28} \lor \neg \left(y \leq 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 5: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+86}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e+86) x (if (<= z 1.55e+86) (* (- y z) (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+86) {
		tmp = x;
	} else if (z <= 1.55e+86) {
		tmp = (y - z) * (x / 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 <= (-1.15d+86)) then
        tmp = x
    else if (z <= 1.55d+86) then
        tmp = (y - z) * (x / 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 <= -1.15e+86) {
		tmp = x;
	} else if (z <= 1.55e+86) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e+86:
		tmp = x
	elif z <= 1.55e+86:
		tmp = (y - z) * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e+86)
		tmp = x;
	elseif (z <= 1.55e+86)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e+86)
		tmp = x;
	elseif (z <= 1.55e+86)
		tmp = (y - z) * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e+86], x, If[LessEqual[z, 1.55e+86], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999995e86 or 1.5500000000000001e86 < z

   1. Initial program 68.7%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -1.14999999999999995e86 < z < 1.5500000000000001e86

   1. Initial program 91.3%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 68.9%

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

      1. associate-/l* 72.3%

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

      2. associate-/r/ 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+86}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 59.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+78) x (if (<= z 4.8e-24) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+78) {
		tmp = x;
	} else if (z <= 4.8e-24) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.5d+78)) then
        tmp = x
    else if (z <= 4.8d-24) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+78) {
		tmp = x;
	} else if (z <= 4.8e-24) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+78:
		tmp = x
	elif z <= 4.8e-24:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+78)
		tmp = x;
	elseif (z <= 4.8e-24)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e+78)
		tmp = x;
	elseif (z <= 4.8e-24)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+78], x, If[LessEqual[z, 4.8e-24], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e78 or 4.7999999999999996e-24 < z

   1. Initial program 71.6%

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

      1. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -4.4999999999999999e78 < z < 4.7999999999999996e-24

   1. Initial program 91.7%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 60.0%

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

      1. associate-/l* 65.4%

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

      2. associate-/r/ 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+78) x (if (<= z 2.5e-18) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+78) {
		tmp = x;
	} else if (z <= 2.5e-18) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.4d+78)) then
        tmp = x
    else if (z <= 2.5d-18) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+78) {
		tmp = x;
	} else if (z <= 2.5e-18) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+78:
		tmp = x
	elif z <= 2.5e-18:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+78)
		tmp = x;
	elseif (z <= 2.5e-18)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.4e+78)
		tmp = x;
	elseif (z <= 2.5e-18)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+78], x, If[LessEqual[z, 2.5e-18], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e78 or 2.50000000000000018e-18 < z

   1. Initial program 71.6%

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

      1. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -2.3999999999999999e78 < z < 2.50000000000000018e-18

   1. Initial program 91.7%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

      1. *-commutative 92.4%

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

      2. clear-num 92.3%

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

      3. un-div-inv 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in z around 0 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-*l/ 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+80) x (if (<= z 1.8e-21) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+80) {
		tmp = x;
	} else if (z <= 1.8e-21) {
		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 <= (-3.8d+80)) then
        tmp = x
    else if (z <= 1.8d-21) 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 <= -3.8e+80) {
		tmp = x;
	} else if (z <= 1.8e-21) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+80:
		tmp = x
	elif z <= 1.8e-21:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+80)
		tmp = x;
	elseif (z <= 1.8e-21)
		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 <= -3.8e+80)
		tmp = x;
	elseif (z <= 1.8e-21)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+80], x, If[LessEqual[z, 1.8e-21], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999997e80 or 1.79999999999999995e-21 < z

   1. Initial program 71.6%

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

      1. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -3.79999999999999997e80 < z < 1.79999999999999995e-21

   1. Initial program 91.7%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 60.0%

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

      1. associate-/l* 65.4%

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

   6. Simplified 65.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 83.4%

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

   1. associate-*l/ 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in z around inf 32.0%

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

5. Final simplification 32.0%

   \[\leadsto x \]

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 2023293 
(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)))