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

Percentage Accurate: 84.6% → 96.5%

Time: 8.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.5%

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

   1. associate-/l* 96.4%

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

3. Simplified 96.4%

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

5. Final simplification 96.4%

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

Alternative 2: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+77} \lor \neg \left(z \leq -6.3 \cdot 10^{-9}\right) \land \left(z \leq -1.05 \cdot 10^{-60} \lor \neg \left(z \leq 4.4 \cdot 10^{-11}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e+77)
         (and (not (<= z -6.3e-9)) (or (<= z -1.05e-60) (not (<= z 4.4e-11)))))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+77) || (!(z <= -6.3e-9) && ((z <= -1.05e-60) || !(z <= 4.4e-11)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.1d+77)) .or. (.not. (z <= (-6.3d-9))) .and. (z <= (-1.05d-60)) .or. (.not. (z <= 4.4d-11))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+77) || (!(z <= -6.3e-9) && ((z <= -1.05e-60) || !(z <= 4.4e-11)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e+77) or (not (z <= -6.3e-9) and ((z <= -1.05e-60) or not (z <= 4.4e-11))):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e+77) || (!(z <= -6.3e-9) && ((z <= -1.05e-60) || !(z <= 4.4e-11))))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.1e+77) || (~((z <= -6.3e-9)) && ((z <= -1.05e-60) || ~((z <= 4.4e-11)))))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e+77], And[N[Not[LessEqual[z, -6.3e-9]], $MachinePrecision], Or[LessEqual[z, -1.05e-60], N[Not[LessEqual[z, 4.4e-11]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e77 or -6.3000000000000002e-9 < z < -1.04999999999999996e-60 or 4.4000000000000003e-11 < z

   1. Initial program 67.0%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-/l* 81.5%

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

      3. distribute-rgt-neg-in 81.5%

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

      4. distribute-frac-neg 81.5%

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

      5. neg-sub0 81.5%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.5%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.5%

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

      8. +-commutative 81.5%

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

      9. sub-neg 81.5%

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

      10. div-sub 81.5%

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

      11. *-inverses 81.5%

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

   7. Simplified 81.5%

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

   if -2.0999999999999999e77 < z < -6.3000000000000002e-9 or -1.04999999999999996e-60 < z < 4.4000000000000003e-11

   1. Initial program 91.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around inf 75.1%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+77} \lor \neg \left(z \leq -6.3 \cdot 10^{-9}\right) \land \left(z \leq -1.05 \cdot 10^{-60} \lor \neg \left(z \leq 4.4 \cdot 10^{-11}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+76} \lor \neg \left(z \leq -1 \cdot 10^{-9}\right) \land \left(z \leq -1.1 \cdot 10^{-60} \lor \neg \left(z \leq 4.8 \cdot 10^{-18}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+76)
         (and (not (<= z -1e-9)) (or (<= z -1.1e-60) (not (<= z 4.8e-18)))))
   (* x (- 1.0 (/ y z)))
   (/ x (/ (- t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+76) || (!(z <= -1e-9) && ((z <= -1.1e-60) || !(z <= 4.8e-18)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / ((t - z) / y);
	}
	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 <= (-1.7d+76)) .or. (.not. (z <= (-1d-9))) .and. (z <= (-1.1d-60)) .or. (.not. (z <= 4.8d-18))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / ((t - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+76) || (!(z <= -1e-9) && ((z <= -1.1e-60) || !(z <= 4.8e-18)))) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+76) or (not (z <= -1e-9) and ((z <= -1.1e-60) or not (z <= 4.8e-18))):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+76) || (!(z <= -1e-9) && ((z <= -1.1e-60) || !(z <= 4.8e-18))))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+76) || (~((z <= -1e-9)) && ((z <= -1.1e-60) || ~((z <= 4.8e-18)))))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / ((t - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e+76], And[N[Not[LessEqual[z, -1e-9]], $MachinePrecision], Or[LessEqual[z, -1.1e-60], N[Not[LessEqual[z, 4.8e-18]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e76 or -1.00000000000000006e-9 < z < -1.0999999999999999e-60 or 4.79999999999999988e-18 < z

   1. Initial program 67.0%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-/l* 81.5%

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

      3. distribute-rgt-neg-in 81.5%

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

      4. distribute-frac-neg 81.5%

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

      5. neg-sub0 81.5%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.5%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.5%

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

      8. +-commutative 81.5%

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

      9. sub-neg 81.5%

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

      10. div-sub 81.5%

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

      11. *-inverses 81.5%

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

   7. Simplified 81.5%

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

   if -1.6999999999999999e76 < z < -1.00000000000000006e-9 or -1.0999999999999999e-60 < z < 4.79999999999999988e-18

   1. Initial program 91.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 93.6%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in y around inf 79.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+76} \lor \neg \left(z \leq -1 \cdot 10^{-9}\right) \land \left(z \leq -1.1 \cdot 10^{-60} \lor \neg \left(z \leq 4.8 \cdot 10^{-18}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-70} \lor \neg \left(z \leq 3.4 \cdot 10^{-54}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.2e+40)
     t_1
     (if (<= z -2.5e-8)
       (* y (/ x t))
       (if (or (<= z -1.26e-70) (not (<= z 3.4e-54))) t_1 (/ x (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.2e+40) {
		tmp = t_1;
	} else if (z <= -2.5e-8) {
		tmp = y * (x / t);
	} else if ((z <= -1.26e-70) || !(z <= 3.4e-54)) {
		tmp = t_1;
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-5.2d+40)) then
        tmp = t_1
    else if (z <= (-2.5d-8)) then
        tmp = y * (x / t)
    else if ((z <= (-1.26d-70)) .or. (.not. (z <= 3.4d-54))) then
        tmp = t_1
    else
        tmp = x / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.2e+40) {
		tmp = t_1;
	} else if (z <= -2.5e-8) {
		tmp = y * (x / t);
	} else if ((z <= -1.26e-70) || !(z <= 3.4e-54)) {
		tmp = t_1;
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -5.2e+40:
		tmp = t_1
	elif z <= -2.5e-8:
		tmp = y * (x / t)
	elif (z <= -1.26e-70) or not (z <= 3.4e-54):
		tmp = t_1
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5.2e+40)
		tmp = t_1;
	elseif (z <= -2.5e-8)
		tmp = Float64(y * Float64(x / t));
	elseif ((z <= -1.26e-70) || !(z <= 3.4e-54))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -5.2e+40)
		tmp = t_1;
	elseif (z <= -2.5e-8)
		tmp = y * (x / t);
	elseif ((z <= -1.26e-70) || ~((z <= 3.4e-54)))
		tmp = t_1;
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+40], t$95$1, If[LessEqual[z, -2.5e-8], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.26e-70], N[Not[LessEqual[z, 3.4e-54]], $MachinePrecision]], t$95$1, N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000001e40 or -2.4999999999999999e-8 < z < -1.2600000000000001e-70 or 3.39999999999999987e-54 < z

   1. Initial program 71.3%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. associate-/l* 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. distribute-frac-neg 76.7%

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

      5. neg-sub0 76.7%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 76.7%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 76.7%

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

      8. +-commutative 76.7%

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

      9. sub-neg 76.7%

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

      10. div-sub 76.7%

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

      11. *-inverses 76.7%

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

   7. Simplified 76.7%

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

   if -5.2000000000000001e40 < z < -2.4999999999999999e-8

   1. Initial program 80.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 41.7%

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

      1. *-commutative 41.7%

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

      2. associate-/l* 60.5%

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

   7. Applied egg-rr 60.5%

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

   if -1.2600000000000001e-70 < z < 3.39999999999999987e-54

   1. Initial program 92.7%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

      1. clear-num 91.5%

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

      2. un-div-inv 91.9%

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

   6. Applied egg-rr 91.9%

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

   7. Taylor expanded in z around 0 71.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-70} \lor \neg \left(z \leq 3.4 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.7e+76)
     t_2
     (if (<= z -8.5e-9)
       t_1
       (if (<= z -4e-70) (/ (* x (- z y)) z) (if (<= z 2.5e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.7e+76) {
		tmp = t_2;
	} else if (z <= -8.5e-9) {
		tmp = t_1;
	} else if (z <= -4e-70) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 2.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-1.7d+76)) then
        tmp = t_2
    else if (z <= (-8.5d-9)) then
        tmp = t_1
    else if (z <= (-4d-70)) then
        tmp = (x * (z - y)) / z
    else if (z <= 2.5d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.7e+76) {
		tmp = t_2;
	} else if (z <= -8.5e-9) {
		tmp = t_1;
	} else if (z <= -4e-70) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 2.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.7e+76:
		tmp = t_2
	elif z <= -8.5e-9:
		tmp = t_1
	elif z <= -4e-70:
		tmp = (x * (z - y)) / z
	elif z <= 2.5e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.7e+76)
		tmp = t_2;
	elseif (z <= -8.5e-9)
		tmp = t_1;
	elseif (z <= -4e-70)
		tmp = Float64(Float64(x * Float64(z - y)) / z);
	elseif (z <= 2.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.7e+76)
		tmp = t_2;
	elseif (z <= -8.5e-9)
		tmp = t_1;
	elseif (z <= -4e-70)
		tmp = (x * (z - y)) / z;
	elseif (z <= 2.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+76], t$95$2, If[LessEqual[z, -8.5e-9], t$95$1, If[LessEqual[z, -4e-70], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.5e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6999999999999999e76 or 2.5000000000000002e-16 < z

   1. Initial program 62.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 83.3%

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

      3. distribute-rgt-neg-in 83.3%

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

      4. distribute-frac-neg 83.3%

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

      5. neg-sub0 83.3%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 83.3%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 83.3%

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

      8. +-commutative 83.3%

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

      9. sub-neg 83.3%

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

      10. div-sub 83.3%

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

      11. *-inverses 83.3%

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

   7. Simplified 83.3%

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

   if -1.6999999999999999e76 < z < -8.5e-9 or -3.99999999999999998e-70 < z < 2.5000000000000002e-16

   1. Initial program 91.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 93.6%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in y around inf 79.2%

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

   if -8.5e-9 < z < -3.99999999999999998e-70

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-lft-neg-out 99.8%

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

      3. distribute-neg-frac 99.8%

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

      4. distribute-neg-frac2 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. sub-neg 99.8%

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

      13. distribute-neg-in 99.8%

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

      14. remove-double-neg 99.8%

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

      15. +-commutative 99.8%

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

      16. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 76.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := \frac{x}{\frac{z}{z - y}}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (/ x (/ z (- z y)))))
   (if (<= z -1.85e+78)
     t_2
     (if (<= z -6.8e-9)
       t_1
       (if (<= z -4.5e-70) (/ (* x (- z y)) z) (if (<= z 2.5e-12) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x / (z / (z - y));
	double tmp;
	if (z <= -1.85e+78) {
		tmp = t_2;
	} else if (z <= -6.8e-9) {
		tmp = t_1;
	} else if (z <= -4.5e-70) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 2.5e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x / (z / (z - y))
    if (z <= (-1.85d+78)) then
        tmp = t_2
    else if (z <= (-6.8d-9)) then
        tmp = t_1
    else if (z <= (-4.5d-70)) then
        tmp = (x * (z - y)) / z
    else if (z <= 2.5d-12) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x / (z / (z - y));
	double tmp;
	if (z <= -1.85e+78) {
		tmp = t_2;
	} else if (z <= -6.8e-9) {
		tmp = t_1;
	} else if (z <= -4.5e-70) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 2.5e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x / (z / (z - y))
	tmp = 0
	if z <= -1.85e+78:
		tmp = t_2
	elif z <= -6.8e-9:
		tmp = t_1
	elif z <= -4.5e-70:
		tmp = (x * (z - y)) / z
	elif z <= 2.5e-12:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x / Float64(z / Float64(z - y)))
	tmp = 0.0
	if (z <= -1.85e+78)
		tmp = t_2;
	elseif (z <= -6.8e-9)
		tmp = t_1;
	elseif (z <= -4.5e-70)
		tmp = Float64(Float64(x * Float64(z - y)) / z);
	elseif (z <= 2.5e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x / (z / (z - y));
	tmp = 0.0;
	if (z <= -1.85e+78)
		tmp = t_2;
	elseif (z <= -6.8e-9)
		tmp = t_1;
	elseif (z <= -4.5e-70)
		tmp = (x * (z - y)) / z;
	elseif (z <= 2.5e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+78], t$95$2, If[LessEqual[z, -6.8e-9], t$95$1, If[LessEqual[z, -4.5e-70], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.5e-12], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999992e78 or 2.49999999999999985e-12 < z

   1. Initial program 62.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. distribute-neg-frac2 83.4%

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

      3. neg-sub0 83.4%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{0 - \left(y - z\right)}}} \]

      4. associate--r- 83.4%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(0 - y\right) + z}}} \]

      5. neg-sub0 83.4%

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

   9. Simplified 83.4%

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

   if -1.84999999999999992e78 < z < -6.7999999999999997e-9 or -4.50000000000000022e-70 < z < 2.49999999999999985e-12

   1. Initial program 91.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 93.6%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in y around inf 79.2%

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

   if -6.7999999999999997e-9 < z < -4.50000000000000022e-70

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-lft-neg-out 99.8%

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

      3. distribute-neg-frac 99.8%

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

      4. distribute-neg-frac2 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. sub-neg 99.8%

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

      13. distribute-neg-in 99.8%

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

      14. remove-double-neg 99.8%

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

      15. +-commutative 99.8%

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

      16. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 76.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e+80) x (if (<= z 1.66e-18) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e+80) {
		tmp = x;
	} else if (z <= 1.66e-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 <= (-2.1d+80)) then
        tmp = x
    else if (z <= 1.66d-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 <= -2.1e+80) {
		tmp = x;
	} else if (z <= 1.66e-18) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e+80:
		tmp = x
	elif z <= 1.66e-18:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e+80)
		tmp = x;
	elseif (z <= 1.66e-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 <= -2.1e+80)
		tmp = x;
	elseif (z <= 1.66e-18)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e+80], x, If[LessEqual[z, 1.66e-18], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000001e80 or 1.66e-18 < z

   1. Initial program 62.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -2.10000000000000001e80 < z < 1.66e-18

   1. Initial program 92.5%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 56.9%

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

      1. associate-/l* 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+76) x (if (<= z 1e-12) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+76) {
		tmp = x;
	} else if (z <= 1e-12) {
		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 <= (-1.7d+76)) then
        tmp = x
    else if (z <= 1d-12) 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 <= -1.7e+76) {
		tmp = x;
	} else if (z <= 1e-12) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+76:
		tmp = x
	elif z <= 1e-12:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+76)
		tmp = x;
	elseif (z <= 1e-12)
		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 <= -1.7e+76)
		tmp = x;
	elseif (z <= 1e-12)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+76], x, If[LessEqual[z, 1e-12], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e76 or 9.9999999999999998e-13 < z

   1. Initial program 62.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -1.6999999999999999e76 < z < 9.9999999999999998e-13

   1. Initial program 92.5%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

      1. clear-num 93.6%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 61.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.5%

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

   1. associate-/l* 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in z around inf 33.4%

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

6. Final simplification 33.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.6% 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 2024115 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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