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

Percentage Accurate: 84.2% → 96.8%

Time: 7.8s

Alternatives: 13

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: 84.2% 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: 96.8% 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]

Derivation

1. Initial program 86.7%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

   1. clear-num 97.6%

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

   2. un-div-inv 98.0%

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

6. Applied egg-rr 98.0%

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

Alternative 2: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.1:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -6.8e+78)
     t_1
     (if (<= z 0.1)
       (/ (* x y) (- t z))
       (if (<= z 8.5e+74)
         (/ x (- 1.0 (/ t z)))
         (if (<= z 4.4e+92) (/ x (/ (- t z) y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -6.8e+78) {
		tmp = t_1;
	} else if (z <= 0.1) {
		tmp = (x * y) / (t - z);
	} else if (z <= 8.5e+74) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 4.4e+92) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-6.8d+78)) then
        tmp = t_1
    else if (z <= 0.1d0) then
        tmp = (x * y) / (t - z)
    else if (z <= 8.5d+74) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 4.4d+92) then
        tmp = x / ((t - z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -6.8e+78) {
		tmp = t_1;
	} else if (z <= 0.1) {
		tmp = (x * y) / (t - z);
	} else if (z <= 8.5e+74) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 4.4e+92) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -6.8e+78:
		tmp = t_1
	elif z <= 0.1:
		tmp = (x * y) / (t - z)
	elif z <= 8.5e+74:
		tmp = x / (1.0 - (t / z))
	elif z <= 4.4e+92:
		tmp = x / ((t - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6.8e+78)
		tmp = t_1;
	elseif (z <= 0.1)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 8.5e+74)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 4.4e+92)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6.8e+78)
		tmp = t_1;
	elseif (z <= 0.1)
		tmp = (x * y) / (t - z);
	elseif (z <= 8.5e+74)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 4.4e+92)
		tmp = x / ((t - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+78], t$95$1, If[LessEqual[z, 0.1], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+74], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+92], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.80000000000000014e78 or 4.39999999999999984e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-/l* 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

      4. distribute-frac-neg 85.3%

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

      5. neg-sub0 85.3%

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

      6. associate--r- 85.3%

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

      7. neg-sub0 85.3%

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

      8. +-commutative 85.3%

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

      9. sub-neg 85.3%

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

      10. div-sub 85.3%

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

      11. *-inverses 85.3%

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

   7. Simplified 85.3%

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

   if -6.80000000000000014e78 < z < 0.10000000000000001

   1. Initial program 96.2%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 78.9%

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

   if 0.10000000000000001 < z < 8.50000000000000028e74

   1. Initial program 91.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 x around 0 91.5%

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

      1. remove-double-neg 91.5%

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

      2. distribute-neg-frac2 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-/l* 89.8%

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

      5. distribute-lft-neg-out 89.8%

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

      6. neg-sub0 89.8%

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

      7. associate--r- 89.8%

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

      8. neg-sub0 89.8%

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

      9. +-commutative 89.8%

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

      10. sub-neg 89.8%

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

      11. neg-sub0 89.8%

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

      12. associate--r- 89.8%

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

      13. neg-sub0 89.8%

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

      14. +-commutative 89.8%

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

      15. sub-neg 89.8%

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

      16. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in y around 0 82.5%

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

      1. associate-*l/ 80.8%

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

      2. associate-/r/ 91.0%

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

      3. div-sub 91.0%

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

      4. *-inverses 91.0%

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

   10. Simplified 91.0%

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

   if 8.50000000000000028e74 < z < 4.39999999999999984e92

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 79.7%

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

Alternative 3: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 0.125:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (/ x (- 1.0 (/ t z)))))
   (if (<= z -3.6e+150)
     t_2
     (if (<= z 0.125)
       t_1
       (if (<= z 2.7e+79)
         t_2
         (if (<= z 4.4e+92) t_1 (* x (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.125) {
		tmp = t_1;
	} else if (z <= 2.7e+79) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x / (1.0d0 - (t / z))
    if (z <= (-3.6d+150)) then
        tmp = t_2
    else if (z <= 0.125d0) then
        tmp = t_1
    else if (z <= 2.7d+79) then
        tmp = t_2
    else if (z <= 4.4d+92) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.125) {
		tmp = t_1;
	} else if (z <= 2.7e+79) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -3.6e+150:
		tmp = t_2
	elif z <= 0.125:
		tmp = t_1
	elif z <= 2.7e+79:
		tmp = t_2
	elif z <= 4.4e+92:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / z))
	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(t / z)))
	tmp = 0.0
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.125)
		tmp = t_1;
	elseif (z <= 2.7e+79)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.125)
		tmp = t_1;
	elseif (z <= 2.7e+79)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / z));
	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[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+150], t$95$2, If[LessEqual[z, 0.125], t$95$1, If[LessEqual[z, 2.7e+79], t$95$2, If[LessEqual[z, 4.4e+92], t$95$1, N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999986e150 or 0.125 < z < 2.7e79

   1. Initial program 65.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. remove-double-neg 65.4%

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

      2. distribute-neg-frac2 65.4%

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

      3. *-commutative 65.4%

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

      4. associate-/l* 75.4%

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

      5. distribute-lft-neg-out 75.4%

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

      6. neg-sub0 75.4%

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

      7. associate--r- 75.4%

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

      8. neg-sub0 75.4%

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

      9. +-commutative 75.4%

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

      10. sub-neg 75.4%

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

      11. neg-sub0 75.4%

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

      12. associate--r- 75.4%

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

      13. neg-sub0 75.4%

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

      14. +-commutative 75.4%

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

      15. sub-neg 75.4%

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

      16. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in y around 0 60.3%

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

      1. associate-*l/ 67.1%

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

      2. associate-/r/ 89.2%

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

      3. div-sub 89.2%

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

      4. *-inverses 89.2%

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

   10. Simplified 89.2%

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

   if -3.59999999999999986e150 < z < 0.125 or 2.7e79 < z < 4.39999999999999984e92

   1. Initial program 95.5%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.4%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in y around inf 77.7%

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

   if 4.39999999999999984e92 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.7%

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

      3. distribute-rgt-neg-in 88.7%

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

      4. distribute-frac-neg 88.7%

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

      5. neg-sub0 88.7%

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

      6. associate--r- 88.7%

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

      7. neg-sub0 88.7%

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

      8. +-commutative 88.7%

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

      9. sub-neg 88.7%

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

      10. div-sub 88.7%

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

      11. *-inverses 88.7%

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

   7. Simplified 88.7%

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

Alternative 4: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 0.0235:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (/ x (- 1.0 (/ t z)))))
   (if (<= z -3.6e+150)
     t_2
     (if (<= z 0.0235)
       t_1
       (if (<= z 4e+80) t_2 (if (<= z 4.4e+92) t_1 (* x (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.0235) {
		tmp = t_1;
	} else if (z <= 4e+80) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x / (1.0d0 - (t / z))
    if (z <= (-3.6d+150)) then
        tmp = t_2
    else if (z <= 0.0235d0) then
        tmp = t_1
    else if (z <= 4d+80) then
        tmp = t_2
    else if (z <= 4.4d+92) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.0235) {
		tmp = t_1;
	} else if (z <= 4e+80) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -3.6e+150:
		tmp = t_2
	elif z <= 0.0235:
		tmp = t_1
	elif z <= 4e+80:
		tmp = t_2
	elif z <= 4.4e+92:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x / Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.0235)
		tmp = t_1;
	elseif (z <= 4e+80)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.0235)
		tmp = t_1;
	elseif (z <= 4e+80)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+150], t$95$2, If[LessEqual[z, 0.0235], t$95$1, If[LessEqual[z, 4e+80], t$95$2, If[LessEqual[z, 4.4e+92], t$95$1, N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999986e150 or 0.0235 < z < 4e80

   1. Initial program 65.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. remove-double-neg 65.4%

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

      2. distribute-neg-frac2 65.4%

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

      3. *-commutative 65.4%

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

      4. associate-/l* 75.4%

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

      5. distribute-lft-neg-out 75.4%

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

      6. neg-sub0 75.4%

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

      7. associate--r- 75.4%

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

      8. neg-sub0 75.4%

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

      9. +-commutative 75.4%

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

      10. sub-neg 75.4%

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

      11. neg-sub0 75.4%

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

      12. associate--r- 75.4%

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

      13. neg-sub0 75.4%

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

      14. +-commutative 75.4%

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

      15. sub-neg 75.4%

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

      16. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in y around 0 60.3%

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

      1. associate-*l/ 67.1%

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

      2. associate-/r/ 89.2%

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

      3. div-sub 89.2%

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

      4. *-inverses 89.2%

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

   10. Simplified 89.2%

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

   if -3.59999999999999986e150 < z < 0.0235 or 4e80 < z < 4.39999999999999984e92

   1. Initial program 95.5%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around inf 77.6%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if 4.39999999999999984e92 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.7%

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

      3. distribute-rgt-neg-in 88.7%

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

      4. distribute-frac-neg 88.7%

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

      5. neg-sub0 88.7%

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

      6. associate--r- 88.7%

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

      7. neg-sub0 88.7%

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

      8. +-commutative 88.7%

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

      9. sub-neg 88.7%

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

      10. div-sub 88.7%

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

      11. *-inverses 88.7%

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

   7. Simplified 88.7%

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

Alternative 5: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 0.0285:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (* x (/ z (- z t)))))
   (if (<= z -3.6e+150)
     t_2
     (if (<= z 0.0285)
       t_1
       (if (<= z 3e+79) t_2 (if (<= z 4.4e+92) t_1 (* x (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.0285) {
		tmp = t_1;
	} else if (z <= 3e+79) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x * (z / (z - t))
    if (z <= (-3.6d+150)) then
        tmp = t_2
    else if (z <= 0.0285d0) then
        tmp = t_1
    else if (z <= 3d+79) then
        tmp = t_2
    else if (z <= 4.4d+92) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -3.6e+150) {
		tmp = t_2;
	} else if (z <= 0.0285) {
		tmp = t_1;
	} else if (z <= 3e+79) {
		tmp = t_2;
	} else if (z <= 4.4e+92) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x * (z / (z - t))
	tmp = 0
	if z <= -3.6e+150:
		tmp = t_2
	elif z <= 0.0285:
		tmp = t_1
	elif z <= 3e+79:
		tmp = t_2
	elif z <= 4.4e+92:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.0285)
		tmp = t_1;
	elseif (z <= 3e+79)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -3.6e+150)
		tmp = t_2;
	elseif (z <= 0.0285)
		tmp = t_1;
	elseif (z <= 3e+79)
		tmp = t_2;
	elseif (z <= 4.4e+92)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+150], t$95$2, If[LessEqual[z, 0.0285], t$95$1, If[LessEqual[z, 3e+79], t$95$2, If[LessEqual[z, 4.4e+92], t$95$1, N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999986e150 or 0.028500000000000001 < z < 2.99999999999999974e79

   1. Initial program 65.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. distribute-neg-frac2 60.3%

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

      3. neg-sub0 60.3%

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

      4. associate--r- 60.3%

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

      5. neg-sub0 60.3%

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

      6. +-commutative 60.3%

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

      7. sub-neg 60.3%

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

      8. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

   if -3.59999999999999986e150 < z < 0.028500000000000001 or 2.99999999999999974e79 < z < 4.39999999999999984e92

   1. Initial program 95.5%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around inf 77.6%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if 4.39999999999999984e92 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.7%

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

      3. distribute-rgt-neg-in 88.7%

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

      4. distribute-frac-neg 88.7%

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

      5. neg-sub0 88.7%

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

      6. associate--r- 88.7%

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

      7. neg-sub0 88.7%

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

      8. +-commutative 88.7%

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

      9. sub-neg 88.7%

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

      10. div-sub 88.7%

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

      11. *-inverses 88.7%

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

   7. Simplified 88.7%

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

Alternative 6: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e+150)
   x
   (if (<= z -5.5e-19) (* x (/ y (- z))) (if (<= z 4.9e+92) (/ (* x y) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+150) {
		tmp = x;
	} else if (z <= -5.5e-19) {
		tmp = x * (y / -z);
	} else if (z <= 4.9e+92) {
		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 <= (-4.2d+150)) then
        tmp = x
    else if (z <= (-5.5d-19)) then
        tmp = x * (y / -z)
    else if (z <= 4.9d+92) 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 <= -4.2e+150) {
		tmp = x;
	} else if (z <= -5.5e-19) {
		tmp = x * (y / -z);
	} else if (z <= 4.9e+92) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+150:
		tmp = x
	elif z <= -5.5e-19:
		tmp = x * (y / -z)
	elif z <= 4.9e+92:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+150)
		tmp = x;
	elseif (z <= -5.5e-19)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= 4.9e+92)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+150)
		tmp = x;
	elseif (z <= -5.5e-19)
		tmp = x * (y / -z);
	elseif (z <= 4.9e+92)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+150], x, If[LessEqual[z, -5.5e-19], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+92], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999996e150 or 4.9000000000000002e92 < z

   1. Initial program 66.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.1%

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

   if -4.19999999999999996e150 < z < -5.4999999999999996e-19

   1. Initial program 94.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. associate-/l* 65.4%

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

      3. distribute-rgt-neg-in 65.4%

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

      4. distribute-frac-neg 65.4%

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

      5. neg-sub0 65.4%

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

      6. associate--r- 65.4%

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

      7. neg-sub0 65.4%

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

      8. +-commutative 65.4%

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

      9. sub-neg 65.4%

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

      10. div-sub 65.3%

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

      11. *-inverses 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in y around inf 46.3%

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

      1. associate-*r/ 46.3%

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

      2. mul-1-neg 46.3%

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

      3. distribute-rgt-neg-in 46.3%

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

      4. associate-*r/ 49.2%

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

   10. Simplified 49.2%

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

   if -5.4999999999999996e-19 < z < 4.9000000000000002e92

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 66.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+79} \lor \neg \left(z \leq 4.4 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e+79) (not (<= z 4.4e+92)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+79) || !(z <= 4.4e+92)) {
		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 <= (-1.35d+79)) .or. (.not. (z <= 4.4d+92))) 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 <= -1.35e+79) || !(z <= 4.4e+92)) {
		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 <= -1.35e+79) or not (z <= 4.4e+92):
		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 <= -1.35e+79) || !(z <= 4.4e+92))
		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 <= -1.35e+79) || ~((z <= 4.4e+92)))
		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, -1.35e+79], N[Not[LessEqual[z, 4.4e+92]], $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 < -1.35e79 or 4.39999999999999984e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-/l* 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

      4. distribute-frac-neg 85.3%

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

      5. neg-sub0 85.3%

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

      6. associate--r- 85.3%

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

      7. neg-sub0 85.3%

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

      8. +-commutative 85.3%

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

      9. sub-neg 85.3%

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

      10. div-sub 85.3%

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

      11. *-inverses 85.3%

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

   7. Simplified 85.3%

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

   if -1.35e79 < z < 4.39999999999999984e92

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+79} \lor \neg \left(z \leq 4.4 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 3.1 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e-19) (not (<= z 3.1e-17)))
   (* x (- 1.0 (/ y z)))
   (/ (* x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e-19) || !(z <= 3.1e-17)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = (x * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.3d-19)) .or. (.not. (z <= 3.1d-17))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = (x * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e-19) || !(z <= 3.1e-17)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = (x * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e-19) or not (z <= 3.1e-17):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = (x * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e-19) || !(z <= 3.1e-17))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(x * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e-19) || ~((z <= 3.1e-17)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = (x * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e-19], N[Not[LessEqual[z, 3.1e-17]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-19 or 3.0999999999999998e-17 < z

   1. Initial program 77.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

      4. distribute-frac-neg 75.2%

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

      5. neg-sub0 75.2%

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

      6. associate--r- 75.2%

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

      7. neg-sub0 75.2%

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

      8. +-commutative 75.2%

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

      9. sub-neg 75.2%

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

      10. div-sub 75.1%

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

      11. *-inverses 75.1%

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

   7. Simplified 75.1%

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

   if -2.2999999999999998e-19 < z < 3.0999999999999998e-17

   1. Initial program 96.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 70.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 3.1 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e+79) x (if (<= z 8e+92) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+79) {
		tmp = x;
	} else if (z <= 8e+92) {
		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 <= (-2.6d+79)) then
        tmp = x
    else if (z <= 8d+92) 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 <= -2.6e+79) {
		tmp = x;
	} else if (z <= 8e+92) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+79:
		tmp = x
	elif z <= 8e+92:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e+79)
		tmp = x;
	elseif (z <= 8e+92)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e+79)
		tmp = x;
	elseif (z <= 8e+92)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+79], x, If[LessEqual[z, 8e+92], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000015e79 or 8.0000000000000003e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.1%

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

   if -2.60000000000000015e79 < z < 8.0000000000000003e92

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 62.5%

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

Alternative 10: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+78) x (if (<= z 4.4e+92) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+78) {
		tmp = x;
	} else if (z <= 4.4e+92) {
		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 <= (-9.5d+78)) then
        tmp = x
    else if (z <= 4.4d+92) 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 <= -9.5e+78) {
		tmp = x;
	} else if (z <= 4.4e+92) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+78:
		tmp = x
	elif z <= 4.4e+92:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+78)
		tmp = x;
	elseif (z <= 4.4e+92)
		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 <= -9.5e+78)
		tmp = x;
	elseif (z <= 4.4e+92)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+78], x, If[LessEqual[z, 4.4e+92], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000006e78 or 4.39999999999999984e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.1%

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

   if -9.5000000000000006e78 < z < 4.39999999999999984e92

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.4%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around 0 61.6%

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

Alternative 11: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+78) x (if (<= z 4.9e+92) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+78) {
		tmp = x;
	} else if (z <= 4.9e+92) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.5d+78)) then
        tmp = x
    else if (z <= 4.9d+92) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+78) {
		tmp = x;
	} else if (z <= 4.9e+92) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+78:
		tmp = x
	elif z <= 4.9e+92:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+78)
		tmp = x;
	elseif (z <= 4.9e+92)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+78)
		tmp = x;
	elseif (z <= 4.9e+92)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+78], x, If[LessEqual[z, 4.9e+92], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000006e78 or 4.9000000000000002e92 < z

   1. Initial program 69.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.1%

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

   if -9.5000000000000006e78 < z < 4.9000000000000002e92

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 62.5%

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

      1. associate-/l* 61.3%

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

   7. Simplified 61.3%

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

Alternative 12: 96.8% 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 86.7%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

Alternative 13: 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 86.7%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around inf 31.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 96.8% 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 2024091 
(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)))