Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.5% → 96.5%

Time: 12.7s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = t / ((z - y) / (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. associate-*l/ 86.4%

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

   2. associate-/l* 80.4%

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

3. Simplified 80.4%

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

   1. associate-*r/ 86.4%

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

   2. associate-*l/ 97.9%

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

   3. *-commutative 97.9%

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

   4. clear-num 97.9%

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

   5. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Final simplification 98.2%

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

Alternative 2: 67.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-157} \lor \neg \left(y \leq 7.5 \cdot 10^{-35}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.5e+38)
     t_1
     (if (<= y -1.25e-7)
       (* t (/ y (- z)))
       (if (or (<= y -4.4e-157) (not (<= y 7.5e-35))) t_1 (/ t (/ z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t_1;
	} else if (y <= -1.25e-7) {
		tmp = t * (y / -z);
	} else if ((y <= -4.4e-157) || !(y <= 7.5e-35)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-2.5d+38)) then
        tmp = t_1
    else if (y <= (-1.25d-7)) then
        tmp = t * (y / -z)
    else if ((y <= (-4.4d-157)) .or. (.not. (y <= 7.5d-35))) then
        tmp = t_1
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t_1;
	} else if (y <= -1.25e-7) {
		tmp = t * (y / -z);
	} else if ((y <= -4.4e-157) || !(y <= 7.5e-35)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.5e+38:
		tmp = t_1
	elif y <= -1.25e-7:
		tmp = t * (y / -z)
	elif (y <= -4.4e-157) or not (y <= 7.5e-35):
		tmp = t_1
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.5e+38)
		tmp = t_1;
	elseif (y <= -1.25e-7)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif ((y <= -4.4e-157) || !(y <= 7.5e-35))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.5e+38)
		tmp = t_1;
	elseif (y <= -1.25e-7)
		tmp = t * (y / -z);
	elseif ((y <= -4.4e-157) || ~((y <= 7.5e-35)))
		tmp = t_1;
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+38], t$95$1, If[LessEqual[y, -1.25e-7], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.4e-157], N[Not[LessEqual[y, 7.5e-35]], $MachinePrecision]], t$95$1, N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999985e38 or -1.24999999999999994e-7 < y < -4.4000000000000002e-157 or 7.5e-35 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. div-sub 75.2%

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

      3. sub-neg 75.2%

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

      4. *-inverses 75.2%

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

      5. metadata-eval 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around 0 71.3%

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

      1. *-rgt-identity 71.3%

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

      2. mul-1-neg 71.3%

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

      3. associate-/l* 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. distribute-frac-neg2 75.2%

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

      6. distribute-lft-in 75.2%

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

      7. distribute-frac-neg2 75.2%

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

      8. sub-neg 75.2%

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

   8. Simplified 75.2%

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

   if -2.49999999999999985e38 < y < -1.24999999999999994e-7

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around inf 72.8%

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

   6. Taylor expanded in x around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-/l* 64.3%

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

      3. distribute-rgt-neg-in 64.3%

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

   8. Simplified 64.3%

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

   if -4.4000000000000002e-157 < y < 7.5e-35

   1. Initial program 95.7%

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

      1. associate-*l/ 95.8%

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

      2. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

      1. associate-*r/ 95.8%

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

      2. associate-*l/ 95.7%

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

      3. *-commutative 95.7%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in y around 0 72.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-157} \lor \neg \left(y \leq 7.5 \cdot 10^{-35}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.05e+88)
   t
   (if (<= y -8.5e-7)
     (* y (/ t (- z)))
     (if (<= y -1.4e-188) (/ x (/ z t)) (if (<= y 5.4e-26) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e+88) {
		tmp = t;
	} else if (y <= -8.5e-7) {
		tmp = y * (t / -z);
	} else if (y <= -1.4e-188) {
		tmp = x / (z / t);
	} else if (y <= 5.4e-26) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.05d+88)) then
        tmp = t
    else if (y <= (-8.5d-7)) then
        tmp = y * (t / -z)
    else if (y <= (-1.4d-188)) then
        tmp = x / (z / t)
    else if (y <= 5.4d-26) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e+88) {
		tmp = t;
	} else if (y <= -8.5e-7) {
		tmp = y * (t / -z);
	} else if (y <= -1.4e-188) {
		tmp = x / (z / t);
	} else if (y <= 5.4e-26) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.05e+88:
		tmp = t
	elif y <= -8.5e-7:
		tmp = y * (t / -z)
	elif y <= -1.4e-188:
		tmp = x / (z / t)
	elif y <= 5.4e-26:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.05e+88)
		tmp = t;
	elseif (y <= -8.5e-7)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (y <= -1.4e-188)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 5.4e-26)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.05e+88)
		tmp = t;
	elseif (y <= -8.5e-7)
		tmp = y * (t / -z);
	elseif (y <= -1.4e-188)
		tmp = x / (z / t);
	elseif (y <= 5.4e-26)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.05e+88], t, If[LessEqual[y, -8.5e-7], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-188], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-26], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0499999999999999e88 or 5.39999999999999963e-26 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 69.5%

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

   if -3.0499999999999999e88 < y < -8.50000000000000014e-7

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 59.8%

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

   6. Taylor expanded in x around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-*r/ 59.6%

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

   8. Simplified 59.6%

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

   if -8.50000000000000014e-7 < y < -1.4000000000000001e-188

   1. Initial program 92.7%

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

      1. associate-*l/ 94.1%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/l* 54.4%

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

   7. Simplified 54.4%

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

      1. clear-num 54.3%

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

      2. un-div-inv 54.6%

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

   9. Applied egg-rr 54.6%

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

   if -1.4000000000000001e-188 < y < 5.39999999999999963e-26

   1. Initial program 97.4%

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

      1. associate-*l/ 95.3%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 97.4%

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

      3. *-commutative 97.4%

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

      4. clear-num 97.4%

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

      5. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around 0 71.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+72)
   t
   (if (<= y -8e-6)
     (/ y (/ z (- t)))
     (if (<= y -7e-190) (/ x (/ z t)) (if (<= y 1.85e-28) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+72) {
		tmp = t;
	} else if (y <= -8e-6) {
		tmp = y / (z / -t);
	} else if (y <= -7e-190) {
		tmp = x / (z / t);
	} else if (y <= 1.85e-28) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.5d+72)) then
        tmp = t
    else if (y <= (-8d-6)) then
        tmp = y / (z / -t)
    else if (y <= (-7d-190)) then
        tmp = x / (z / t)
    else if (y <= 1.85d-28) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+72) {
		tmp = t;
	} else if (y <= -8e-6) {
		tmp = y / (z / -t);
	} else if (y <= -7e-190) {
		tmp = x / (z / t);
	} else if (y <= 1.85e-28) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+72:
		tmp = t
	elif y <= -8e-6:
		tmp = y / (z / -t)
	elif y <= -7e-190:
		tmp = x / (z / t)
	elif y <= 1.85e-28:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+72)
		tmp = t;
	elseif (y <= -8e-6)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif (y <= -7e-190)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 1.85e-28)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+72)
		tmp = t;
	elseif (y <= -8e-6)
		tmp = y / (z / -t);
	elseif (y <= -7e-190)
		tmp = x / (z / t);
	elseif (y <= 1.85e-28)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+72], t, If[LessEqual[y, -8e-6], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-190], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-28], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.50000000000000001e72 or 1.8500000000000001e-28 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 69.5%

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

   if -1.50000000000000001e72 < y < -7.99999999999999964e-6

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 71.2%

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

   6. Taylor expanded in x around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-rgt-neg-out 59.8%

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

   8. Simplified 59.8%

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

      1. associate-/l* 59.6%

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

      2. add-sqr-sqrt 59.5%

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

      3. sqrt-unprod 59.6%

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

      4. sqr-neg 59.6%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 26.2%

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

   10. Applied egg-rr 26.2%

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

       1. *-commutative 26.2%

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

       2. associate-*l/ 26.3%

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

       3. associate-*r/ 26.3%

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

   12. Simplified 26.3%

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

       1. add-sqr-sqrt 25.0%

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

       2. sqrt-unprod 37.2%

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

       3. sqr-neg 37.2%

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

       4. sqrt-unprod 36.0%

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

       5. add-sqr-sqrt 59.6%

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

       6. distribute-rgt-neg-out 59.6%

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

       7. clear-num 59.7%

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

       8. un-div-inv 59.7%

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

   14. Applied egg-rr 59.7%

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

   if -7.99999999999999964e-6 < y < -6.9999999999999999e-190

   1. Initial program 92.7%

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

      1. associate-*l/ 94.1%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/l* 54.4%

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

   7. Simplified 54.4%

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

      1. clear-num 54.3%

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

      2. un-div-inv 54.6%

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

   9. Applied egg-rr 54.6%

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

   if -6.9999999999999999e-190 < y < 1.8500000000000001e-28

   1. Initial program 97.4%

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

      1. associate-*l/ 95.3%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 97.4%

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

      3. *-commutative 97.4%

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

      4. clear-num 97.4%

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

      5. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around 0 71.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0036:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+73)
   t
   (if (<= y -0.0036)
     (/ (* t (- y)) z)
     (if (<= y -2.4e-193) (/ x (/ z t)) (if (<= y 5.9e-25) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+73) {
		tmp = t;
	} else if (y <= -0.0036) {
		tmp = (t * -y) / z;
	} else if (y <= -2.4e-193) {
		tmp = x / (z / t);
	} else if (y <= 5.9e-25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d+73)) then
        tmp = t
    else if (y <= (-0.0036d0)) then
        tmp = (t * -y) / z
    else if (y <= (-2.4d-193)) then
        tmp = x / (z / t)
    else if (y <= 5.9d-25) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+73) {
		tmp = t;
	} else if (y <= -0.0036) {
		tmp = (t * -y) / z;
	} else if (y <= -2.4e-193) {
		tmp = x / (z / t);
	} else if (y <= 5.9e-25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+73:
		tmp = t
	elif y <= -0.0036:
		tmp = (t * -y) / z
	elif y <= -2.4e-193:
		tmp = x / (z / t)
	elif y <= 5.9e-25:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+73)
		tmp = t;
	elseif (y <= -0.0036)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= -2.4e-193)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 5.9e-25)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+73)
		tmp = t;
	elseif (y <= -0.0036)
		tmp = (t * -y) / z;
	elseif (y <= -2.4e-193)
		tmp = x / (z / t);
	elseif (y <= 5.9e-25)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+73], t, If[LessEqual[y, -0.0036], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.4e-193], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-25], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.80000000000000008e73 or 5.8999999999999998e-25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 69.5%

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

   if -2.80000000000000008e73 < y < -0.0035999999999999999

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 71.2%

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

   6. Taylor expanded in x around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-rgt-neg-out 59.8%

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

   8. Simplified 59.8%

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

   if -0.0035999999999999999 < y < -2.4e-193

   1. Initial program 92.7%

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

      1. associate-*l/ 94.1%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/l* 54.4%

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

   7. Simplified 54.4%

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

      1. clear-num 54.3%

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

      2. un-div-inv 54.6%

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

   9. Applied egg-rr 54.6%

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

   if -2.4e-193 < y < 5.8999999999999998e-25

   1. Initial program 97.4%

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

      1. associate-*l/ 95.3%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 97.4%

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

      3. *-commutative 97.4%

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

      4. clear-num 97.4%

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

      5. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around 0 71.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0036:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -3.7e+77)
     t_1
     (if (<= y 1.75e-151)
       (* t (/ x (- z y)))
       (if (<= y 7.2e-34) (* t (/ (- x y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.7e+77) {
		tmp = t_1;
	} else if (y <= 1.75e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 7.2e-34) {
		tmp = t * ((x - y) / z);
	} 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 = t * (1.0d0 - (x / y))
    if (y <= (-3.7d+77)) then
        tmp = t_1
    else if (y <= 1.75d-151) then
        tmp = t * (x / (z - y))
    else if (y <= 7.2d-34) then
        tmp = t * ((x - y) / z)
    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 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.7e+77) {
		tmp = t_1;
	} else if (y <= 1.75e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 7.2e-34) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -3.7e+77:
		tmp = t_1
	elif y <= 1.75e-151:
		tmp = t * (x / (z - y))
	elif y <= 7.2e-34:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.7e+77)
		tmp = t_1;
	elseif (y <= 1.75e-151)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 7.2e-34)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.7e+77)
		tmp = t_1;
	elseif (y <= 1.75e-151)
		tmp = t * (x / (z - y));
	elseif (y <= 7.2e-34)
		tmp = t * ((x - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+77], t$95$1, If[LessEqual[y, 1.75e-151], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-34], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.69999999999999995e77 or 7.20000000000000016e-34 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. div-sub 82.6%

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

      3. sub-neg 82.6%

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

      4. *-inverses 82.6%

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

      5. metadata-eval 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in x around 0 76.7%

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

      1. *-rgt-identity 76.7%

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

      2. mul-1-neg 76.7%

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

      3. associate-/l* 82.6%

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

      4. distribute-rgt-neg-in 82.6%

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

      5. distribute-frac-neg2 82.6%

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

      6. distribute-lft-in 82.6%

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

      7. distribute-frac-neg2 82.6%

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

      8. sub-neg 82.6%

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

   8. Simplified 82.6%

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

   if -3.69999999999999995e77 < y < 1.74999999999999998e-151

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 82.0%

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

   if 1.74999999999999998e-151 < y < 7.20000000000000016e-34

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 73.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e+35)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.45e-151)
     (* t (/ x (- z y)))
     (if (<= y 6.5e-40) (* t (/ (- x y) z)) (* t (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+35) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.45e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.5e-40) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (1.0 - (x / 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 (y <= (-4.8d+35)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.45d-151) then
        tmp = t * (x / (z - y))
    else if (y <= 6.5d-40) then
        tmp = t * ((x - y) / z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+35) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.45e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.5e-40) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e+35:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.45e-151:
		tmp = t * (x / (z - y))
	elif y <= 6.5e-40:
		tmp = t * ((x - y) / z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e+35)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.45e-151)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 6.5e-40)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e+35)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.45e-151)
		tmp = t * (x / (z - y));
	elseif (y <= 6.5e-40)
		tmp = t * ((x - y) / z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e+35], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-151], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-40], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000029e35

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 69.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. div-sub 88.0%

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

      3. sub-neg 88.0%

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

      4. *-inverses 88.0%

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

      5. metadata-eval 88.0%

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

   9. Simplified 88.0%

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

   10. Taylor expanded in t around 0 88.0%

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

   if -4.80000000000000029e35 < y < 1.45000000000000006e-151

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 84.8%

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

   if 1.45000000000000006e-151 < y < 6.4999999999999999e-40

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 73.8%

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

   if 6.4999999999999999e-40 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. div-sub 77.8%

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

      3. sub-neg 77.8%

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

      4. *-inverses 77.8%

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

      5. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 69.6%

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

      1. *-rgt-identity 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate-/l* 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. distribute-frac-neg2 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. distribute-frac-neg2 77.8%

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

      8. sub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+37)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.95e-151)
     (* t (/ x (- z y)))
     (if (<= y 6.2e-53) (/ t (/ z (- x y))) (* t (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+37) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.95e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.2e-53) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (x / 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 (y <= (-1.65d+37)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.95d-151) then
        tmp = t * (x / (z - y))
    else if (y <= 6.2d-53) then
        tmp = t / (z / (x - y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+37) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.95e-151) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.2e-53) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+37:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.95e-151:
		tmp = t * (x / (z - y))
	elif y <= 6.2e-53:
		tmp = t / (z / (x - y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+37)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.95e-151)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 6.2e-53)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+37)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.95e-151)
		tmp = t * (x / (z - y));
	elseif (y <= 6.2e-53)
		tmp = t / (z / (x - y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+37], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-151], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-53], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65e37

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 69.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. div-sub 88.0%

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

      3. sub-neg 88.0%

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

      4. *-inverses 88.0%

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

      5. metadata-eval 88.0%

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

   9. Simplified 88.0%

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

   10. Taylor expanded in t around 0 88.0%

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

   if -1.65e37 < y < 1.95000000000000003e-151

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 84.8%

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

   if 1.95000000000000003e-151 < y < 6.20000000000000031e-53

   1. Initial program 95.5%

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

      1. associate-*l/ 91.4%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

      1. associate-*r/ 91.4%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in z around inf 73.8%

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

   if 6.20000000000000031e-53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. div-sub 77.8%

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

      3. sub-neg 77.8%

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

      4. *-inverses 77.8%

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

      5. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 69.6%

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

      1. *-rgt-identity 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate-/l* 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. distribute-frac-neg2 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. distribute-frac-neg2 77.8%

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

      8. sub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-152}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e+35)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 7.6e-152)
     (/ (* t x) (- z y))
     (if (<= y 1.55e-34) (/ t (/ z (- x y))) (* t (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+35) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 7.6e-152) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.55e-34) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (x / 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 (y <= (-4.8d+35)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 7.6d-152) then
        tmp = (t * x) / (z - y)
    else if (y <= 1.55d-34) then
        tmp = t / (z / (x - y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+35) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 7.6e-152) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.55e-34) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e+35:
		tmp = t / (1.0 - (z / y))
	elif y <= 7.6e-152:
		tmp = (t * x) / (z - y)
	elif y <= 1.55e-34:
		tmp = t / (z / (x - y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e+35)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 7.6e-152)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 1.55e-34)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e+35)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 7.6e-152)
		tmp = (t * x) / (z - y);
	elseif (y <= 1.55e-34)
		tmp = t / (z / (x - y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e+35], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-152], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-34], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000029e35

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 69.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. div-sub 88.0%

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

      3. sub-neg 88.0%

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

      4. *-inverses 88.0%

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

      5. metadata-eval 88.0%

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

   9. Simplified 88.0%

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

   10. Taylor expanded in t around 0 88.0%

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

   if -4.80000000000000029e35 < y < 7.60000000000000024e-152

   1. Initial program 96.2%

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

      1. associate-*l/ 95.9%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 85.7%

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

   if 7.60000000000000024e-152 < y < 1.5499999999999999e-34

   1. Initial program 95.5%

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

      1. associate-*l/ 91.4%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

      1. associate-*r/ 91.4%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in z around inf 73.8%

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

   if 1.5499999999999999e-34 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. div-sub 77.8%

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

      3. sub-neg 77.8%

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

      4. *-inverses 77.8%

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

      5. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 69.6%

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

      1. *-rgt-identity 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate-/l* 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. distribute-frac-neg2 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. distribute-frac-neg2 77.8%

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

      8. sub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-152}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+36)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.9e-151)
     (/ (* t x) (- z y))
     (if (<= y 6e-37) (/ (* t (- x y)) z) (* t (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+36) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.9e-151) {
		tmp = (t * x) / (z - y);
	} else if (y <= 6e-37) {
		tmp = (t * (x - y)) / z;
	} else {
		tmp = t * (1.0 - (x / 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 (y <= (-8d+36)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.9d-151) then
        tmp = (t * x) / (z - y)
    else if (y <= 6d-37) then
        tmp = (t * (x - y)) / z
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+36) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.9e-151) {
		tmp = (t * x) / (z - y);
	} else if (y <= 6e-37) {
		tmp = (t * (x - y)) / z;
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+36:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.9e-151:
		tmp = (t * x) / (z - y)
	elif y <= 6e-37:
		tmp = (t * (x - y)) / z
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+36)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.9e-151)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 6e-37)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+36)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.9e-151)
		tmp = (t * x) / (z - y);
	elseif (y <= 6e-37)
		tmp = (t * (x - y)) / z;
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+36], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-151], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-37], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.00000000000000034e36

   1. Initial program 99.8%

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

      1. associate-*l/ 69.1%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

      1. associate-*r/ 69.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. div-sub 88.0%

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

      3. sub-neg 88.0%

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

      4. *-inverses 88.0%

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

      5. metadata-eval 88.0%

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

   9. Simplified 88.0%

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

   10. Taylor expanded in t around 0 88.0%

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

   if -8.00000000000000034e36 < y < 1.89999999999999985e-151

   1. Initial program 96.2%

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

      1. associate-*l/ 95.9%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 85.7%

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

   if 1.89999999999999985e-151 < y < 6e-37

   1. Initial program 95.5%

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

      1. associate-*l/ 91.4%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around inf 74.0%

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

   if 6e-37 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. div-sub 77.8%

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

      3. sub-neg 77.8%

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

      4. *-inverses 77.8%

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

      5. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 69.6%

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

      1. *-rgt-identity 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate-/l* 77.8%

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

      4. distribute-rgt-neg-in 77.8%

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

      5. distribute-frac-neg2 77.8%

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

      6. distribute-lft-in 77.8%

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

      7. distribute-frac-neg2 77.8%

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

      8. sub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+197}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+130)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 2.2e+197) (* (- x y) (/ t (- z y))) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+130) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 2.2e+197) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (1.0 - (x / 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 (y <= (-5.8d+130)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 2.2d+197) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+130) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 2.2e+197) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+130:
		tmp = t / (1.0 - (z / y))
	elif y <= 2.2e+197:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+130)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 2.2e+197)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+130)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 2.2e+197)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+130], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+197], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999998e130

   1. Initial program 99.9%

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

      1. associate-*l/ 57.7%

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

      2. associate-/l* 57.3%

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

   3. Simplified 57.3%

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

      1. associate-*r/ 57.7%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 93.2%

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

      1. mul-1-neg 93.2%

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

      2. div-sub 93.2%

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

      3. sub-neg 93.2%

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

      4. *-inverses 93.2%

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

      5. metadata-eval 93.2%

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

   9. Simplified 93.2%

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

   10. Taylor expanded in t around 0 93.2%

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

   if -5.7999999999999998e130 < y < 2.19999999999999989e197

   1. Initial program 97.2%

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

      1. associate-*l/ 94.6%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   if 2.19999999999999989e197 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 79.6%

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

      1. *-rgt-identity 79.6%

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

      2. mul-1-neg 79.6%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-frac-neg2 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. sub-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+197}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+79} \lor \neg \left(z \leq 9.4 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e+79) (not (<= z 9.4e-23)))
   (* (- x y) (/ t z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e+79) || !(z <= 9.4e-23)) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t * (1.0 - (x / 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 <= (-1.95d+79)) .or. (.not. (z <= 9.4d-23))) then
        tmp = (x - y) * (t / z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e+79) || !(z <= 9.4e-23)) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e+79) or not (z <= 9.4e-23):
		tmp = (x - y) * (t / z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e+79) || !(z <= 9.4e-23))
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e+79) || ~((z <= 9.4e-23)))
		tmp = (x - y) * (t / z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e+79], N[Not[LessEqual[z, 9.4e-23]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e79 or 9.4000000000000001e-23 < z

   1. Initial program 97.9%

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

      1. associate-*l/ 86.7%

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

      2. associate-/l* 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in z around inf 68.4%

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

   if -1.9499999999999999e79 < z < 9.4000000000000001e-23

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. div-sub 78.4%

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

      3. sub-neg 78.4%

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

      4. *-inverses 78.4%

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

      5. metadata-eval 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around 0 76.4%

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

      1. *-rgt-identity 76.4%

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

      2. mul-1-neg 76.4%

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

      3. associate-/l* 78.4%

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

      4. distribute-rgt-neg-in 78.4%

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

      5. distribute-frac-neg2 78.4%

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

      6. distribute-lft-in 78.4%

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

      7. distribute-frac-neg2 78.4%

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

      8. sub-neg 78.4%

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

   8. Simplified 78.4%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+79} \lor \neg \left(z \leq 9.4 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+77} \lor \neg \left(y \leq 9.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.7e+77) (not (<= y 9.5e-46)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.7e+77) || !(y <= 9.5e-46)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (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 ((y <= (-3.7d+77)) .or. (.not. (y <= 9.5d-46))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.7e+77) || !(y <= 9.5e-46)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.7e+77) or not (y <= 9.5e-46):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.7e+77) || !(y <= 9.5e-46))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.7e+77) || ~((y <= 9.5e-46)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.7e+77], N[Not[LessEqual[y, 9.5e-46]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999995e77 or 9.49999999999999993e-46 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. div-sub 82.6%

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

      3. sub-neg 82.6%

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

      4. *-inverses 82.6%

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

      5. metadata-eval 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in x around 0 76.7%

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

      1. *-rgt-identity 76.7%

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

      2. mul-1-neg 76.7%

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

      3. associate-/l* 82.6%

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

      4. distribute-rgt-neg-in 82.6%

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

      5. distribute-frac-neg2 82.6%

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

      6. distribute-lft-in 82.6%

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

      7. distribute-frac-neg2 82.6%

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

      8. sub-neg 82.6%

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

   8. Simplified 82.6%

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

   if -3.69999999999999995e77 < y < 9.49999999999999993e-46

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 77.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+77} \lor \neg \left(y \leq 9.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+50) t (if (<= y 4.9e-29) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+50) {
		tmp = t;
	} else if (y <= 4.9e-29) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d+50)) then
        tmp = t
    else if (y <= 4.9d-29) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+50) {
		tmp = t;
	} else if (y <= 4.9e-29) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+50:
		tmp = t
	elif y <= 4.9e-29:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+50)
		tmp = t;
	elseif (y <= 4.9e-29)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e+50)
		tmp = t;
	elseif (y <= 4.9e-29)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+50], t, If[LessEqual[y, 4.9e-29], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000008e50 or 4.8999999999999998e-29 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.3%

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

      2. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -1.10000000000000008e50 < y < 4.8999999999999998e-29

   1. Initial program 96.2%

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

      1. associate-*l/ 95.3%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+72) t (if (<= y 3.6e-25) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+72) {
		tmp = t;
	} else if (y <= 3.6e-25) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+72)) then
        tmp = t
    else if (y <= 3.6d-25) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+72) {
		tmp = t;
	} else if (y <= 3.6e-25) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+72:
		tmp = t
	elif y <= 3.6e-25:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+72)
		tmp = t;
	elseif (y <= 3.6e-25)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+72)
		tmp = t;
	elseif (y <= 3.6e-25)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+72], t, If[LessEqual[y, 3.6e-25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999998e72 or 3.5999999999999999e-25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 69.5%

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

   if -1.24999999999999998e72 < y < 3.5999999999999999e-25

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 61.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+72) t (if (<= y 8.5e-25) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+72) {
		tmp = t;
	} else if (y <= 8.5e-25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+72)) then
        tmp = t
    else if (y <= 8.5d-25) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+72) {
		tmp = t;
	} else if (y <= 8.5e-25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+72:
		tmp = t
	elif y <= 8.5e-25:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+72)
		tmp = t;
	elseif (y <= 8.5e-25)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+72)
		tmp = t;
	elseif (y <= 8.5e-25)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+72], t, If[LessEqual[y, 8.5e-25], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999998e72 or 8.49999999999999981e-25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.3%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 69.5%

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

   if -1.24999999999999998e72 < y < 8.49999999999999981e-25

   1. Initial program 96.4%

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

      1. associate-*l/ 95.5%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 95.5%

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

      2. associate-*l/ 96.4%

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

      3. *-commutative 96.4%

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

      4. clear-num 96.3%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in y around 0 61.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = t * ((x - y) / (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Final simplification 97.9%

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

Alternative 18: 34.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. associate-*l/ 86.4%

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

   2. associate-/l* 80.4%

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

3. Simplified 80.4%

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

5. Taylor expanded in y around inf 37.1%

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

6. Final simplification 37.1%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = t / ((z - y) / (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024043 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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