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

Percentage Accurate: 97.2% → 97.2%

Time: 11.3s

Alternatives: 13

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: 97.2% 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: 97.2% 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]

Derivation

1. Initial program 97.0%

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

Alternative 2: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+206)
   (* t (- 1.0 (/ x y)))
   (if (<= y -3e+32)
     (* t (/ y (- y z)))
     (if (<= y 1.5e-251)
       (/ (- x y) (/ z t))
       (if (<= y 4.5e+46) (* t (/ x (- z y))) (/ t (/ (- y z) y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+206) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -3e+32) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e-251) {
		tmp = (x - y) / (z / t);
	} else if (y <= 4.5e+46) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / ((y - 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 <= (-1d+206)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-3d+32)) then
        tmp = t * (y / (y - z))
    else if (y <= 1.5d-251) then
        tmp = (x - y) / (z / t)
    else if (y <= 4.5d+46) then
        tmp = t * (x / (z - y))
    else
        tmp = t / ((y - 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 <= -1e+206) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -3e+32) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e-251) {
		tmp = (x - y) / (z / t);
	} else if (y <= 4.5e+46) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e+206:
		tmp = t * (1.0 - (x / y))
	elif y <= -3e+32:
		tmp = t * (y / (y - z))
	elif y <= 1.5e-251:
		tmp = (x - y) / (z / t)
	elif y <= 4.5e+46:
		tmp = t * (x / (z - y))
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+206)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -3e+32)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1.5e-251)
		tmp = Float64(Float64(x - y) / Float64(z / t));
	elseif (y <= 4.5e+46)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e+206)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -3e+32)
		tmp = t * (y / (y - z));
	elseif (y <= 1.5e-251)
		tmp = (x - y) / (z / t);
	elseif (y <= 4.5e+46)
		tmp = t * (x / (z - y));
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e+206], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+32], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-251], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+46], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1e206

   1. Initial program 99.8%

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

      1. associate-*l/ 57.8%

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

      2. associate-/l* 49.8%

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

   3. Simplified 49.8%

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

      1. clear-num 47.5%

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

      2. un-div-inv 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 57.8%

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

      4. *-commutative 57.8%

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

      5. neg-mul-1 57.8%

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

      6. neg-sub0 57.8%

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

      7. associate--r- 57.8%

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

      8. neg-sub0 57.8%

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

      9. +-commutative 57.8%

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

      10. sub-neg 57.8%

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

      11. associate-/l* 99.8%

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

      12. div-sub 99.9%

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

      13. *-inverses 99.9%

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

   9. Simplified 99.9%

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

   if -1e206 < y < -3e32

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. neg-mul-1 76.7%

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

      2. distribute-neg-frac2 76.7%

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

      3. neg-sub0 76.7%

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

      4. sub-neg 76.7%

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

      5. +-commutative 76.7%

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

      6. associate--r+ 76.7%

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

      7. neg-sub0 76.7%

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

      8. remove-double-neg 76.7%

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

   5. Simplified 76.7%

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

   if -3e32 < y < 1.4999999999999999e-251

   1. Initial program 92.3%

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

      1. associate-*l/ 90.2%

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

      2. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

   if 1.4999999999999999e-251 < y < 4.5000000000000001e46

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 77.0%

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

   if 4.5000000000000001e46 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.3%

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

      2. associate-/l* 78.0%

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

   3. Simplified 78.0%

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

      1. associate-*r/ 70.3%

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

      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 99.8%

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

      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 78.8%

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

      1. neg-mul-1 78.8%

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

   9. Simplified 78.8%

      \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{-y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-251}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-254}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -3.2e+207)
     (* t (- 1.0 (/ x y)))
     (if (<= y -2.2e+31)
       t_1
       (if (<= y 2.7e-254)
         (/ (- x y) (/ z t))
         (if (<= y 1.4e+44) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -3.2e+207) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.2e+31) {
		tmp = t_1;
	} else if (y <= 2.7e-254) {
		tmp = (x - y) / (z / t);
	} else if (y <= 1.4e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-3.2d+207)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-2.2d+31)) then
        tmp = t_1
    else if (y <= 2.7d-254) then
        tmp = (x - y) / (z / t)
    else if (y <= 1.4d+44) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -3.2e+207) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.2e+31) {
		tmp = t_1;
	} else if (y <= 2.7e-254) {
		tmp = (x - y) / (z / t);
	} else if (y <= 1.4e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -3.2e+207:
		tmp = t * (1.0 - (x / y))
	elif y <= -2.2e+31:
		tmp = t_1
	elif y <= 2.7e-254:
		tmp = (x - y) / (z / t)
	elif y <= 1.4e+44:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -3.2e+207)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -2.2e+31)
		tmp = t_1;
	elseif (y <= 2.7e-254)
		tmp = Float64(Float64(x - y) / Float64(z / t));
	elseif (y <= 1.4e+44)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -3.2e+207)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -2.2e+31)
		tmp = t_1;
	elseif (y <= 2.7e-254)
		tmp = (x - y) / (z / t);
	elseif (y <= 1.4e+44)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+207], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e+31], t$95$1, If[LessEqual[y, 2.7e-254], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+44], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.2000000000000001e207

   1. Initial program 99.8%

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

      1. associate-*l/ 57.8%

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

      2. associate-/l* 49.8%

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

   3. Simplified 49.8%

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

      1. clear-num 47.5%

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

      2. un-div-inv 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 57.8%

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

      4. *-commutative 57.8%

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

      5. neg-mul-1 57.8%

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

      6. neg-sub0 57.8%

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

      7. associate--r- 57.8%

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

      8. neg-sub0 57.8%

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

      9. +-commutative 57.8%

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

      10. sub-neg 57.8%

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

      11. associate-/l* 99.8%

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

      12. div-sub 99.9%

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

      13. *-inverses 99.9%

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

   9. Simplified 99.9%

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

   if -3.2000000000000001e207 < y < -2.2000000000000001e31 or 1.4e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

      3. neg-sub0 77.9%

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

      4. sub-neg 77.9%

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

      5. +-commutative 77.9%

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

      6. associate--r+ 77.9%

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

      7. neg-sub0 77.9%

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

      8. remove-double-neg 77.9%

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

   5. Simplified 77.9%

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

   if -2.2000000000000001e31 < y < 2.70000000000000007e-254

   1. Initial program 92.3%

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

      1. associate-*l/ 90.2%

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

      2. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

   if 2.70000000000000007e-254 < y < 1.4e44

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 77.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-254}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-253}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -5.8e+207)
     (* t (- 1.0 (/ x y)))
     (if (<= y -2.2e+31)
       t_1
       (if (<= y 8.5e-253)
         (* (- x y) (/ t z))
         (if (<= y 9.5e+45) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -5.8e+207) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.2e+31) {
		tmp = t_1;
	} else if (y <= 8.5e-253) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.5e+45) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-5.8d+207)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-2.2d+31)) then
        tmp = t_1
    else if (y <= 8.5d-253) then
        tmp = (x - y) * (t / z)
    else if (y <= 9.5d+45) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -5.8e+207) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.2e+31) {
		tmp = t_1;
	} else if (y <= 8.5e-253) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.5e+45) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -5.8e+207:
		tmp = t * (1.0 - (x / y))
	elif y <= -2.2e+31:
		tmp = t_1
	elif y <= 8.5e-253:
		tmp = (x - y) * (t / z)
	elif y <= 9.5e+45:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -5.8e+207)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -2.2e+31)
		tmp = t_1;
	elseif (y <= 8.5e-253)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 9.5e+45)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -5.8e+207)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -2.2e+31)
		tmp = t_1;
	elseif (y <= 8.5e-253)
		tmp = (x - y) * (t / z);
	elseif (y <= 9.5e+45)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+207], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e+31], t$95$1, If[LessEqual[y, 8.5e-253], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+45], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999994e207

   1. Initial program 99.8%

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

      1. associate-*l/ 57.8%

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

      2. associate-/l* 49.8%

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

   3. Simplified 49.8%

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

      1. clear-num 47.5%

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

      2. un-div-inv 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 57.8%

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

      4. *-commutative 57.8%

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

      5. neg-mul-1 57.8%

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

      6. neg-sub0 57.8%

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

      7. associate--r- 57.8%

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

      8. neg-sub0 57.8%

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

      9. +-commutative 57.8%

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

      10. sub-neg 57.8%

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

      11. associate-/l* 99.8%

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

      12. div-sub 99.9%

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

      13. *-inverses 99.9%

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

   9. Simplified 99.9%

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

   if -5.79999999999999994e207 < y < -2.2000000000000001e31 or 9.4999999999999998e45 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac2 77.9%

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

      3. neg-sub0 77.9%

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

      4. sub-neg 77.9%

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

      5. +-commutative 77.9%

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

      6. associate--r+ 77.9%

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

      7. neg-sub0 77.9%

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

      8. remove-double-neg 77.9%

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

   5. Simplified 77.9%

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

   if -2.2000000000000001e31 < y < 8.4999999999999999e-253

   1. Initial program 92.3%

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

      1. associate-*l/ 90.2%

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

      2. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around inf 82.4%

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

   if 8.4999999999999999e-253 < y < 9.4999999999999998e45

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 77.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-253}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-254}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 0.0035:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -7e+44)
     t_1
     (if (<= y 1.65e-254)
       (* (- x y) (/ t z))
       (if (<= y 0.0035) (* t (/ x (- z y))) 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 <= -7e+44) {
		tmp = t_1;
	} else if (y <= 1.65e-254) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.0035) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-7d+44)) then
        tmp = t_1
    else if (y <= 1.65d-254) then
        tmp = (x - y) * (t / z)
    else if (y <= 0.0035d0) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -7e+44) {
		tmp = t_1;
	} else if (y <= 1.65e-254) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.0035) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -7e+44:
		tmp = t_1
	elif y <= 1.65e-254:
		tmp = (x - y) * (t / z)
	elif y <= 0.0035:
		tmp = t * (x / (z - y))
	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 <= -7e+44)
		tmp = t_1;
	elseif (y <= 1.65e-254)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 0.0035)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	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 <= -7e+44)
		tmp = t_1;
	elseif (y <= 1.65e-254)
		tmp = (x - y) * (t / z);
	elseif (y <= 0.0035)
		tmp = t * (x / (z - y));
	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, -7e+44], t$95$1, If[LessEqual[y, 1.65e-254], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0035], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999998e44 or 0.00350000000000000007 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.4%

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

      2. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

      1. clear-num 72.7%

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

      2. un-div-inv 72.9%

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

   6. Applied egg-rr 72.9%

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

   7. Taylor expanded in z around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. *-commutative 56.4%

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

      3. associate-*l* 56.4%

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

      4. *-commutative 56.4%

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

      5. neg-mul-1 56.4%

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

      6. neg-sub0 56.4%

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

      7. associate--r- 56.4%

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

      8. neg-sub0 56.4%

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

      9. +-commutative 56.4%

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

      10. sub-neg 56.4%

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

      11. associate-/l* 75.4%

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

      12. div-sub 75.4%

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

      13. *-inverses 75.4%

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

   9. Simplified 75.4%

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

   if -6.9999999999999998e44 < y < 1.65000000000000008e-254

   1. Initial program 92.6%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 81.0%

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

   if 1.65000000000000008e-254 < y < 0.00350000000000000007

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 79.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-254}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 0.0035:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-283}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 0.00105:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.8e+44)
     t_1
     (if (<= y -2e-283)
       (* (- x y) (/ t z))
       (if (<= y 0.00105) (* x (/ t (- z y))) 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 <= -4.8e+44) {
		tmp = t_1;
	} else if (y <= -2e-283) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.00105) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-4.8d+44)) then
        tmp = t_1
    else if (y <= (-2d-283)) then
        tmp = (x - y) * (t / z)
    else if (y <= 0.00105d0) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+44) {
		tmp = t_1;
	} else if (y <= -2e-283) {
		tmp = (x - y) * (t / z);
	} else if (y <= 0.00105) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.8e+44:
		tmp = t_1
	elif y <= -2e-283:
		tmp = (x - y) * (t / z)
	elif y <= 0.00105:
		tmp = x * (t / (z - y))
	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 <= -4.8e+44)
		tmp = t_1;
	elseif (y <= -2e-283)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 0.00105)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	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 <= -4.8e+44)
		tmp = t_1;
	elseif (y <= -2e-283)
		tmp = (x - y) * (t / z);
	elseif (y <= 0.00105)
		tmp = x * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+44], t$95$1, If[LessEqual[y, -2e-283], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00105], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000026e44 or 0.00104999999999999994 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.4%

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

      2. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

      1. clear-num 72.7%

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

      2. un-div-inv 72.9%

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

   6. Applied egg-rr 72.9%

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

   7. Taylor expanded in z around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. *-commutative 56.4%

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

      3. associate-*l* 56.4%

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

      4. *-commutative 56.4%

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

      5. neg-mul-1 56.4%

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

      6. neg-sub0 56.4%

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

      7. associate--r- 56.4%

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

      8. neg-sub0 56.4%

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

      9. +-commutative 56.4%

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

      10. sub-neg 56.4%

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

      11. associate-/l* 75.4%

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

      12. div-sub 75.4%

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

      13. *-inverses 75.4%

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

   9. Simplified 75.4%

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

   if -4.80000000000000026e44 < y < -1.99999999999999989e-283

   1. Initial program 92.8%

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

      1. associate-*l/ 92.6%

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

      2. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 77.9%

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

   if -1.99999999999999989e-283 < y < 0.00104999999999999994

   1. Initial program 96.1%

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

      1. associate-*l/ 89.3%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 80.4%

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

Alternative 7: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+147}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+169)
   (* t (- 1.0 (/ x y)))
   (if (<= y 8.8e+147) (* (- x y) (/ t (- z y))) (/ t (/ (- y z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+169) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 8.8e+147) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((y - 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 <= (-9d+169)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 8.8d+147) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / ((y - 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 <= -9e+169) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 8.8e+147) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+169:
		tmp = t * (1.0 - (x / y))
	elif y <= 8.8e+147:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+169)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 8.8e+147)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e+169)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 8.8e+147)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+169], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+147], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e169

   1. Initial program 99.9%

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

      1. associate-*l/ 67.6%

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

      2. associate-/l* 51.6%

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

   3. Simplified 51.6%

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

      1. clear-num 49.9%

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

      2. un-div-inv 50.1%

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

   6. Applied egg-rr 50.1%

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

   7. Taylor expanded in z around 0 56.3%

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

      1. associate-*r/ 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*l* 56.3%

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

      4. *-commutative 56.3%

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

      5. neg-mul-1 56.3%

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

      6. neg-sub0 56.3%

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

      7. associate--r- 56.3%

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

      8. neg-sub0 56.3%

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

      9. +-commutative 56.3%

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

      10. sub-neg 56.3%

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

      11. associate-/l* 88.5%

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

      12. div-sub 88.6%

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

      13. *-inverses 88.6%

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

   9. Simplified 88.6%

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

   if -8.9999999999999999e169 < y < 8.8000000000000007e147

   1. Initial program 96.1%

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

      1. associate-*l/ 87.5%

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

      2. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   if 8.8000000000000007e147 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 65.9%

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

      2. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

      1. associate-*r/ 65.9%

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

      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 97.2%

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

      1. neg-mul-1 97.2%

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

   9. Simplified 97.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+147}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+31} \lor \neg \left(y \leq 0.0039\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e+31) (not (<= y 0.0039)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+31) || !(y <= 0.0039)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d+31)) .or. (.not. (y <= 0.0039d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+31) || !(y <= 0.0039)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e+31) or not (y <= 0.0039):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e+31) || !(y <= 0.0039))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e+31) || ~((y <= 0.0039)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e+31], N[Not[LessEqual[y, 0.0039]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000004e31 or 0.0038999999999999998 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.2%

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

      2. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

      1. clear-num 73.6%

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

      2. un-div-inv 73.8%

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

   6. Applied egg-rr 73.8%

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

   7. Taylor expanded in z around 0 56.2%

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

      1. associate-*r/ 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*l* 56.2%

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

      4. *-commutative 56.2%

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

      5. neg-mul-1 56.2%

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

      6. neg-sub0 56.2%

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

      7. associate--r- 56.2%

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

      8. neg-sub0 56.2%

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

      9. +-commutative 56.2%

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

      10. sub-neg 56.2%

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

      11. associate-/l* 74.6%

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

      12. div-sub 74.6%

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

      13. *-inverses 74.6%

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

   9. Simplified 74.6%

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

   if -6.5000000000000004e31 < y < 0.0038999999999999998

   1. Initial program 94.2%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 75.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+31} \lor \neg \left(y \leq 0.0039\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-38} \lor \neg \left(y \leq 2.2 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-38) (not (<= y 2.2e+26)))
   (* t (- 1.0 (/ x y)))
   (/ t (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-38) || !(y <= 2.2e+26)) {
		tmp = t * (1.0 - (x / y));
	} 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) :: tmp
    if ((y <= (-2.1d-38)) .or. (.not. (y <= 2.2d+26))) then
        tmp = t * (1.0d0 - (x / y))
    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 tmp;
	if ((y <= -2.1e-38) || !(y <= 2.2e+26)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-38) or not (y <= 2.2e+26):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-38) || !(y <= 2.2e+26))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-38) || ~((y <= 2.2e+26)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-38], N[Not[LessEqual[y, 2.2e+26]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000013e-38 or 2.20000000000000007e26 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.0%

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

      2. associate-/l* 76.1%

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

   3. Simplified 76.1%

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

      1. clear-num 75.1%

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

      2. un-div-inv 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in z around 0 56.1%

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

      1. associate-*r/ 56.1%

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

      2. *-commutative 56.1%

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

      3. associate-*l* 56.1%

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

      4. *-commutative 56.1%

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

      5. neg-mul-1 56.1%

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

      6. neg-sub0 56.1%

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

      7. associate--r- 56.1%

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

      8. neg-sub0 56.1%

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

      9. +-commutative 56.1%

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

      10. sub-neg 56.1%

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

      11. associate-/l* 74.0%

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

      12. div-sub 74.0%

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

      13. *-inverses 74.0%

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

   9. Simplified 74.0%

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

   if -2.10000000000000013e-38 < y < 2.20000000000000007e26

   1. Initial program 94.0%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. associate-*r/ 90.5%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

      4. clear-num 94.0%

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

      5. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in y around 0 66.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-38} \lor \neg \left(y \leq 2.2 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+31) t (if (<= y 6.8e+31) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e+31) {
		tmp = t;
	} else if (y <= 6.8e+31) {
		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 <= (-3.1d+31)) then
        tmp = t
    else if (y <= 6.8d+31) 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 <= -3.1e+31) {
		tmp = t;
	} else if (y <= 6.8e+31) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e+31:
		tmp = t
	elif y <= 6.8e+31:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e+31)
		tmp = t;
	elseif (y <= 6.8e+31)
		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 <= -3.1e+31)
		tmp = t;
	elseif (y <= 6.8e+31)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e+31], t, If[LessEqual[y, 6.8e+31], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000002e31 or 6.7999999999999996e31 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.4%

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

      2. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around inf 60.3%

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

   if -3.1000000000000002e31 < y < 6.7999999999999996e31

   1. Initial program 94.4%

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

      1. associate-*l/ 91.0%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

      1. associate-*r/ 91.0%

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

      2. associate-*l/ 94.4%

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

      3. *-commutative 94.4%

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

      4. clear-num 94.3%

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

      5. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around 0 65.2%

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

Alternative 11: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+31) t (if (<= y 1.06e+32) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+31) {
		tmp = t;
	} else if (y <= 1.06e+32) {
		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 <= (-3.3d+31)) then
        tmp = t
    else if (y <= 1.06d+32) 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 <= -3.3e+31) {
		tmp = t;
	} else if (y <= 1.06e+32) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+31:
		tmp = t
	elif y <= 1.06e+32:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+31)
		tmp = t;
	elseif (y <= 1.06e+32)
		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 <= -3.3e+31)
		tmp = t;
	elseif (y <= 1.06e+32)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+31], t, If[LessEqual[y, 1.06e+32], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999992e31 or 1.0600000000000001e32 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.4%

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

      2. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around inf 60.3%

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

   if -3.29999999999999992e31 < y < 1.0600000000000001e32

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 65.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e+32) t (if (<= y 0.0026) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e+32) {
		tmp = t;
	} else if (y <= 0.0026) {
		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 <= (-1.55d+32)) then
        tmp = t
    else if (y <= 0.0026d0) 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 <= -1.55e+32) {
		tmp = t;
	} else if (y <= 0.0026) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e+32:
		tmp = t
	elif y <= 0.0026:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e+32)
		tmp = t;
	elseif (y <= 0.0026)
		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 <= -1.55e+32)
		tmp = t;
	elseif (y <= 0.0026)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e+32], t, If[LessEqual[y, 0.0026], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999997e32 or 0.0025999999999999999 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.2%

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

      2. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around inf 60.1%

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

   if -1.54999999999999997e32 < y < 0.0025999999999999999

   1. Initial program 94.2%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. clear-num 93.6%

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

      2. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in y around 0 60.6%

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

      1. associate-*l/ 64.9%

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

      2. *-commutative 64.9%

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

   9. Simplified 64.9%

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

Alternative 13: 35.7% 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 97.0%

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

   1. associate-*l/ 82.5%

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

   2. associate-/l* 84.1%

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

3. Simplified 84.1%

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

5. Taylor expanded in y around inf 35.1%

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

Developer target: 97.2% 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 2024111 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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