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

Percentage Accurate: 97.4% → 97.4%

Time: 9.2s

Alternatives: 14

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: 97.4% 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: 97.4% 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 97.5%

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

   1. associate-*l/ 82.2%

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

   2. associate-/l* 88.1%

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

3. Simplified 88.1%

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

   1. associate-*r/ 82.2%

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

   2. associate-*l/ 97.5%

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

   3. *-commutative 97.5%

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

   4. clear-num 97.5%

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

   5. un-div-inv 97.8%

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

6. Applied egg-rr 97.8%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+42)
   (* t (/ y (- y z)))
   (if (<= y -5e-135)
     (* x (/ t (- z y)))
     (if (<= y 2.2e+64) (* (- x y) (/ t z)) (/ t (/ y (- y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t * (y / (y - z));
	} else if (y <= -5e-135) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.2e+64) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t / (y / (y - 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 <= (-1.7d+42)) then
        tmp = t * (y / (y - z))
    else if (y <= (-5d-135)) then
        tmp = x * (t / (z - y))
    else if (y <= 2.2d+64) then
        tmp = (x - y) * (t / z)
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t * (y / (y - z));
	} else if (y <= -5e-135) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.2e+64) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+42:
		tmp = t * (y / (y - z))
	elif y <= -5e-135:
		tmp = x * (t / (z - y))
	elif y <= 2.2e+64:
		tmp = (x - y) * (t / z)
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+42)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= -5e-135)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 2.2e+64)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+42)
		tmp = t * (y / (y - z));
	elseif (y <= -5e-135)
		tmp = x * (t / (z - y));
	elseif (y <= 2.2e+64)
		tmp = (x - y) * (t / z);
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+42], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-135], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+64], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999988e42

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. neg-mul-1 80.8%

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

      2. distribute-neg-frac2 80.8%

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

      3. neg-sub0 80.8%

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

      4. sub-neg 80.8%

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

      5. +-commutative 80.8%

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

      6. associate--r+ 80.8%

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

      7. neg-sub0 80.8%

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

      8. remove-double-neg 80.8%

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

   5. Simplified 80.8%

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

   if -1.69999999999999988e42 < y < -5.0000000000000002e-135

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 71.8%

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

   if -5.0000000000000002e-135 < y < 2.20000000000000002e64

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 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 z around inf 83.6%

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

   if 2.20000000000000002e64 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. neg-mul-1 81.1%

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

      3. neg-sub0 81.1%

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

      4. sub-neg 81.1%

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

      5. +-commutative 81.1%

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

      6. associate--r+ 81.1%

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

      7. neg-sub0 81.1%

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

      8. remove-double-neg 81.1%

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

   5. Simplified 81.1%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

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

      3. un-div-inv 81.2%

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

   7. Applied egg-rr 81.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+63}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.9e+33)
   (* t (/ y (- y z)))
   (if (<= y -4.8e-135)
     (* x (/ t (- z y)))
     (if (<= y 9.8e+63) (* (- x y) (/ t z)) (* t (/ (- y x) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.9e+33) {
		tmp = t * (y / (y - z));
	} else if (y <= -4.8e-135) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.8e+63) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t * ((y - 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 <= (-4.9d+33)) then
        tmp = t * (y / (y - z))
    else if (y <= (-4.8d-135)) then
        tmp = x * (t / (z - y))
    else if (y <= 9.8d+63) then
        tmp = (x - y) * (t / z)
    else
        tmp = t * ((y - 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 <= -4.9e+33) {
		tmp = t * (y / (y - z));
	} else if (y <= -4.8e-135) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.8e+63) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.9e+33:
		tmp = t * (y / (y - z))
	elif y <= -4.8e-135:
		tmp = x * (t / (z - y))
	elif y <= 9.8e+63:
		tmp = (x - y) * (t / z)
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.9e+33)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= -4.8e-135)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 9.8e+63)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.9e+33)
		tmp = t * (y / (y - z));
	elseif (y <= -4.8e-135)
		tmp = x * (t / (z - y));
	elseif (y <= 9.8e+63)
		tmp = (x - y) * (t / z);
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.9e+33], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-135], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+63], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.90000000000000014e33

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. neg-mul-1 80.8%

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

      2. distribute-neg-frac2 80.8%

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

      3. neg-sub0 80.8%

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

      4. sub-neg 80.8%

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

      5. +-commutative 80.8%

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

      6. associate--r+ 80.8%

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

      7. neg-sub0 80.8%

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

      8. remove-double-neg 80.8%

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

   5. Simplified 80.8%

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

   if -4.90000000000000014e33 < y < -4.7999999999999997e-135

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 71.8%

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

   if -4.7999999999999997e-135 < y < 9.7999999999999994e63

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 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 z around inf 83.6%

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

   if 9.7999999999999994e63 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. neg-mul-1 81.1%

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

      3. neg-sub0 81.1%

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

      4. sub-neg 81.1%

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

      5. +-commutative 81.1%

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

      6. associate--r+ 81.1%

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

      7. neg-sub0 81.1%

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

      8. remove-double-neg 81.1%

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

   5. Simplified 81.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+63}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{t \cdot \left(y - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.8e-226)
   (/ t (/ (- z y) x))
   (if (<= t 6.2e-201) (/ (* t (- y x)) y) (* (- x y) (/ t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.8e-226) {
		tmp = t / ((z - y) / x);
	} else if (t <= 6.2e-201) {
		tmp = (t * (y - x)) / y;
	} else {
		tmp = (x - y) * (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 (t <= 8.8d-226) then
        tmp = t / ((z - y) / x)
    else if (t <= 6.2d-201) then
        tmp = (t * (y - x)) / y
    else
        tmp = (x - y) * (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 (t <= 8.8e-226) {
		tmp = t / ((z - y) / x);
	} else if (t <= 6.2e-201) {
		tmp = (t * (y - x)) / y;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 8.8e-226:
		tmp = t / ((z - y) / x)
	elif t <= 6.2e-201:
		tmp = (t * (y - x)) / y
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.8e-226)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (t <= 6.2e-201)
		tmp = Float64(Float64(t * Float64(y - x)) / y);
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 8.8e-226)
		tmp = t / ((z - y) / x);
	elseif (t <= 6.2e-201)
		tmp = (t * (y - x)) / y;
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 8.8e-226], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-201], N[(N[(t * N[(y - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 8.8e-226

   1. Initial program 96.4%

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

      1. associate-*l/ 84.0%

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

      2. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

      1. associate-*r/ 84.0%

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

      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 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in x around inf 61.6%

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

   if 8.8e-226 < t < 6.1999999999999998e-201

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 21.3%

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

   3. Simplified 21.3%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

   7. Simplified 100.0%

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

   if 6.1999999999999998e-201 < t

   1. Initial program 98.9%

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

      1. associate-*l/ 78.9%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{t \cdot \left(y - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.1 \cdot 10^{+128}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e+30) (not (<= y 2.1e+128)))
   (* t (/ y (- y z)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e+30) || !(y <= 2.1e+128)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.5d+30)) .or. (.not. (y <= 2.1d+128))) then
        tmp = t * (y / (y - z))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e+30) || !(y <= 2.1e+128)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.5e+30) or not (y <= 2.1e+128):
		tmp = t * (y / (y - z))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.5e+30) || !(y <= 2.1e+128))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -5.5e+30) || ~((y <= 2.1e+128)))
		tmp = t * (y / (y - z));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.5e+30], N[Not[LessEqual[y, 2.1e+128]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000025e30 or 2.1e128 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 81.6%

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

      1. neg-mul-1 81.6%

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

      2. distribute-neg-frac2 81.6%

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

      3. neg-sub0 81.6%

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

      4. sub-neg 81.6%

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

      5. +-commutative 81.6%

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

      6. associate--r+ 81.6%

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

      7. neg-sub0 81.6%

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

      8. remove-double-neg 81.6%

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

   5. Simplified 81.6%

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

   if -5.50000000000000025e30 < y < 2.1e128

   1. Initial program 96.3%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 76.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.1 \cdot 10^{+128}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 32500000:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e+30)
   (* t (/ y (- y z)))
   (if (<= y 32500000.0) (/ t (/ (- z y) x)) (/ t (/ y (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e+30) {
		tmp = t * (y / (y - z));
	} else if (y <= 32500000.0) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t / (y / (y - 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 <= (-1.35d+30)) then
        tmp = t * (y / (y - z))
    else if (y <= 32500000.0d0) then
        tmp = t / ((z - y) / x)
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e+30) {
		tmp = t * (y / (y - z));
	} else if (y <= 32500000.0) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e+30:
		tmp = t * (y / (y - z))
	elif y <= 32500000.0:
		tmp = t / ((z - y) / x)
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e+30)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 32500000.0)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e+30)
		tmp = t * (y / (y - z));
	elseif (y <= 32500000.0)
		tmp = t / ((z - y) / x);
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e+30], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 32500000.0], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e30

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. neg-mul-1 80.8%

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

      2. distribute-neg-frac2 80.8%

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

      3. neg-sub0 80.8%

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

      4. sub-neg 80.8%

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

      5. +-commutative 80.8%

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

      6. associate--r+ 80.8%

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

      7. neg-sub0 80.8%

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

      8. remove-double-neg 80.8%

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

   5. Simplified 80.8%

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

   if -1.3499999999999999e30 < y < 3.25e7

   1. Initial program 95.9%

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

      1. associate-*l/ 92.8%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

      1. associate-*r/ 92.8%

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

      2. associate-*l/ 95.9%

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

      3. *-commutative 95.9%

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

      4. clear-num 95.8%

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

      5. un-div-inv 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in x around inf 81.8%

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

   if 3.25e7 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

      3. neg-sub0 75.8%

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

      4. sub-neg 75.8%

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

      5. +-commutative 75.8%

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

      6. associate--r+ 75.8%

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

      7. neg-sub0 75.8%

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

      8. remove-double-neg 75.8%

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

   5. Simplified 75.8%

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

      1. *-commutative 75.8%

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

      2. clear-num 75.8%

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

      3. un-div-inv 75.9%

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

   7. Applied egg-rr 75.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 32500000:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+35)
   (* y (/ t (- y z)))
   (if (<= y 6.2e+128) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+35) {
		tmp = y * (t / (y - z));
	} else if (y <= 6.2e+128) {
		tmp = x * (t / (z - y));
	} 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 <= (-9d+35)) then
        tmp = y * (t / (y - z))
    else if (y <= 6.2d+128) then
        tmp = x * (t / (z - y))
    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 <= -9e+35) {
		tmp = y * (t / (y - z));
	} else if (y <= 6.2e+128) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+35:
		tmp = y * (t / (y - z))
	elif y <= 6.2e+128:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+35)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 6.2e+128)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e+35)
		tmp = y * (t / (y - z));
	elseif (y <= 6.2e+128)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+35], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+128], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999993e35

   1. Initial program 99.8%

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

      1. associate-*l/ 62.0%

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

      2. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. mul-1-neg 49.4%

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

      3. distribute-rgt-neg-out 49.4%

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

      4. associate-*l/ 66.7%

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

      5. *-commutative 66.7%

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

      6. distribute-lft-neg-out 66.7%

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

      7. distribute-rgt-neg-in 66.7%

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

      8. distribute-frac-neg2 66.7%

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

      9. neg-sub0 66.7%

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

      10. sub-neg 66.7%

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

      11. +-commutative 66.7%

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

      12. associate--r+ 66.7%

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

      13. neg-sub0 66.7%

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

      14. remove-double-neg 66.7%

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

   7. Simplified 66.7%

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

   if -8.9999999999999993e35 < y < 6.20000000000000008e128

   1. Initial program 96.3%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 76.6%

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

   if 6.20000000000000008e128 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 65.3%

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

      2. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in y around inf 70.4%

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

Alternative 8: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+36) t (if (<= y 2.4e+128) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+36) {
		tmp = t;
	} else if (y <= 2.4e+128) {
		tmp = x * (t / (z - y));
	} 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 <= (-7.6d+36)) then
        tmp = t
    else if (y <= 2.4d+128) then
        tmp = x * (t / (z - y))
    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 <= -7.6e+36) {
		tmp = t;
	} else if (y <= 2.4e+128) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+36:
		tmp = t
	elif y <= 2.4e+128:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+36)
		tmp = t;
	elseif (y <= 2.4e+128)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+36)
		tmp = t;
	elseif (y <= 2.4e+128)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+36], t, If[LessEqual[y, 2.4e+128], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6000000000000005e36 or 2.4000000000000002e128 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 63.1%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 65.0%

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

   if -7.6000000000000005e36 < y < 2.4000000000000002e128

   1. Initial program 96.3%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 76.6%

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

Alternative 9: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e-16) t (if (<= y 2.1e+128) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-16) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		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 <= (-1.02d-16)) then
        tmp = t
    else if (y <= 2.1d+128) 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 <= -1.02e-16) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e-16:
		tmp = t
	elif y <= 2.1e+128:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e-16)
		tmp = t;
	elseif (y <= 2.1e+128)
		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 <= -1.02e-16)
		tmp = t;
	elseif (y <= 2.1e+128)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e-16], t, If[LessEqual[y, 2.1e+128], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0200000000000001e-16 or 2.1e128 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 64.7%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -1.0200000000000001e-16 < y < 2.1e128

   1. Initial program 96.2%

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

      1. associate-*l/ 91.9%

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

      2. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

      1. associate-*r/ 91.9%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around 0 67.8%

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

Alternative 10: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-14) t (if (<= y 2.1e+128) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-14) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		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 <= (-7.5d-14)) then
        tmp = t
    else if (y <= 2.1d+128) 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 <= -7.5e-14) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-14:
		tmp = t
	elif y <= 2.1e+128:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-14)
		tmp = t;
	elseif (y <= 2.1e+128)
		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 <= -7.5e-14)
		tmp = t;
	elseif (y <= 2.1e+128)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-14], t, If[LessEqual[y, 2.1e+128], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999996e-14 or 2.1e128 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 64.7%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -7.4999999999999996e-14 < y < 2.1e128

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0 67.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-18) t (if (<= y 2.1e+128) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-18) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		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 <= (-3.4d-18)) then
        tmp = t
    else if (y <= 2.1d+128) 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 <= -3.4e-18) {
		tmp = t;
	} else if (y <= 2.1e+128) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-18:
		tmp = t
	elif y <= 2.1e+128:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-18)
		tmp = t;
	elseif (y <= 2.1e+128)
		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 <= -3.4e-18)
		tmp = t;
	elseif (y <= 2.1e+128)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-18], t, If[LessEqual[y, 2.1e+128], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000001e-18 or 2.1e128 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 64.7%

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

      2. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -3.40000000000000001e-18 < y < 2.1e128

   1. Initial program 96.2%

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

      1. associate-*l/ 91.9%

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

      2. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

      1. clear-num 94.4%

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

      2. un-div-inv 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*l/ 65.6%

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

      2. *-commutative 65.6%

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

   9. Simplified 65.6%

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

Alternative 12: 39.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-160}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-160) t (if (<= y 7.5e-162) (* t (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-160) {
		tmp = t;
	} else if (y <= 7.5e-162) {
		tmp = t * (y / 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 <= (-8.5d-160)) then
        tmp = t
    else if (y <= 7.5d-162) then
        tmp = t * (y / 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 <= -8.5e-160) {
		tmp = t;
	} else if (y <= 7.5e-162) {
		tmp = t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-160:
		tmp = t
	elif y <= 7.5e-162:
		tmp = t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-160)
		tmp = t;
	elseif (y <= 7.5e-162)
		tmp = Float64(t * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e-160)
		tmp = t;
	elseif (y <= 7.5e-162)
		tmp = t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-160], t, If[LessEqual[y, 7.5e-162], N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999959e-160 or 7.49999999999999972e-162 < y

   1. Initial program 99.2%

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

      1. associate-*l/ 78.6%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in y around inf 41.5%

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

   if -8.49999999999999959e-160 < y < 7.49999999999999972e-162

   1. Initial program 93.3%

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

      1. associate-*l/ 91.1%

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

      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 0 20.3%

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

      1. associate-*r/ 20.3%

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

      2. mul-1-neg 20.3%

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

      3. distribute-rgt-neg-out 20.3%

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

      4. associate-*l/ 24.0%

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

      5. *-commutative 24.0%

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

      6. distribute-lft-neg-out 24.0%

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

      7. distribute-rgt-neg-in 24.0%

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

      8. distribute-frac-neg2 24.0%

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

      9. neg-sub0 24.0%

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

      10. sub-neg 24.0%

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

      11. +-commutative 24.0%

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

      12. associate--r+ 24.0%

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

      13. neg-sub0 24.0%

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

      14. remove-double-neg 24.0%

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

   7. Simplified 24.0%

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

   8. Taylor expanded in y around 0 20.2%

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

      1. mul-1-neg 20.2%

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

      2. associate-/l* 19.2%

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

      3. distribute-rgt-neg-in 19.2%

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

      4. mul-1-neg 19.2%

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

      5. associate-*r/ 19.2%

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

      6. neg-mul-1 19.2%

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

   10. Simplified 19.2%

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

       1. clear-num 19.2%

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

       2. un-div-inv 19.2%

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

       3. add-sqr-sqrt 10.8%

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

       4. sqrt-unprod 15.4%

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

       5. sqr-neg 15.4%

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

       6. sqrt-unprod 7.5%

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

       7. add-sqr-sqrt 15.8%

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

   12. Applied egg-rr 15.8%

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

       1. associate-/r/ 22.2%

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

       2. associate-*l/ 15.8%

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

       3. associate-/l* 15.8%

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

   14. Simplified 15.8%

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

Alternative 13: 97.4% 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 97.5%

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

3. Final simplification 97.5%

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

Alternative 14: 36.0% 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 97.5%

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

   1. associate-*l/ 82.2%

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

   2. associate-/l* 88.1%

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

3. Simplified 88.1%

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

5. Taylor expanded in y around inf 30.8%

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

Developer Target 1: 97.4% 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 2024172 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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