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

Percentage Accurate: 96.9% → 96.9%

Time: 8.4s

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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% 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 96.5%

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

   1. associate-*l/ 84.8%

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

   2. associate-/l* 82.6%

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

3. Simplified 82.6%

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

   1. associate-*r/ 84.8%

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

   2. associate-*l/ 96.5%

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

   3. *-commutative 96.5%

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

   4. clear-num 96.4%

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

   5. un-div-inv 96.5%

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

6. Applied egg-rr 96.5%

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

7. Final simplification 96.5%

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

Alternative 2: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;x \leq -35:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* x (/ t (- z y)))))
   (if (<= x -35.0)
     t_2
     (if (<= x -5.8e-155)
       t_1
       (if (<= x -6.8e-177)
         (* (- x y) (/ t z))
         (if (<= x 1.12e-40) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (x <= -35.0) {
		tmp = t_2;
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 1.12e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = x * (t / (z - y))
    if (x <= (-35.0d0)) then
        tmp = t_2
    else if (x <= (-5.8d-155)) then
        tmp = t_1
    else if (x <= (-6.8d-177)) then
        tmp = (x - y) * (t / z)
    else if (x <= 1.12d-40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (x <= -35.0) {
		tmp = t_2;
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 1.12e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = x * (t / (z - y))
	tmp = 0
	if x <= -35.0:
		tmp = t_2
	elif x <= -5.8e-155:
		tmp = t_1
	elif x <= -6.8e-177:
		tmp = (x - y) * (t / z)
	elif x <= 1.12e-40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (x <= -35.0)
		tmp = t_2;
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 1.12e-40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (x <= -35.0)
		tmp = t_2;
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = (x - y) * (t / z);
	elseif (x <= 1.12e-40)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -35.0], t$95$2, If[LessEqual[x, -5.8e-155], t$95$1, If[LessEqual[x, -6.8e-177], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e-40], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -35 or 1.1200000000000001e-40 < x

   1. Initial program 97.1%

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

      1. associate-*l/ 84.4%

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

      2. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-/l* 70.1%

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

   7. Applied egg-rr 70.1%

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

   if -35 < x < -5.80000000000000021e-155 or -6.8000000000000001e-177 < x < 1.1200000000000001e-40

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. distribute-neg-frac2 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate--r- 86.8%

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

      5. neg-sub0 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in t around 0 74.6%

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

      1. associate-/l* 86.8%

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

   8. Simplified 86.8%

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

   if -5.80000000000000021e-155 < x < -6.8000000000000001e-177

   1. Initial program 72.6%

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

      1. associate-*l/ 86.5%

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

      2. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -35:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -950000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -950000.0)
     t_2
     (if (<= x -5.8e-155)
       t_1
       (if (<= x -6.8e-177)
         (* (- x y) (/ t z))
         (if (<= x 4.3e-17) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -950000.0) {
		tmp = t_2;
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 4.3e-17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-950000.0d0)) then
        tmp = t_2
    else if (x <= (-5.8d-155)) then
        tmp = t_1
    else if (x <= (-6.8d-177)) then
        tmp = (x - y) * (t / z)
    else if (x <= 4.3d-17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -950000.0) {
		tmp = t_2;
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 4.3e-17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -950000.0:
		tmp = t_2
	elif x <= -5.8e-155:
		tmp = t_1
	elif x <= -6.8e-177:
		tmp = (x - y) * (t / z)
	elif x <= 4.3e-17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -950000.0)
		tmp = t_2;
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 4.3e-17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -950000.0)
		tmp = t_2;
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = (x - y) * (t / z);
	elseif (x <= 4.3e-17)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -950000.0], t$95$2, If[LessEqual[x, -5.8e-155], t$95$1, If[LessEqual[x, -6.8e-177], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e-17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5e5 or 4.30000000000000023e-17 < x

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 78.5%

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

   if -9.5e5 < x < -5.80000000000000021e-155 or -6.8000000000000001e-177 < x < 4.30000000000000023e-17

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 85.6%

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

      1. neg-mul-1 85.6%

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

      2. distribute-neg-frac2 85.6%

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

      3. neg-sub0 85.6%

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

      4. associate--r- 85.6%

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

      5. neg-sub0 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 85.6%

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

   8. Simplified 85.6%

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

   if -5.80000000000000021e-155 < x < -6.8000000000000001e-177

   1. Initial program 72.6%

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

      1. associate-*l/ 86.5%

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

      2. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -950000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;x \leq -550000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= x -550000.0)
     (* t (/ x (- z y)))
     (if (<= x -1e-154)
       t_1
       (if (<= x -6.8e-177)
         (* (- x y) (/ t z))
         (if (<= x 2.15e-17) t_1 (/ t (/ (- z y) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (x <= -550000.0) {
		tmp = t * (x / (z - y));
	} else if (x <= -1e-154) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 2.15e-17) {
		tmp = t_1;
	} else {
		tmp = t / ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (x <= (-550000.0d0)) then
        tmp = t * (x / (z - y))
    else if (x <= (-1d-154)) then
        tmp = t_1
    else if (x <= (-6.8d-177)) then
        tmp = (x - y) * (t / z)
    else if (x <= 2.15d-17) then
        tmp = t_1
    else
        tmp = t / ((z - y) / x)
    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 (x <= -550000.0) {
		tmp = t * (x / (z - y));
	} else if (x <= -1e-154) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 2.15e-17) {
		tmp = t_1;
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if x <= -550000.0:
		tmp = t * (x / (z - y))
	elif x <= -1e-154:
		tmp = t_1
	elif x <= -6.8e-177:
		tmp = (x - y) * (t / z)
	elif x <= 2.15e-17:
		tmp = t_1
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (x <= -550000.0)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= -1e-154)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 2.15e-17)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (x <= -550000.0)
		tmp = t * (x / (z - y));
	elseif (x <= -1e-154)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = (x - y) * (t / z);
	elseif (x <= 2.15e-17)
		tmp = t_1;
	else
		tmp = t / ((z - y) / x);
	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[x, -550000.0], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-154], t$95$1, If[LessEqual[x, -6.8e-177], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e-17], t$95$1, N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5e5

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 78.0%

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

   if -5.5e5 < x < -9.9999999999999997e-155 or -6.8000000000000001e-177 < x < 2.15000000000000012e-17

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 85.6%

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

      1. neg-mul-1 85.6%

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

      2. distribute-neg-frac2 85.6%

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

      3. neg-sub0 85.6%

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

      4. associate--r- 85.6%

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

      5. neg-sub0 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 85.6%

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

   8. Simplified 85.6%

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

   if -9.9999999999999997e-155 < x < -6.8000000000000001e-177

   1. Initial program 72.6%

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

      1. associate-*l/ 86.5%

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

      2. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if 2.15000000000000012e-17 < x

   1. Initial program 97.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 76.4%

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

   3. Simplified 76.4%

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

      1. associate-*r/ 89.3%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in x around inf 79.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -550000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;x \leq -450:\\ \;\;\;\;t \cdot \left(x \cdot \frac{1}{z - y}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= x -450.0)
     (* t (* x (/ 1.0 (- z y))))
     (if (<= x -5.8e-155)
       t_1
       (if (<= x -6.8e-177)
         (* (- x y) (/ t z))
         (if (<= x 8.2e-18) t_1 (/ t (/ (- z y) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (x <= -450.0) {
		tmp = t * (x * (1.0 / (z - y)));
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 8.2e-18) {
		tmp = t_1;
	} else {
		tmp = t / ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (x <= (-450.0d0)) then
        tmp = t * (x * (1.0d0 / (z - y)))
    else if (x <= (-5.8d-155)) then
        tmp = t_1
    else if (x <= (-6.8d-177)) then
        tmp = (x - y) * (t / z)
    else if (x <= 8.2d-18) then
        tmp = t_1
    else
        tmp = t / ((z - y) / x)
    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 (x <= -450.0) {
		tmp = t * (x * (1.0 / (z - y)));
	} else if (x <= -5.8e-155) {
		tmp = t_1;
	} else if (x <= -6.8e-177) {
		tmp = (x - y) * (t / z);
	} else if (x <= 8.2e-18) {
		tmp = t_1;
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if x <= -450.0:
		tmp = t * (x * (1.0 / (z - y)))
	elif x <= -5.8e-155:
		tmp = t_1
	elif x <= -6.8e-177:
		tmp = (x - y) * (t / z)
	elif x <= 8.2e-18:
		tmp = t_1
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (x <= -450.0)
		tmp = Float64(t * Float64(x * Float64(1.0 / Float64(z - y))));
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 8.2e-18)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (x <= -450.0)
		tmp = t * (x * (1.0 / (z - y)));
	elseif (x <= -5.8e-155)
		tmp = t_1;
	elseif (x <= -6.8e-177)
		tmp = (x - y) * (t / z);
	elseif (x <= 8.2e-18)
		tmp = t_1;
	else
		tmp = t / ((z - y) / x);
	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[x, -450.0], N[(t * N[(x * N[(1.0 / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-155], t$95$1, If[LessEqual[x, -6.8e-177], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-18], t$95$1, N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -450

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 78.0%

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

      1. clear-num 78.0%

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

      2. associate-/r/ 78.1%

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

   5. Applied egg-rr 78.1%

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

   if -450 < x < -5.80000000000000021e-155 or -6.8000000000000001e-177 < x < 8.1999999999999995e-18

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 85.6%

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

      1. neg-mul-1 85.6%

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

      2. distribute-neg-frac2 85.6%

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

      3. neg-sub0 85.6%

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

      4. associate--r- 85.6%

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

      5. neg-sub0 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 85.6%

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

   8. Simplified 85.6%

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

   if -5.80000000000000021e-155 < x < -6.8000000000000001e-177

   1. Initial program 72.6%

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

      1. associate-*l/ 86.5%

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

      2. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if 8.1999999999999995e-18 < x

   1. Initial program 97.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 76.4%

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

   3. Simplified 76.4%

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

      1. associate-*r/ 89.3%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in x around inf 79.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -450:\\ \;\;\;\;t \cdot \left(x \cdot \frac{1}{z - y}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+177} \lor \neg \left(y \leq 10^{+194}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.82e+177) (not (<= y 1e+194)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.82e+177) || !(y <= 1e+194)) {
		tmp = t * (y / (y - z));
	} 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 ((y <= (-1.82d+177)) .or. (.not. (y <= 1d+194))) then
        tmp = t * (y / (y - z))
    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 ((y <= -1.82e+177) || !(y <= 1e+194)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.82e+177) or not (y <= 1e+194):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.82e+177) || !(y <= 1e+194))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 ((y <= -1.82e+177) || ~((y <= 1e+194)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.82e+177], N[Not[LessEqual[y, 1e+194]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.82e177 or 9.99999999999999945e193 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.1%

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

      1. neg-mul-1 89.1%

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

      2. distribute-neg-frac2 89.1%

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

      3. neg-sub0 89.1%

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

      4. associate--r- 89.1%

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

      5. neg-sub0 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in t around 0 59.8%

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

      1. associate-/l* 89.1%

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

   8. Simplified 89.1%

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

   if -1.82e177 < y < 9.99999999999999945e193

   1. Initial program 95.8%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+177} \lor \neg \left(y \leq 10^{+194}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -56000000000 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -56000000000.0) (not (<= y 1.25)))
   (* t (/ y (- y z)))
   (/ t (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -56000000000.0) || !(y <= 1.25)) {
		tmp = t * (y / (y - z));
	} 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 <= (-56000000000.0d0)) .or. (.not. (y <= 1.25d0))) then
        tmp = t * (y / (y - z))
    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 <= -56000000000.0) || !(y <= 1.25)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -56000000000.0) or not (y <= 1.25):
		tmp = t * (y / (y - z))
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -56000000000.0) || !(y <= 1.25))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -56000000000.0) || ~((y <= 1.25)))
		tmp = t * (y / (y - z));
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -56000000000.0], N[Not[LessEqual[y, 1.25]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e10 or 1.25 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-neg-frac2 73.8%

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

      3. neg-sub0 73.8%

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

      4. associate--r- 73.8%

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

      5. neg-sub0 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around 0 58.8%

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

      1. associate-/l* 73.8%

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

   8. Simplified 73.8%

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

   if -5.6e10 < y < 1.25

   1. Initial program 92.9%

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

      1. associate-*l/ 94.4%

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

      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
   5. Step-by-step derivation

      1. associate-*r/ 94.4%

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

      2. associate-*l/ 92.9%

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

      3. *-commutative 92.9%

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

      4. clear-num 92.8%

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

      5. un-div-inv 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around 0 64.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -56000000000 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000 \lor \neg \left(x \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -900000.0) (not (<= x 1.3e-40)))
   (* x (/ t (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -900000.0) || !(x <= 1.3e-40)) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-900000.0d0)) .or. (.not. (x <= 1.3d-40))) then
        tmp = x * (t / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -900000.0) || !(x <= 1.3e-40)) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -900000.0) or not (x <= 1.3e-40):
		tmp = x * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -900000.0) || !(x <= 1.3e-40))
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -900000.0) || ~((x <= 1.3e-40)))
		tmp = x * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -900000.0], N[Not[LessEqual[x, 1.3e-40]], $MachinePrecision]], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e5 or 1.3000000000000001e-40 < x

   1. Initial program 97.1%

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

      1. associate-*l/ 84.4%

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

      2. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-/l* 70.1%

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

   7. Applied egg-rr 70.1%

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

   if -9e5 < x < 1.3000000000000001e-40

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 83.3%

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

      1. neg-mul-1 83.3%

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

      2. distribute-neg-frac2 83.3%

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

      3. neg-sub0 83.3%

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

      4. associate--r- 83.3%

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

      5. neg-sub0 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around 0 72.7%

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

      1. associate-/l* 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -900000 \lor \neg \left(x \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7000000000000.0) t (if (<= y 3.3e+24) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7000000000000.0) {
		tmp = t;
	} else if (y <= 3.3e+24) {
		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 <= (-7000000000000.0d0)) then
        tmp = t
    else if (y <= 3.3d+24) 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 <= -7000000000000.0) {
		tmp = t;
	} else if (y <= 3.3e+24) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7000000000000.0:
		tmp = t
	elif y <= 3.3e+24:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7000000000000.0)
		tmp = t;
	elseif (y <= 3.3e+24)
		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 <= -7000000000000.0)
		tmp = t;
	elseif (y <= 3.3e+24)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7000000000000.0], t, If[LessEqual[y, 3.3e+24], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7e12 or 3.2999999999999999e24 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in y around inf 56.8%

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

   if -7e12 < y < 3.2999999999999999e24

   1. Initial program 93.1%

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

      1. associate-*l/ 94.6%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/l* 62.8%

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

   7. Simplified 62.8%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+29) t (if (<= y 1.25e+25) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+29) {
		tmp = t;
	} else if (y <= 1.25e+25) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.75d+29)) then
        tmp = t
    else if (y <= 1.25d+25) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+29) {
		tmp = t;
	} else if (y <= 1.25e+25) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+29:
		tmp = t
	elif y <= 1.25e+25:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+29)
		tmp = t;
	elseif (y <= 1.25e+25)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e+29)
		tmp = t;
	elseif (y <= 1.25e+25)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+29], t, If[LessEqual[y, 1.25e+25], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999989e29 or 1.25000000000000006e25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 74.0%

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

      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. Taylor expanded in y around inf 57.8%

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

   if -1.74999999999999989e29 < y < 1.25000000000000006e25

   1. Initial program 93.4%

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

   3. Taylor expanded in y around 0 64.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+31) t (if (<= y 5e+25) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+31) {
		tmp = t;
	} else if (y <= 5e+25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.7d+31)) then
        tmp = t
    else if (y <= 5d+25) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+31) {
		tmp = t;
	} else if (y <= 5e+25) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+31:
		tmp = t
	elif y <= 5e+25:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+31)
		tmp = t;
	elseif (y <= 5e+25)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e+31)
		tmp = t;
	elseif (y <= 5e+25)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+31], t, If[LessEqual[y, 5e+25], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6999999999999998e31 or 5.00000000000000024e25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 74.0%

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

      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. Taylor expanded in y around inf 57.8%

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

   if -3.6999999999999998e31 < y < 5.00000000000000024e25

   1. Initial program 93.4%

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

      1. associate-*l/ 94.7%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

      1. associate-*r/ 94.7%

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

      2. associate-*l/ 93.4%

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

      3. *-commutative 93.4%

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

      4. clear-num 93.3%

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

      5. un-div-inv 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in y around 0 64.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 96.9% 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 96.5%

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

3. Final simplification 96.5%

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

Alternative 13: 35.2% 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 96.5%

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

   1. associate-*l/ 84.8%

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

   2. associate-/l* 82.6%

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

3. Simplified 82.6%

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

5. Taylor expanded in y around inf 34.9%

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

6. Final simplification 34.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.9% 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 2024095 
(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))