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

Percentage Accurate: 96.9% → 97.1%

Time: 7.0s

Alternatives: 12

Speedup: 0.5×

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: 97.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 10^{+110}:\\ \;\;\;\;t\_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 1e+110) (* t_1 t) (* (/ t (- z y)) x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 1e+110) {
		tmp = t_1 * t;
	} 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 = (x - y) / (z - y)
    if (t_1 <= 1d+110) then
        tmp = t_1 * t
    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 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 1e+110) {
		tmp = t_1 * t;
	} else {
		tmp = (t / (z - y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 1e+110:
		tmp = t_1 * t
	else:
		tmp = (t / (z - y)) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 1e+110)
		tmp = Float64(t_1 * t);
	else
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 1e+110)
		tmp = t_1 * t;
	else
		tmp = (t / (z - y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+110], N[(t$95$1 * t), $MachinePrecision], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1e110

   1. Initial program 98.0%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. difference-of-squares N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 98.0

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

   4. Applied rewrites 98.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lift-+.f64 N/A

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

      5. lift--.f64 N/A

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

      6. difference-of-squares-rev N/A

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

      7. lift-+.f64 N/A

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

      8. flip-- N/A

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

      9. lift--.f64 98.0

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

   6. Applied rewrites 98.0%

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

   if 1e110 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

Alternative 2: 81.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 2e-271)
     t_2
     (if (<= t_1 5e-57)
       (* (- t) (/ y z))
       (if (<= t_1 5e-10) (* (/ x z) t) (if (<= t_1 1.5) (* 1.0 t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= 2e-271) {
		tmp = t_2;
	} else if (t_1 <= 5e-57) {
		tmp = -t * (y / z);
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} 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 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= 2d-271) then
        tmp = t_2
    else if (t_1 <= 5d-57) then
        tmp = -t * (y / z)
    else if (t_1 <= 5d-10) then
        tmp = (x / z) * t
    else if (t_1 <= 1.5d0) then
        tmp = 1.0d0 * t
    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 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= 2e-271) {
		tmp = t_2;
	} else if (t_1 <= 5e-57) {
		tmp = -t * (y / z);
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= 2e-271:
		tmp = t_2
	elif t_1 <= 5e-57:
		tmp = -t * (y / z)
	elif t_1 <= 5e-10:
		tmp = (x / z) * t
	elif t_1 <= 1.5:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= 2e-271)
		tmp = t_2;
	elseif (t_1 <= 5e-57)
		tmp = Float64(Float64(-t) * Float64(y / z));
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 1.5)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= 2e-271)
		tmp = t_2;
	elseif (t_1 <= 5e-57)
		tmp = -t * (y / z);
	elseif (t_1 <= 5e-10)
		tmp = (x / z) * t;
	elseif (t_1 <= 1.5)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-271], t$95$2, If[LessEqual[t$95$1, 5e-57], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-10], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999993e-271 or 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if 1.99999999999999993e-271 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000002e-57

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 74.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 69.2%

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

   if 5.0000000000000002e-57 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 81.1

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

   5. Applied rewrites 81.1%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.5%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-271}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;\frac{-y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) (- x y))))
   (if (<= t_1 0.0)
     t_2
     (if (<= t_1 5e-10)
       (* (/ (- x y) z) t)
       (if (<= t_1 1.0) (* (/ (- y) (- z y)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * (x - y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 1.0) {
		tmp = (-y / (z - y)) * t;
	} 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 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * (x - y)
    if (t_1 <= 0.0d0) then
        tmp = t_2
    else if (t_1 <= 5d-10) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 1.0d0) then
        tmp = (-y / (z - y)) * t
    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 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * (x - y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 1.0) {
		tmp = (-y / (z - y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * (x - y)
	tmp = 0
	if t_1 <= 0.0:
		tmp = t_2
	elif t_1 <= 5e-10:
		tmp = ((x - y) / z) * t
	elif t_1 <= 1.0:
		tmp = (-y / (z - y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * Float64(x - y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 1.0)
		tmp = Float64(Float64(Float64(-y) / Float64(z - y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * (x - y);
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 1.0)
		tmp = (-y / (z - y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], t$95$2, If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1.0], N[(N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.0 or 1 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 92.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   if 0.0 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 98.7

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

   5. Applied rewrites 98.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1:\\ \;\;\;\;\frac{-y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{-8}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5.0)
     (* (/ x (- z y)) t)
     (if (<= t_1 1e-8)
       (* (/ (- x y) z) t)
       (if (<= t_1 1.5) (* (- 1.0 (/ x y)) t) (* (/ t (- z y)) x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = (x / (z - y)) * t;
	} else if (t_1 <= 1e-8) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} 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 = (x - y) / (z - y)
    if (t_1 <= (-5.0d0)) then
        tmp = (x / (z - y)) * t
    else if (t_1 <= 1d-8) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 1.5d0) then
        tmp = (1.0d0 - (x / y)) * t
    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 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = (x / (z - y)) * t;
	} else if (t_1 <= 1e-8) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (t / (z - y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -5.0:
		tmp = (x / (z - y)) * t
	elif t_1 <= 1e-8:
		tmp = ((x - y) / z) * t
	elif t_1 <= 1.5:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (t / (z - y)) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -5.0)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	elseif (t_1 <= 1e-8)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 1.5)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -5.0)
		tmp = (x / (z - y)) * t;
	elseif (t_1 <= 1e-8)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 1.5)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (t / (z - y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5.0], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1e-8], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.8

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

   5. Applied rewrites 96.8%

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

   if -5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e-8

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 94.5

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

   5. Applied rewrites 94.5%

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

   if 1e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. difference-of-squares N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 98.9

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

   7. Applied rewrites 98.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 98.9%

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

   if 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{-8}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.5:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1e-24)
     (* (/ x (- z y)) t)
     (if (<= t_1 5e-10)
       (/ (* (- x y) t) z)
       (if (<= t_1 1.5) (* (- 1.0 (/ x y)) t) (* (/ t (- z y)) x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = (x / (z - y)) * t;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} 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 = (x - y) / (z - y)
    if (t_1 <= (-1d-24)) then
        tmp = (x / (z - y)) * t
    else if (t_1 <= 5d-10) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 1.5d0) then
        tmp = (1.0d0 - (x / y)) * t
    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 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = (x / (z - y)) * t;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (t / (z - y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1e-24:
		tmp = (x / (z - y)) * t
	elif t_1 <= 5e-10:
		tmp = ((x - y) * t) / z
	elif t_1 <= 1.5:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (t / (z - y)) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e-24)
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 1.5)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e-24)
		tmp = (x / (z - y)) * t;
	elseif (t_1 <= 5e-10)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 1.5)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (t / (z - y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-24], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999924e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -9.99999999999999924e-25 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. difference-of-squares N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 98.0

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

   7. Applied rewrites 98.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 98.0%

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

   if 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.5:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -1e-24)
     t_2
     (if (<= t_1 5e-10)
       (/ (* (- x y) t) z)
       (if (<= t_1 1.5) (* (- 1.0 (/ x y)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} 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 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-1d-24)) then
        tmp = t_2
    else if (t_1 <= 5d-10) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 1.5d0) then
        tmp = (1.0d0 - (x / y)) * t
    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 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -1e-24:
		tmp = t_2
	elif t_1 <= 5e-10:
		tmp = ((x - y) * t) / z
	elif t_1 <= 1.5:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -1e-24)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 1.5)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -1e-24)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 1.5)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-24], t$95$2, If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999924e-25 or 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if -9.99999999999999924e-25 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. difference-of-squares N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 98.0

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

   7. Applied rewrites 98.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 98.0%

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

Alternative 7: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -1e-24)
     t_2
     (if (<= t_1 5e-10) (/ (* (- x y) t) z) (if (<= t_1 1.5) (* 1.0 t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} 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 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-1d-24)) then
        tmp = t_2
    else if (t_1 <= 5d-10) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 1.5d0) then
        tmp = 1.0d0 * t
    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 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e-24) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -1e-24:
		tmp = t_2
	elif t_1 <= 5e-10:
		tmp = ((x - y) * t) / z
	elif t_1 <= 1.5:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -1e-24)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 1.5)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -1e-24)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 1.5)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-24], t$95$2, If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999924e-25 or 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if -9.99999999999999924e-25 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.5%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -1e+81)
     (* (/ x (- y)) t)
     (if (<= t_1 5e-10)
       (* (/ x z) t)
       (if (<= t_1 2.0) (* 1.0 t) (* (/ (- t) y) x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+81) {
		tmp = (x / -y) * t;
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (-t / 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 = (x - y) / (z - y)
    if (t_1 <= (-1d+81)) then
        tmp = (x / -y) * t
    else if (t_1 <= 5d-10) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (-t / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -1e+81) {
		tmp = (x / -y) * t;
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (-t / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -1e+81:
		tmp = (x / -y) * t
	elif t_1 <= 5e-10:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = (-t / y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+81)
		tmp = Float64(Float64(x / Float64(-y)) * t);
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(Float64(-t) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+81)
		tmp = (x / -y) * t;
	elseif (t_1 <= 5e-10)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = (-t / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+81], N[(N[(x / (-y)), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5e-10], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999921e80

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. difference-of-squares N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 72.7

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

   7. Applied rewrites 72.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 72.7%

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

   if -9.99999999999999921e80 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{-t}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ (- t) y) x)))
   (if (<= t_1 -1e+81)
     t_2
     (if (<= t_1 5e-10) (* (/ x z) t) (if (<= t_1 2.0) (* 1.0 t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (-t / y) * x;
	double tmp;
	if (t_1 <= -1e+81) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} 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 = (x - y) / (z - y)
    t_2 = (-t / y) * x
    if (t_1 <= (-1d+81)) then
        tmp = t_2
    else if (t_1 <= 5d-10) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    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 = (x - y) / (z - y);
	double t_2 = (-t / y) * x;
	double tmp;
	if (t_1 <= -1e+81) {
		tmp = t_2;
	} else if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (-t / y) * x
	tmp = 0
	if t_1 <= -1e+81:
		tmp = t_2
	elif t_1 <= 5e-10:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(Float64(-t) / y) * x)
	tmp = 0.0
	if (t_1 <= -1e+81)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (-t / y) * x;
	tmp = 0.0;
	if (t_1 <= -1e+81)
		tmp = t_2;
	elseif (t_1 <= 5e-10)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+81], t$95$2, If[LessEqual[t$95$1, 5e-10], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999921e80 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 95.9

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.1%

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

   if -9.99999999999999921e80 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+81}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-13} \lor \neg \left(t\_1 \leq 1.5\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 5e-13) (not (<= t_1 1.5))) (* x (/ t z)) (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 5e-13) || !(t_1 <= 1.5)) {
		tmp = x * (t / z);
	} else {
		tmp = 1.0 * 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if ((t_1 <= 5d-13) .or. (.not. (t_1 <= 1.5d0))) then
        tmp = x * (t / z)
    else
        tmp = 1.0d0 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 5e-13) || !(t_1 <= 1.5)) {
		tmp = x * (t / z);
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 5e-13) or not (t_1 <= 1.5):
		tmp = x * (t / z)
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 5e-13) || !(t_1 <= 1.5))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 5e-13) || ~((t_1 <= 1.5)))
		tmp = x * (t / z);
	else
		tmp = 1.0 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 5e-13], N[Not[LessEqual[t$95$1, 1.5]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.9999999999999999e-13 or 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 51.8

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

   5. Applied rewrites 51.8%

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

   7. Applied rewrites 53.9%

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

   if 4.9999999999999999e-13 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-13} \lor \neg \left(\frac{x - y}{z - y} \leq 1.5\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-10)
     (* (/ x z) t)
     (if (<= t_1 1.5) (* 1.0 t) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-10) then
        tmp = (x / z) * t
    else if (t_1 <= 1.5d0) then
        tmp = 1.0d0 * t
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = (x / z) * t;
	} else if (t_1 <= 1.5) {
		tmp = 1.0 * t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-10:
		tmp = (x / z) * t
	elif t_1 <= 1.5:
		tmp = 1.0 * t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-10)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 1.5)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-10)
		tmp = (x / z) * t;
	elseif (t_1 <= 1.5)
		tmp = 1.0 * t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-10], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1.5], N[(1.0 * t), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 58.6

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

   5. Applied rewrites 58.6%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.5%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 1.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 42.7

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

   5. Applied rewrites 42.7%

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

   7. Applied rewrites 47.7%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.5:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 t))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * t;
}

Python

def code(x, y, z, t):
	return 1.0 * t

Julia

function code(x, y, z, t)
	return Float64(1.0 * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * t;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * t), $MachinePrecision]

Derivation

1. Initial program 96.4%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \cdot t \]
4. Step-by-step derivation

5. Applied rewrites 37.4%

   \[\leadsto \color{blue}{1} \cdot t \]

6. Final simplification 37.4%

   \[\leadsto 1 \cdot t \]
7. Add Preprocessing

Developer Target 1: 96.8% accurate, 0.8× 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 2024326 
(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))