Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 69.0% → 70.8%

Time: 2.1s

Alternatives: 9

Speedup: 0.7×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right)\\ \mathbf{if}\;t \leq -2.22 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y x))))
   (if (<= t -2.22e+167)
     t_1
     (if (<= t 3.4e+121) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -2.22e+167) {
		tmp = t_1;
	} else if (t <= 3.4e+121) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y - x)
    if (t <= (-2.22d+167)) then
        tmp = t_1
    else if (t <= 3.4d+121) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -2.22e+167) {
		tmp = t_1;
	} else if (t <= 3.4e+121) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - x)
	tmp = 0
	if t <= -2.22e+167:
		tmp = t_1
	elif t <= 3.4e+121:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - x))
	tmp = 0.0
	if (t <= -2.22e+167)
		tmp = t_1;
	elseif (t <= 3.4e+121)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - x);
	tmp = 0.0;
	if (t <= -2.22e+167)
		tmp = t_1;
	elseif (t <= 3.4e+121)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.22e+167], t$95$1, If[LessEqual[t, 3.4e+121], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.22e167 or 3.4000000000000001e121 < t

   1. Initial program 13.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 2.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.1%

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

   if -2.22e167 < t < 3.4000000000000001e121

   1. Initial program 80.3%

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

Alternative 2: 55.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+224}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (- a t)))))
   (if (<= a -5.5e+146)
     t_1
     (if (<= a 3.5e+224) (/ (* (- y x) (- z t)) (- a t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -5.5e+146) {
		tmp = t_1;
	} else if (a <= 3.5e+224) {
		tmp = ((y - x) * (z - t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a - t))
    if (a <= (-5.5d+146)) then
        tmp = t_1
    else if (a <= 3.5d+224) then
        tmp = ((y - x) * (z - t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -5.5e+146) {
		tmp = t_1;
	} else if (a <= 3.5e+224) {
		tmp = ((y - x) * (z - t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a - t))
	tmp = 0
	if a <= -5.5e+146:
		tmp = t_1
	elif a <= 3.5e+224:
		tmp = ((y - x) * (z - t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -5.5e+146)
		tmp = t_1;
	elseif (a <= 3.5e+224)
		tmp = Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -5.5e+146)
		tmp = t_1;
	elseif (a <= 3.5e+224)
		tmp = ((y - x) * (z - t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+146], t$95$1, If[LessEqual[a, 3.5e+224], N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5000000000000004e146 or 3.5e224 < a

   1. Initial program 60.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.4%

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

   if -5.5000000000000004e146 < a < 3.5e224

   1. Initial program 61.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 50.7%

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

Alternative 3: 31.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{+72}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (- a t)))))
   (if (<= a -1.7e-70) t_1 (if (<= a 1.68e+72) (+ x (- y x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -1.7e-70) {
		tmp = t_1;
	} else if (a <= 1.68e+72) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a - t))
    if (a <= (-1.7d-70)) then
        tmp = t_1
    else if (a <= 1.68d+72) then
        tmp = x + (y - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -1.7e-70) {
		tmp = t_1;
	} else if (a <= 1.68e+72) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a - t))
	tmp = 0
	if a <= -1.7e-70:
		tmp = t_1
	elif a <= 1.68e+72:
		tmp = x + (y - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.7e-70)
		tmp = t_1;
	elseif (a <= 1.68e+72)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -1.7e-70)
		tmp = t_1;
	elseif (a <= 1.68e+72)
		tmp = x + (y - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e-70], t$95$1, If[LessEqual[a, 1.68e+72], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999998e-70 or 1.67999999999999991e72 < a

   1. Initial program 59.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 39.5%

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

   if -1.69999999999999998e-70 < a < 1.67999999999999991e72

   1. Initial program 62.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 11.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 31.6%

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

Alternative 4: 29.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a - t}{a - t}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+30}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- a t) (- a t)))))
   (if (<= x -1.9e+39) t_1 (if (<= x 2.15e+30) (+ x (- y x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a - t) / (a - t));
	double tmp;
	if (x <= -1.9e+39) {
		tmp = t_1;
	} else if (x <= 2.15e+30) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((a - t) / (a - t))
    if (x <= (-1.9d+39)) then
        tmp = t_1
    else if (x <= 2.15d+30) then
        tmp = x + (y - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a - t) / (a - t));
	double tmp;
	if (x <= -1.9e+39) {
		tmp = t_1;
	} else if (x <= 2.15e+30) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a - t) / (a - t))
	tmp = 0
	if x <= -1.9e+39:
		tmp = t_1
	elif x <= 2.15e+30:
		tmp = x + (y - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a - t) / Float64(a - t)))
	tmp = 0.0
	if (x <= -1.9e+39)
		tmp = t_1;
	elseif (x <= 2.15e+30)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a - t) / (a - t));
	tmp = 0.0;
	if (x <= -1.9e+39)
		tmp = t_1;
	elseif (x <= 2.15e+30)
		tmp = x + (y - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+39], t$95$1, If[LessEqual[x, 2.15e+30], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e39 or 2.15e30 < x

   1. Initial program 47.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 30.0%

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

   if -1.8999999999999999e39 < x < 2.15e30

   1. Initial program 74.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 8.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 32.1%

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

Alternative 5: 30.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y x))))
   (if (<= t -7.8e+15) t_1 (if (<= t 3.8e-7) (+ x (* (- y x) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -7.8e+15) {
		tmp = t_1;
	} else if (t <= 3.8e-7) {
		tmp = x + ((y - x) * (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y - x)
    if (t <= (-7.8d+15)) then
        tmp = t_1
    else if (t <= 3.8d-7) then
        tmp = x + ((y - x) * (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -7.8e+15) {
		tmp = t_1;
	} else if (t <= 3.8e-7) {
		tmp = x + ((y - x) * (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - x)
	tmp = 0
	if t <= -7.8e+15:
		tmp = t_1
	elif t <= 3.8e-7:
		tmp = x + ((y - x) * (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - x))
	tmp = 0.0
	if (t <= -7.8e+15)
		tmp = t_1;
	elseif (t <= 3.8e-7)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - x);
	tmp = 0.0;
	if (t <= -7.8e+15)
		tmp = t_1;
	elseif (t <= 3.8e-7)
		tmp = x + ((y - x) * (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+15], t$95$1, If[LessEqual[t, 3.8e-7], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8e15 or 3.80000000000000015e-7 < t

   1. Initial program 38.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 2.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.2%

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

   if -7.8e15 < t < 3.80000000000000015e-7

   1. Initial program 86.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 25.8%

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

Alternative 6: 23.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- a t))))
   (if (<= x -2.9e+144) t_1 (if (<= x 6.5e+151) (+ x (- y x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -2.9e+144) {
		tmp = t_1;
	} else if (x <= 6.5e+151) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a - t)
    if (x <= (-2.9d+144)) then
        tmp = t_1
    else if (x <= 6.5d+151) then
        tmp = x + (y - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -2.9e+144) {
		tmp = t_1;
	} else if (x <= 6.5e+151) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a - t)
	tmp = 0
	if x <= -2.9e+144:
		tmp = t_1
	elif x <= 6.5e+151:
		tmp = x + (y - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a - t))
	tmp = 0.0
	if (x <= -2.9e+144)
		tmp = t_1;
	elseif (x <= 6.5e+151)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a - t);
	tmp = 0.0;
	if (x <= -2.9e+144)
		tmp = t_1;
	elseif (x <= 6.5e+151)
		tmp = x + (y - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+144], t$95$1, If[LessEqual[x, 6.5e+151], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999998e144 or 6.5000000000000002e151 < x

   1. Initial program 52.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 19.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 5.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 18.8%

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

   if -2.89999999999999998e144 < x < 6.5000000000000002e151

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 11.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 26.4%

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

Alternative 7: 22.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+150}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- a t))))
   (if (<= x -3e+144) t_1 (if (<= x 4e+150) (- y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -3e+144) {
		tmp = t_1;
	} else if (x <= 4e+150) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a - t)
    if (x <= (-3d+144)) then
        tmp = t_1
    else if (x <= 4d+150) then
        tmp = y - x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -3e+144) {
		tmp = t_1;
	} else if (x <= 4e+150) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a - t)
	tmp = 0
	if x <= -3e+144:
		tmp = t_1
	elif x <= 4e+150:
		tmp = y - x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a - t))
	tmp = 0.0
	if (x <= -3e+144)
		tmp = t_1;
	elseif (x <= 4e+150)
		tmp = Float64(y - x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a - t);
	tmp = 0.0;
	if (x <= -3e+144)
		tmp = t_1;
	elseif (x <= 4e+150)
		tmp = y - x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+144], t$95$1, If[LessEqual[x, 4e+150], N[(y - x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9999999999999999e144 or 3.99999999999999992e150 < x

   1. Initial program 52.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 19.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 5.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 18.8%

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

   if -2.9999999999999999e144 < x < 3.99999999999999992e150

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 11.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 26.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 26.0%

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

Alternative 8: 19.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+275}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+275) (* (- y x) (- z t)) (+ x (- y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+275) {
		tmp = (y - x) * (z - t);
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+275)) then
        tmp = (y - x) * (z - t)
    else
        tmp = x + (y - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+275) {
		tmp = (y - x) * (z - t);
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+275:
		tmp = (y - x) * (z - t)
	else:
		tmp = x + (y - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+275)
		tmp = Float64(Float64(y - x) * Float64(z - t));
	else
		tmp = Float64(x + Float64(y - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+275)
		tmp = (y - x) * (z - t);
	else
		tmp = x + (y - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+275], N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999968e275

   1. Initial program 89.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 66.7%

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

   if -7.99999999999999968e275 < z

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 11.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 21.2%

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

Alternative 9: 18.5% accurate, 7.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.2%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 13.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 20.5%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 20.0%

    \[\leadsto \color{blue}{y - x} \]
12. Add Preprocessing

Developer Target 1: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

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