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

Percentage Accurate: 68.3% → 89.2%

Time: 17.5s

Alternatives: 19

Speedup: 0.8×

Specification

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: 68.3% 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: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_2 \leq 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y x) (- a t)) (- z t) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -2e-281)
     t_1
     (if (<= t_2 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (if (<= t_2 1e+304) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - x) / (a - t)), (z - t), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-281) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 1e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - x) / Float64(a - t)), Float64(z - t), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-281)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 1e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-281], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+304], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-281 or 9.9999999999999994e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 62.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.0%

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

      2. associate-*l/ 91.1%

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

      3. fma-def 91.2%

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

   3. Simplified 91.2%

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

   if -2e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e303

   1. Initial program 98.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-281}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \end{array} \]

Alternative 2: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_2 \leq 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -2e-281)
     t_1
     (if (<= t_2 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (if (<= t_2 1e+304) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-281) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 1e+304) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / (a - t)))
    t_2 = x + (((y - x) * (z - t)) / (a - t))
    if (t_2 <= (-2d-281)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = y + (((z - a) * (x - y)) / t)
    else if (t_2 <= 1d+304) then
        tmp = t_2
    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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-281) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 1e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -2e-281:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_2 <= 1e+304:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-281)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 1e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-281)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_2 <= 1e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-281], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+304], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-281 or 9.9999999999999994e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 62.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   if -2e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e303

   1. Initial program 98.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-281}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 3: 89.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_1 \leq 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -2e-281)
     (+ x (/ (- z t) (/ (- a t) (- y x))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (if (<= t_1 1e+304) t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-281) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	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) * (z - t)) / (a - t))
    if (t_1 <= (-2d-281)) then
        tmp = x + ((z - t) / ((a - t) / (y - x)))
    else if (t_1 <= 0.0d0) then
        tmp = y + (((z - a) * (x - y)) / t)
    else if (t_1 <= 1d+304) then
        tmp = t_1
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    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) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-281) {
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-281:
		tmp = x + ((z - t) / ((a - t) / (y - x)))
	elif t_1 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_1 <= 1e+304:
		tmp = t_1
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-281)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(y - x))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-281)
		tmp = x + ((z - t) / ((a - t) / (y - x)));
	elseif (t_1 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-281], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-281

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

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

      2. associate-*l/ 92.6%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

      1. fma-udef 92.6%

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

      2. *-commutative 92.6%

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

      3. clear-num 92.5%

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

      4. un-div-inv 92.7%

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

   5. Applied egg-rr 92.7%

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

   if -2e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e303

   1. Initial program 98.8%

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

   if 9.9999999999999994e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 35.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 4: 47.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(-y\right)}{a - t}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+37}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y)) (- a t))))
   (if (<= t -6e+37)
     (/ (- y) (/ t (- z t)))
     (if (<= t -3.2e-69)
       (/ y (/ (- a t) z))
       (if (<= t -2.05e-97)
         t_1
         (if (<= t 6.8e-60)
           (* x (- 1.0 (/ z a)))
           (if (<= t 2e-28)
             t_1
             (if (<= t 3.2e+39) (/ (* y z) (- a t)) (* t (/ y (- t a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * -y) / (a - t);
	double tmp;
	if (t <= -6e+37) {
		tmp = -y / (t / (z - t));
	} else if (t <= -3.2e-69) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.05e-97) {
		tmp = t_1;
	} else if (t <= 6.8e-60) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2e-28) {
		tmp = t_1;
	} else if (t <= 3.2e+39) {
		tmp = (y * z) / (a - t);
	} else {
		tmp = t * (y / (t - a));
	}
	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 = (t * -y) / (a - t)
    if (t <= (-6d+37)) then
        tmp = -y / (t / (z - t))
    else if (t <= (-3.2d-69)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-2.05d-97)) then
        tmp = t_1
    else if (t <= 6.8d-60) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2d-28) then
        tmp = t_1
    else if (t <= 3.2d+39) then
        tmp = (y * z) / (a - t)
    else
        tmp = t * (y / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * -y) / (a - t);
	double tmp;
	if (t <= -6e+37) {
		tmp = -y / (t / (z - t));
	} else if (t <= -3.2e-69) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.05e-97) {
		tmp = t_1;
	} else if (t <= 6.8e-60) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2e-28) {
		tmp = t_1;
	} else if (t <= 3.2e+39) {
		tmp = (y * z) / (a - t);
	} else {
		tmp = t * (y / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * -y) / (a - t)
	tmp = 0
	if t <= -6e+37:
		tmp = -y / (t / (z - t))
	elif t <= -3.2e-69:
		tmp = y / ((a - t) / z)
	elif t <= -2.05e-97:
		tmp = t_1
	elif t <= 6.8e-60:
		tmp = x * (1.0 - (z / a))
	elif t <= 2e-28:
		tmp = t_1
	elif t <= 3.2e+39:
		tmp = (y * z) / (a - t)
	else:
		tmp = t * (y / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(-y)) / Float64(a - t))
	tmp = 0.0
	if (t <= -6e+37)
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	elseif (t <= -3.2e-69)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -2.05e-97)
		tmp = t_1;
	elseif (t <= 6.8e-60)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2e-28)
		tmp = t_1;
	elseif (t <= 3.2e+39)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	else
		tmp = Float64(t * Float64(y / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * -y) / (a - t);
	tmp = 0.0;
	if (t <= -6e+37)
		tmp = -y / (t / (z - t));
	elseif (t <= -3.2e-69)
		tmp = y / ((a - t) / z);
	elseif (t <= -2.05e-97)
		tmp = t_1;
	elseif (t <= 6.8e-60)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2e-28)
		tmp = t_1;
	elseif (t <= 3.2e+39)
		tmp = (y * z) / (a - t);
	else
		tmp = t * (y / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * (-y)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+37], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-69], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e-97], t$95$1, If[LessEqual[t, 6.8e-60], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-28], t$95$1, If[LessEqual[t, 3.2e+39], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.00000000000000043e37

   1. Initial program 47.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 47.2%

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

      2. associate-*l/ 66.7%

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

      3. fma-def 66.8%

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

   3. Simplified 66.8%

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

      1. fma-udef 66.7%

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

      2. *-commutative 66.7%

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

      3. clear-num 65.0%

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

      4. un-div-inv 65.2%

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

   5. Applied egg-rr 65.2%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. div-sub 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-/r/ 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in a around 0 44.2%

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

       1. mul-1-neg 44.2%

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

       2. associate-/l* 59.2%

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

       3. distribute-neg-frac 59.2%

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

   11. Simplified 59.2%

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

   if -6.00000000000000043e37 < t < -3.19999999999999999e-69

   1. Initial program 75.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 75.9%

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

      2. associate-*l/ 80.8%

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

      3. fma-def 81.3%

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

   3. Simplified 81.3%

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

      1. fma-udef 80.8%

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

      2. *-commutative 80.8%

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

      3. clear-num 80.7%

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

      4. un-div-inv 80.9%

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

   5. Applied egg-rr 80.9%

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

   6. Taylor expanded in y around inf 51.8%

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

      1. div-sub 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-/r/ 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in z around inf 46.5%

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

       1. associate-/l* 46.6%

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

   11. Simplified 46.6%

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

   if -3.19999999999999999e-69 < t < -2.04999999999999996e-97 or 6.80000000000000013e-60 < t < 1.99999999999999994e-28

   1. Initial program 94.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in x around 0 88.3%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. distribute-lft-neg-out 65.8%

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

      3. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   if -2.04999999999999996e-97 < t < 6.80000000000000013e-60

   1. Initial program 91.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.3%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

      1. fma-udef 96.6%

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

      2. *-commutative 96.6%

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

      3. clear-num 96.6%

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

      4. un-div-inv 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in a around inf 85.0%

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

      1. associate-/l* 92.5%

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

   8. Simplified 92.5%

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

   9. Taylor expanded in y around 0 69.2%

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

       1. *-lft-identity 69.2%

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

       2. associate-*r/ 69.2%

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

       3. *-commutative 69.2%

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

       4. associate-*r* 69.2%

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

       5. associate-*l/ 77.8%

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

       6. associate-*r/ 77.8%

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

       7. distribute-rgt-in 77.8%

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

       8. mul-1-neg 77.8%

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

       9. unsub-neg 77.8%

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

   11. Simplified 77.8%

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

   12. Taylor expanded in t around 0 77.8%

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

   if 1.99999999999999994e-28 < t < 3.19999999999999993e39

   1. Initial program 77.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 47.7%

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

      1. associate-/l* 55.2%

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

      2. associate-/r/ 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in z around inf 48.4%

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

   if 3.19999999999999993e39 < t

   1. Initial program 49.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 40.6%

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

   5. Taylor expanded in z around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. distribute-lft-neg-out 32.4%

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

      3. *-commutative 32.4%

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

   7. Simplified 32.4%

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

      1. frac-2neg 32.4%

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

      2. div-inv 32.5%

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

      3. distribute-rgt-neg-out 32.5%

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

      4. remove-double-neg 32.5%

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

      5. sub-neg 32.5%

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

      6. distribute-neg-in 32.5%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 11.9%

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

      9. sqr-neg 11.9%

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

      10. sqrt-unprod 13.5%

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

      11. add-sqr-sqrt 13.5%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 17.1%

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

      14. sqr-neg 17.1%

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

      15. sqrt-unprod 32.4%

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

      16. add-sqr-sqrt 32.5%

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

   9. Applied egg-rr 32.5%

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

       1. *-commutative 32.5%

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

       2. associate-*r* 48.9%

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

       3. associate-*l/ 48.9%

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

       4. *-lft-identity 48.9%

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

       5. +-commutative 48.9%

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

       6. unsub-neg 48.9%

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

   11. Simplified 48.9%

       \[\leadsto \color{blue}{\frac{y}{t - a} \cdot t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+37}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a - t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-28}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 5: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -3.45 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-128}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -3.45e-34)
     t_1
     (if (<= a 1.2e-153)
       (* y (/ (- z t) (- a t)))
       (if (<= a 3.1e-128)
         (* (- z a) (/ x t))
         (if (<= a 1.5e+37) (/ (- z t) (/ (- a t) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -3.45e-34) {
		tmp = t_1;
	} else if (a <= 1.2e-153) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 3.1e-128) {
		tmp = (z - a) * (x / t);
	} else if (a <= 1.5e+37) {
		tmp = (z - t) / ((a - t) / y);
	} 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 / (z - t)))
    if (a <= (-3.45d-34)) then
        tmp = t_1
    else if (a <= 1.2d-153) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 3.1d-128) then
        tmp = (z - a) * (x / t)
    else if (a <= 1.5d+37) then
        tmp = (z - t) / ((a - t) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -3.45e-34) {
		tmp = t_1;
	} else if (a <= 1.2e-153) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 3.1e-128) {
		tmp = (z - a) * (x / t);
	} else if (a <= 1.5e+37) {
		tmp = (z - t) / ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -3.45e-34:
		tmp = t_1
	elif a <= 1.2e-153:
		tmp = y * ((z - t) / (a - t))
	elif a <= 3.1e-128:
		tmp = (z - a) * (x / t)
	elif a <= 1.5e+37:
		tmp = (z - t) / ((a - t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -3.45e-34)
		tmp = t_1;
	elseif (a <= 1.2e-153)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 3.1e-128)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (a <= 1.5e+37)
		tmp = Float64(Float64(z - t) / Float64(Float64(a - t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -3.45e-34)
		tmp = t_1;
	elseif (a <= 1.2e-153)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 3.1e-128)
		tmp = (z - a) * (x / t);
	elseif (a <= 1.5e+37)
		tmp = (z - t) / ((a - t) / y);
	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 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.45e-34], t$95$1, If[LessEqual[a, 1.2e-153], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-128], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+37], N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.45e-34 or 1.50000000000000011e37 < a

   1. Initial program 73.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 65.3%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   if -3.45e-34 < a < 1.2000000000000001e-153

   1. Initial program 68.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around inf 79.5%

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

      1. div-sub 79.5%

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

   6. Simplified 79.5%

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

   if 1.2000000000000001e-153 < a < 3.10000000000000003e-128

   1. Initial program 22.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 19.9%

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

   3. Simplified 19.9%

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

   4. Taylor expanded in t around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. distribute-lft-out-- 99.4%

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

      3. div-sub 99.4%

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

      4. mul-1-neg 99.4%

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

      5. unsub-neg 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around 0 88.1%

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

      1. associate-/l* 88.1%

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

      2. associate-/r/ 88.7%

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

   9. Simplified 88.7%

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

   if 3.10000000000000003e-128 < a < 1.50000000000000011e37

   1. Initial program 62.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.1%

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

      2. associate-*l/ 80.4%

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

      3. fma-def 80.4%

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

   3. Simplified 80.4%

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

      1. fma-udef 80.4%

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

      2. *-commutative 80.4%

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

      3. clear-num 80.1%

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

      4. un-div-inv 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in y around inf 65.9%

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

      1. div-sub 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-/r/ 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-128}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 6: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.86 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-106}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t))))))
   (if (<= a -9.5e-37)
     t_1
     (if (<= a -1.86e-224)
       (* y (/ (- z t) (- a t)))
       (if (<= a 9.6e-106) (+ y (/ (* (- z a) (- x y)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (a <= -9.5e-37) {
		tmp = t_1;
	} else if (a <= -1.86e-224) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.6e-106) {
		tmp = y + (((z - a) * (x - y)) / 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 + ((z - t) * ((y - x) / (a - t)))
    if (a <= (-9.5d-37)) then
        tmp = t_1
    else if (a <= (-1.86d-224)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 9.6d-106) then
        tmp = y + (((z - a) * (x - y)) / 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 + ((z - t) * ((y - x) / (a - t)));
	double tmp;
	if (a <= -9.5e-37) {
		tmp = t_1;
	} else if (a <= -1.86e-224) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.6e-106) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	tmp = 0
	if a <= -9.5e-37:
		tmp = t_1
	elif a <= -1.86e-224:
		tmp = y * ((z - t) / (a - t))
	elif a <= 9.6e-106:
		tmp = y + (((z - a) * (x - y)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (a <= -9.5e-37)
		tmp = t_1;
	elseif (a <= -1.86e-224)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 9.6e-106)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	tmp = 0.0;
	if (a <= -9.5e-37)
		tmp = t_1;
	elseif (a <= -1.86e-224)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 9.6e-106)
		tmp = y + (((z - a) * (x - y)) / 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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-37], t$95$1, If[LessEqual[a, -1.86e-224], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e-106], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999927e-37 or 9.599999999999999e-106 < a

   1. Initial program 71.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   if -9.49999999999999927e-37 < a < -1.8600000000000001e-224

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in y around inf 84.9%

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

      1. div-sub 84.9%

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

   6. Simplified 84.9%

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

   if -1.8600000000000001e-224 < a < 9.599999999999999e-106

   1. Initial program 70.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 90.3%

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

      1. associate--l+ 90.3%

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

      2. distribute-lft-out-- 90.3%

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

      3. div-sub 90.3%

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

      4. mul-1-neg 90.3%

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

      5. unsub-neg 90.3%

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

      6. distribute-rgt-out-- 90.3%

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

   6. Simplified 90.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -1.86 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-106}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 7: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75} \lor \neg \left(t \leq -7.2 \cdot 10^{-43}\right) \land \left(t \leq -2.05 \cdot 10^{-97} \lor \neg \left(t \leq 3.2 \cdot 10^{-62}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+75)
         (and (not (<= t -7.2e-43))
              (or (<= t -2.05e-97) (not (<= t 3.2e-62)))))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+75) || (!(t <= -7.2e-43) && ((t <= -2.05e-97) || !(t <= 3.2e-62)))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (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 ((t <= (-6.6d+75)) .or. (.not. (t <= (-7.2d-43))) .and. (t <= (-2.05d-97)) .or. (.not. (t <= 3.2d-62))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / (a / (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 ((t <= -6.6e+75) || (!(t <= -7.2e-43) && ((t <= -2.05e-97) || !(t <= 3.2e-62)))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+75) or (not (t <= -7.2e-43) and ((t <= -2.05e-97) or not (t <= 3.2e-62))):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+75) || (!(t <= -7.2e-43) && ((t <= -2.05e-97) || !(t <= 3.2e-62))))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.6e+75) || (~((t <= -7.2e-43)) && ((t <= -2.05e-97) || ~((t <= 3.2e-62)))))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+75], And[N[Not[LessEqual[t, -7.2e-43]], $MachinePrecision], Or[LessEqual[t, -2.05e-97], N[Not[LessEqual[t, 3.2e-62]], $MachinePrecision]]]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999996e75 or -7.1999999999999998e-43 < t < -2.04999999999999996e-97 or 3.20000000000000021e-62 < t

   1. Initial program 54.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.5%

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

   6. Simplified 68.5%

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

   if -6.59999999999999996e75 < t < -7.1999999999999998e-43 or -2.04999999999999996e-97 < t < 3.20000000000000021e-62

   1. Initial program 89.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75} \lor \neg \left(t \leq -7.2 \cdot 10^{-43}\right) \land \left(t \leq -2.05 \cdot 10^{-97} \lor \neg \left(t \leq 3.2 \cdot 10^{-62}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 8: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75} \lor \neg \left(t \leq -1.05 \cdot 10^{-41} \lor \neg \left(t \leq -2.05 \cdot 10^{-97}\right) \land t \leq 4.3 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+75)
         (not
          (or (<= t -1.05e-41) (and (not (<= t -2.05e-97)) (<= t 4.3e-60)))))
   (* y (/ (- z t) (- a t)))
   (- x (/ (- x y) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+75) || !((t <= -1.05e-41) || (!(t <= -2.05e-97) && (t <= 4.3e-60)))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	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 ((t <= (-6.6d+75)) .or. (.not. (t <= (-1.05d-41)) .or. (.not. (t <= (-2.05d-97))) .and. (t <= 4.3d-60))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+75) || !((t <= -1.05e-41) || (!(t <= -2.05e-97) && (t <= 4.3e-60)))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+75) or not ((t <= -1.05e-41) or (not (t <= -2.05e-97) and (t <= 4.3e-60))):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+75) || !((t <= -1.05e-41) || (!(t <= -2.05e-97) && (t <= 4.3e-60))))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.6e+75) || ~(((t <= -1.05e-41) || (~((t <= -2.05e-97)) && (t <= 4.3e-60)))))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+75], N[Not[Or[LessEqual[t, -1.05e-41], And[N[Not[LessEqual[t, -2.05e-97]], $MachinePrecision], LessEqual[t, 4.3e-60]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999996e75 or -1.05000000000000006e-41 < t < -2.04999999999999996e-97 or 4.3000000000000001e-60 < t

   1. Initial program 54.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. div-sub 68.5%

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

   6. Simplified 68.5%

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

   if -6.59999999999999996e75 < t < -1.05000000000000006e-41 or -2.04999999999999996e-97 < t < 4.3000000000000001e-60

   1. Initial program 89.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 89.8%

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

      2. associate-*l/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

      1. fma-udef 95.5%

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

      2. *-commutative 95.5%

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

      3. clear-num 94.7%

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

      4. un-div-inv 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in a around inf 78.5%

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

      1. associate-/l* 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in z around inf 84.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75} \lor \neg \left(t \leq -1.05 \cdot 10^{-41} \lor \neg \left(t \leq -2.05 \cdot 10^{-97}\right) \land t \leq 4.3 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97} \lor \neg \left(t \leq 3.8 \cdot 10^{-77}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.1e+37)
     t_1
     (if (<= t -1.8e-38)
       (* z (/ (- y x) (- a t)))
       (if (or (<= t -2.05e-97) (not (<= t 3.8e-77)))
         t_1
         (* x (- 1.0 (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.1e+37) {
		tmp = t_1;
	} else if (t <= -1.8e-38) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -2.05e-97) || !(t <= 3.8e-77)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	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 = y * ((z - t) / (a - t))
    if (t <= (-4.1d+37)) then
        tmp = t_1
    else if (t <= (-1.8d-38)) then
        tmp = z * ((y - x) / (a - t))
    else if ((t <= (-2.05d-97)) .or. (.not. (t <= 3.8d-77))) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.1e+37) {
		tmp = t_1;
	} else if (t <= -1.8e-38) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -2.05e-97) || !(t <= 3.8e-77)) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.1e+37:
		tmp = t_1
	elif t <= -1.8e-38:
		tmp = z * ((y - x) / (a - t))
	elif (t <= -2.05e-97) or not (t <= 3.8e-77):
		tmp = t_1
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.1e+37)
		tmp = t_1;
	elseif (t <= -1.8e-38)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif ((t <= -2.05e-97) || !(t <= 3.8e-77))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -4.1e+37)
		tmp = t_1;
	elseif (t <= -1.8e-38)
		tmp = z * ((y - x) / (a - t));
	elseif ((t <= -2.05e-97) || ~((t <= 3.8e-77)))
		tmp = t_1;
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+37], t$95$1, If[LessEqual[t, -1.8e-38], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.05e-97], N[Not[LessEqual[t, 3.8e-77]], $MachinePrecision]], t$95$1, N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0999999999999998e37 or -1.8e-38 < t < -2.04999999999999996e-97 or 3.7999999999999999e-77 < t

   1. Initial program 57.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   6. Simplified 65.6%

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

   if -4.0999999999999998e37 < t < -1.8e-38

   1. Initial program 79.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around inf 80.8%

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

      1. div-sub 80.8%

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

   6. Simplified 80.8%

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

   if -2.04999999999999996e-97 < t < 3.7999999999999999e-77

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.9%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

      1. fma-udef 96.4%

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

      2. *-commutative 96.4%

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

      3. clear-num 96.4%

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

      4. un-div-inv 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in a around inf 87.3%

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

      1. associate-/l* 94.3%

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

   8. Simplified 94.3%

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

   9. Taylor expanded in y around 0 71.7%

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

       1. *-lft-identity 71.7%

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

       2. associate-*r/ 71.7%

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

       3. *-commutative 71.7%

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

       4. associate-*r* 71.7%

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

       5. associate-*l/ 79.8%

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

       6. associate-*r/ 79.8%

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

       7. distribute-rgt-in 79.7%

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

       8. mul-1-neg 79.7%

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

       9. unsub-neg 79.7%

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

   11. Simplified 79.7%

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

   12. Taylor expanded in t around 0 79.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97} \lor \neg \left(t \leq 3.8 \cdot 10^{-77}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 10: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -3.45 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2100000000000:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -3.45e-34)
     t_1
     (if (<= a -3.2e-219)
       (* y (/ (- z t) (- a t)))
       (if (<= a 2100000000000.0) (+ y (/ (* (- z a) (- x y)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -3.45e-34) {
		tmp = t_1;
	} else if (a <= -3.2e-219) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2100000000000.0) {
		tmp = y + (((z - a) * (x - y)) / 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 / (z - t)))
    if (a <= (-3.45d-34)) then
        tmp = t_1
    else if (a <= (-3.2d-219)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 2100000000000.0d0) then
        tmp = y + (((z - a) * (x - y)) / 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 / (z - t)));
	double tmp;
	if (a <= -3.45e-34) {
		tmp = t_1;
	} else if (a <= -3.2e-219) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2100000000000.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -3.45e-34:
		tmp = t_1
	elif a <= -3.2e-219:
		tmp = y * ((z - t) / (a - t))
	elif a <= 2100000000000.0:
		tmp = y + (((z - a) * (x - y)) / 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 / Float64(z - t))))
	tmp = 0.0
	if (a <= -3.45e-34)
		tmp = t_1;
	elseif (a <= -3.2e-219)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 2100000000000.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / 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 / (z - t)));
	tmp = 0.0;
	if (a <= -3.45e-34)
		tmp = t_1;
	elseif (a <= -3.2e-219)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 2100000000000.0)
		tmp = y + (((z - a) * (x - y)) / 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 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.45e-34], t$95$1, If[LessEqual[a, -3.2e-219], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2100000000000.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.45e-34 or 2.1e12 < a

   1. Initial program 72.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 65.1%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   if -3.45e-34 < a < -3.19999999999999998e-219

   1. Initial program 59.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in y around inf 82.8%

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

      1. div-sub 82.8%

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

   6. Simplified 82.8%

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

   if -3.19999999999999998e-219 < a < 2.1e12

   1. Initial program 69.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. distribute-lft-out-- 82.3%

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

      3. div-sub 82.3%

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

      4. mul-1-neg 82.3%

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

      5. unsub-neg 82.3%

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

      6. distribute-rgt-out-- 82.3%

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

   6. Simplified 82.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2100000000000:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 11: 47.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+237}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e+75)
   y
   (if (<= t 9e+52)
     (* x (- 1.0 (/ z a)))
     (if (<= t 1.18e+145)
       (* t (/ (- y) a))
       (if (<= t 3e+237) (* (- z a) (/ x t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 9e+52) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.18e+145) {
		tmp = t * (-y / a);
	} else if (t <= 3e+237) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = y;
	}
	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 (t <= (-6.6d+75)) then
        tmp = y
    else if (t <= 9d+52) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.18d+145) then
        tmp = t * (-y / a)
    else if (t <= 3d+237) then
        tmp = (z - a) * (x / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 9e+52) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.18e+145) {
		tmp = t * (-y / a);
	} else if (t <= 3e+237) {
		tmp = (z - a) * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+75:
		tmp = y
	elif t <= 9e+52:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.18e+145:
		tmp = t * (-y / a)
	elif t <= 3e+237:
		tmp = (z - a) * (x / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 9e+52)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.18e+145)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 3e+237)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 9e+52)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.18e+145)
		tmp = t * (-y / a);
	elseif (t <= 3e+237)
		tmp = (z - a) * (x / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+75], y, If[LessEqual[t, 9e+52], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+145], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+237], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.59999999999999996e75 or 3e237 < t

   1. Initial program 38.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in t around inf 60.8%

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

   if -6.59999999999999996e75 < t < 8.9999999999999999e52

   1. Initial program 87.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.8%

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

      2. associate-*l/ 90.9%

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

      3. fma-def 90.9%

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

   3. Simplified 90.9%

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

      1. fma-udef 90.9%

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

      2. *-commutative 90.9%

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

      3. clear-num 90.3%

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

      4. un-div-inv 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in a around inf 71.3%

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

      1. associate-/l* 77.6%

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

   8. Simplified 77.6%

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

   9. Taylor expanded in y around 0 51.3%

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

       1. *-lft-identity 51.3%

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

       2. associate-*r/ 51.3%

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

       3. *-commutative 51.3%

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

       4. associate-*r* 51.3%

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

       5. associate-*l/ 58.2%

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

       6. associate-*r/ 58.2%

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

       7. distribute-rgt-in 58.2%

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

       8. mul-1-neg 58.2%

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

       9. unsub-neg 58.2%

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

   11. Simplified 58.2%

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

   12. Taylor expanded in t around 0 58.3%

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

   if 8.9999999999999999e52 < t < 1.17999999999999998e145

   1. Initial program 80.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 70.1%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in a around inf 49.2%

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

      1. associate-/l* 54.2%

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

   9. Simplified 54.2%

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

   10. Taylor expanded in z around 0 39.1%

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

       1. associate-*r/ 39.1%

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

       2. mul-1-neg 39.1%

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

       3. *-commutative 39.1%

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

       4. distribute-rgt-neg-out 39.1%

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

       5. associate-*l/ 44.2%

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

   12. Simplified 44.2%

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

   if 1.17999999999999998e145 < t < 3e237

   1. Initial program 34.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. distribute-lft-out-- 61.5%

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

      3. div-sub 61.5%

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

      4. mul-1-neg 61.5%

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

      5. unsub-neg 61.5%

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

      6. distribute-rgt-out-- 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 30.5%

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

      1. associate-/l* 45.9%

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

      2. associate-/r/ 42.1%

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

   9. Simplified 42.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+237}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+37}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+37)
   (/ (- y) (/ t (- z t)))
   (if (<= t -5.2e-59)
     (/ y (/ (- a t) z))
     (if (<= t -2.05e-97)
       (/ (- t) (/ (- a t) y))
       (if (<= t 1.02e+48) (* x (- 1.0 (/ z a))) (* t (/ y (- t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+37) {
		tmp = -y / (t / (z - t));
	} else if (t <= -5.2e-59) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.05e-97) {
		tmp = -t / ((a - t) / y);
	} else if (t <= 1.02e+48) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t * (y / (t - a));
	}
	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 (t <= (-3.1d+37)) then
        tmp = -y / (t / (z - t))
    else if (t <= (-5.2d-59)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-2.05d-97)) then
        tmp = -t / ((a - t) / y)
    else if (t <= 1.02d+48) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t * (y / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+37) {
		tmp = -y / (t / (z - t));
	} else if (t <= -5.2e-59) {
		tmp = y / ((a - t) / z);
	} else if (t <= -2.05e-97) {
		tmp = -t / ((a - t) / y);
	} else if (t <= 1.02e+48) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t * (y / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+37:
		tmp = -y / (t / (z - t))
	elif t <= -5.2e-59:
		tmp = y / ((a - t) / z)
	elif t <= -2.05e-97:
		tmp = -t / ((a - t) / y)
	elif t <= 1.02e+48:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t * (y / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+37)
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	elseif (t <= -5.2e-59)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -2.05e-97)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (t <= 1.02e+48)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(t * Float64(y / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e+37)
		tmp = -y / (t / (z - t));
	elseif (t <= -5.2e-59)
		tmp = y / ((a - t) / z);
	elseif (t <= -2.05e-97)
		tmp = -t / ((a - t) / y);
	elseif (t <= 1.02e+48)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t * (y / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+37], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-59], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e-97], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+48], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.1000000000000002e37

   1. Initial program 47.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 47.2%

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

      2. associate-*l/ 66.7%

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

      3. fma-def 66.8%

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

   3. Simplified 66.8%

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

      1. fma-udef 66.7%

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

      2. *-commutative 66.7%

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

      3. clear-num 65.0%

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

      4. un-div-inv 65.2%

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

   5. Applied egg-rr 65.2%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. div-sub 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-/r/ 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in a around 0 44.2%

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

       1. mul-1-neg 44.2%

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

       2. associate-/l* 59.2%

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

       3. distribute-neg-frac 59.2%

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

   11. Simplified 59.2%

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

   if -3.1000000000000002e37 < t < -5.19999999999999996e-59

   1. Initial program 79.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 79.8%

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

      2. associate-*l/ 84.9%

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

      3. fma-def 85.2%

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

   3. Simplified 85.2%

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

      1. fma-udef 84.9%

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

      2. *-commutative 84.9%

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

      3. clear-num 84.7%

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

      4. un-div-inv 84.8%

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

   5. Applied egg-rr 84.8%

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

   6. Taylor expanded in y around inf 54.3%

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

      1. div-sub 54.3%

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

      2. *-commutative 54.3%

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

      3. associate-/r/ 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in z around inf 48.8%

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

       1. associate-/l* 48.9%

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

   11. Simplified 48.9%

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

   if -5.19999999999999996e-59 < t < -2.04999999999999996e-97

   1. Initial program 78.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in x around 0 78.3%

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

      1. associate-/l* 78.4%

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

      2. associate-/r/ 68.0%

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

   6. Simplified 68.0%

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

      1. associate-*l/ 78.3%

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

      2. associate-/l* 78.4%

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

      3. clear-num 78.4%

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

   8. Applied egg-rr 78.4%

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

   9. Taylor expanded in z around 0 56.6%

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

       1. mul-1-neg 56.6%

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

       2. associate-/l* 46.6%

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

   11. Simplified 46.6%

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

   if -2.04999999999999996e-97 < t < 1.02e48

   1. Initial program 90.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 90.5%

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

      2. associate-*l/ 94.8%

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

      3. fma-def 94.7%

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

   3. Simplified 94.7%

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

      1. fma-udef 94.8%

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

      2. *-commutative 94.8%

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

      3. clear-num 94.8%

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

      4. un-div-inv 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in a around inf 78.3%

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

      1. associate-/l* 85.1%

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

   8. Simplified 85.1%

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

   9. Taylor expanded in y around 0 60.8%

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

       1. *-lft-identity 60.8%

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

       2. associate-*r/ 60.8%

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

       3. *-commutative 60.8%

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

       4. associate-*r* 60.8%

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

       5. associate-*l/ 68.4%

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

       6. associate-*r/ 68.4%

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

       7. distribute-rgt-in 68.4%

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

       8. mul-1-neg 68.4%

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

       9. unsub-neg 68.4%

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

   11. Simplified 68.4%

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

   12. Taylor expanded in t around 0 68.4%

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

   if 1.02e48 < t

   1. Initial program 49.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around 0 41.2%

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

   5. Taylor expanded in z around 0 32.9%

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

      1. mul-1-neg 32.9%

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

      2. distribute-lft-neg-out 32.9%

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

      3. *-commutative 32.9%

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

   7. Simplified 32.9%

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

      1. frac-2neg 32.9%

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

      2. div-inv 33.0%

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

      3. distribute-rgt-neg-out 33.0%

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

      4. remove-double-neg 33.0%

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

      5. sub-neg 33.0%

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

      6. distribute-neg-in 33.0%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 12.1%

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

      9. sqr-neg 12.1%

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

      10. sqrt-unprod 13.7%

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

      11. add-sqr-sqrt 13.7%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 17.3%

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

      14. sqr-neg 17.3%

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

      15. sqrt-unprod 32.8%

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

      16. add-sqr-sqrt 33.0%

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

   9. Applied egg-rr 33.0%

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

       1. *-commutative 33.0%

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

       2. associate-*r* 49.6%

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

       3. associate-*l/ 49.6%

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

       4. *-lft-identity 49.6%

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

       5. +-commutative 49.6%

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

       6. unsub-neg 49.6%

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

   11. Simplified 49.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+37}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 13: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+142}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e+75)
   y
   (if (<= t 6.8e-34)
     (* x (- 1.0 (/ z a)))
     (if (<= t 6.8e+142) (* (- z t) (/ y a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 6.8e-34) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.8e+142) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = y;
	}
	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 (t <= (-6.6d+75)) then
        tmp = y
    else if (t <= 6.8d-34) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6.8d+142) then
        tmp = (z - t) * (y / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 6.8e-34) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.8e+142) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+75:
		tmp = y
	elif t <= 6.8e-34:
		tmp = x * (1.0 - (z / a))
	elif t <= 6.8e+142:
		tmp = (z - t) * (y / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 6.8e-34)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.8e+142)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 6.8e-34)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6.8e+142)
		tmp = (z - t) * (y / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+75], y, If[LessEqual[t, 6.8e-34], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+142], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.59999999999999996e75 or 6.7999999999999996e142 < t

   1. Initial program 37.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in t around inf 54.3%

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

   if -6.59999999999999996e75 < t < 6.8000000000000001e-34

   1. Initial program 88.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.9%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.5%

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

   3. Simplified 92.5%

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

      1. fma-udef 92.4%

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

      2. *-commutative 92.4%

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

      3. clear-num 91.7%

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

      4. un-div-inv 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in a around inf 73.6%

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

      1. associate-/l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in y around 0 54.3%

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

       1. *-lft-identity 54.3%

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

       2. associate-*r/ 54.3%

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

       3. *-commutative 54.3%

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

       4. associate-*r* 54.3%

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

       5. associate-*l/ 62.3%

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

       6. associate-*r/ 62.3%

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

       7. distribute-rgt-in 62.3%

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

       8. mul-1-neg 62.3%

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

       9. unsub-neg 62.3%

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

   11. Simplified 62.3%

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

   12. Taylor expanded in t around 0 62.3%

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

   if 6.8000000000000001e-34 < t < 6.7999999999999996e142

   1. Initial program 80.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around 0 65.5%

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

      1. associate-/l* 72.7%

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

      2. associate-/r/ 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in a around inf 45.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+142}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 58.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-97} \lor \neg \left(t \leq 4 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e-97) (not (<= t 4e-79)))
   (* y (/ (- z t) (- a t)))
   (* x (- 1.0 (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e-97) || !(t <= 4e-79)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	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 ((t <= (-2d-97)) .or. (.not. (t <= 4d-79))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e-97) || !(t <= 4e-79)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e-97) or not (t <= 4e-79):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e-97) || !(t <= 4e-79))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e-97) || ~((t <= 4e-79)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e-97], N[Not[LessEqual[t, 4e-79]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000007e-97 or 4e-79 < t

   1. Initial program 59.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in y around inf 64.5%

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

      1. div-sub 64.5%

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

   6. Simplified 64.5%

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

   if -2.00000000000000007e-97 < t < 4e-79

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.9%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

      1. fma-udef 96.4%

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

      2. *-commutative 96.4%

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

      3. clear-num 96.4%

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

      4. un-div-inv 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in a around inf 87.3%

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

      1. associate-/l* 94.3%

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

   8. Simplified 94.3%

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

   9. Taylor expanded in y around 0 71.7%

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

       1. *-lft-identity 71.7%

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

       2. associate-*r/ 71.7%

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

       3. *-commutative 71.7%

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

       4. associate-*r* 71.7%

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

       5. associate-*l/ 79.8%

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

       6. associate-*r/ 79.8%

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

       7. distribute-rgt-in 79.7%

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

       8. mul-1-neg 79.7%

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

       9. unsub-neg 79.7%

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

   11. Simplified 79.7%

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

   12. Taylor expanded in t around 0 79.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-97} \lor \neg \left(t \leq 4 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 15: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+81}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e-37) x (if (<= a 9e+81) y (* x (+ (/ t a) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e-37) {
		tmp = x;
	} else if (a <= 9e+81) {
		tmp = y;
	} else {
		tmp = x * ((t / a) + 1.0);
	}
	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 (a <= (-9d-37)) then
        tmp = x
    else if (a <= 9d+81) then
        tmp = y
    else
        tmp = x * ((t / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e-37) {
		tmp = x;
	} else if (a <= 9e+81) {
		tmp = y;
	} else {
		tmp = x * ((t / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e-37:
		tmp = x
	elif a <= 9e+81:
		tmp = y
	else:
		tmp = x * ((t / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e-37)
		tmp = x;
	elseif (a <= 9e+81)
		tmp = y;
	else
		tmp = Float64(x * Float64(Float64(t / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e-37)
		tmp = x;
	elseif (a <= 9e+81)
		tmp = y;
	else
		tmp = x * ((t / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e-37], x, If[LessEqual[a, 9e+81], y, N[(x * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.00000000000000081e-37

   1. Initial program 71.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in a around inf 45.9%

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

   if -9.00000000000000081e-37 < a < 9.00000000000000034e81

   1. Initial program 66.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 47.8%

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

   if 9.00000000000000034e81 < a

   1. Initial program 75.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 75.4%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 92.1%

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

   3. Simplified 92.1%

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

      1. fma-udef 91.8%

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

      2. *-commutative 91.8%

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

      3. clear-num 91.7%

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

      4. un-div-inv 91.7%

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

   5. Applied egg-rr 91.7%

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

   6. Taylor expanded in a around inf 71.5%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in y around 0 47.5%

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

       1. *-lft-identity 47.5%

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

       2. associate-*r/ 47.5%

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

       3. *-commutative 47.5%

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

       4. associate-*r* 47.5%

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

       5. associate-*l/ 52.8%

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

       6. associate-*r/ 52.8%

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

       7. distribute-rgt-in 52.8%

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

       8. mul-1-neg 52.8%

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

       9. unsub-neg 52.8%

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

   11. Simplified 52.8%

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

   12. Taylor expanded in z around 0 40.7%

       \[\leadsto \color{blue}{x \cdot \left(1 + \frac{t}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+81}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \]

Alternative 16: 50.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e+75) y (if (<= t 9.5e+47) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 9.5e+47) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	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 (t <= (-6.6d+75)) then
        tmp = y
    else if (t <= 9.5d+47) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 9.5e+47) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+75:
		tmp = y
	elif t <= 9.5e+47:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 9.5e+47)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 9.5e+47)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+75], y, If[LessEqual[t, 9.5e+47], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999996e75 or 9.50000000000000001e47 < t

   1. Initial program 44.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around inf 48.6%

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

   if -6.59999999999999996e75 < t < 9.50000000000000001e47

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.3%

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

      2. associate-*l/ 91.4%

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

      3. fma-def 91.5%

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

   3. Simplified 91.5%

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

      1. fma-udef 91.4%

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

      2. *-commutative 91.4%

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

      3. clear-num 90.8%

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

      4. un-div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. *-lft-identity 51.6%

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

       2. associate-*r/ 51.6%

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

       3. *-commutative 51.6%

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

       4. associate-*r* 51.6%

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

       5. associate-*l/ 58.6%

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

       6. associate-*r/ 58.6%

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

       7. distribute-rgt-in 58.6%

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

       8. mul-1-neg 58.6%

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

       9. unsub-neg 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in t around 0 58.7%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 49.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e+75)
   y
   (if (<= t 6.1e+47) (* x (- 1.0 (/ z a))) (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 6.1e+47) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t * (y / (t - a));
	}
	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 (t <= (-6.6d+75)) then
        tmp = y
    else if (t <= 6.1d+47) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t * (y / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e+75) {
		tmp = y;
	} else if (t <= 6.1e+47) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t * (y / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e+75:
		tmp = y
	elif t <= 6.1e+47:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t * (y / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 6.1e+47)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(t * Float64(y / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e+75)
		tmp = y;
	elseif (t <= 6.1e+47)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t * (y / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e+75], y, If[LessEqual[t, 6.1e+47], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.59999999999999996e75

   1. Initial program 39.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in t around inf 60.6%

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

   if -6.59999999999999996e75 < t < 6.10000000000000019e47

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.3%

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

      2. associate-*l/ 91.4%

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

      3. fma-def 91.5%

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

   3. Simplified 91.5%

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

      1. fma-udef 91.4%

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

      2. *-commutative 91.4%

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

      3. clear-num 90.8%

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

      4. un-div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. *-lft-identity 51.6%

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

       2. associate-*r/ 51.6%

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

       3. *-commutative 51.6%

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

       4. associate-*r* 51.6%

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

       5. associate-*l/ 58.6%

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

       6. associate-*r/ 58.6%

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

       7. distribute-rgt-in 58.6%

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

       8. mul-1-neg 58.6%

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

       9. unsub-neg 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in t around 0 58.7%

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

   if 6.10000000000000019e47 < t

   1. Initial program 49.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around 0 41.2%

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

   5. Taylor expanded in z around 0 32.9%

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

      1. mul-1-neg 32.9%

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

      2. distribute-lft-neg-out 32.9%

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

      3. *-commutative 32.9%

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

   7. Simplified 32.9%

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

      1. frac-2neg 32.9%

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

      2. div-inv 33.0%

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

      3. distribute-rgt-neg-out 33.0%

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

      4. remove-double-neg 33.0%

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

      5. sub-neg 33.0%

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

      6. distribute-neg-in 33.0%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 12.1%

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

      9. sqr-neg 12.1%

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

      10. sqrt-unprod 13.7%

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

      11. add-sqr-sqrt 13.7%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 17.3%

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

      14. sqr-neg 17.3%

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

      15. sqrt-unprod 32.8%

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

      16. add-sqr-sqrt 33.0%

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

   9. Applied egg-rr 33.0%

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

       1. *-commutative 33.0%

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

       2. associate-*r* 49.6%

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

       3. associate-*l/ 49.6%

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

       4. *-lft-identity 49.6%

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

       5. +-commutative 49.6%

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

       6. unsub-neg 49.6%

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

   11. Simplified 49.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 18: 39.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e-37) x (if (<= a 7.6e+80) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e-37) {
		tmp = x;
	} else if (a <= 7.6e+80) {
		tmp = y;
	} else {
		tmp = 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 (a <= (-9d-37)) then
        tmp = x
    else if (a <= 7.6d+80) then
        tmp = y
    else
        tmp = 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 (a <= -9e-37) {
		tmp = x;
	} else if (a <= 7.6e+80) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e-37:
		tmp = x
	elif a <= 7.6e+80:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e-37)
		tmp = x;
	elseif (a <= 7.6e+80)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e-37)
		tmp = x;
	elseif (a <= 7.6e+80)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e-37], x, If[LessEqual[a, 7.6e+80], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.00000000000000081e-37 or 7.59999999999999995e80 < a

   1. Initial program 73.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in a around inf 43.6%

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

   if -9.00000000000000081e-37 < a < 7.59999999999999995e80

   1. Initial program 66.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around inf 47.8%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 25.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 69.9%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 82.1%

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

3. Simplified 82.1%

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

4. Taylor expanded in a around inf 27.8%

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

5. Final simplification 27.8%

   \[\leadsto x \]

Developer target: 86.4% accurate, 0.7× 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 2023322 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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