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

Percentage Accurate: 68.1% → 91.1%

Time: 28.5s

Alternatives: 24

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: 68.1% 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: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\mathsf{fma}\left(t_1, z - t, x\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- a t))) (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 -1e+284)
     (fma t_1 (- z t) x)
     (if (<= t_2 -2e-294)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 1e+299) t_2 (+ x (* (- z t) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) / (a - t);
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -1e+284) {
		tmp = fma(t_1, (z - t), x);
	} else if (t_2 <= -2e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = x + ((z - t) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) / Float64(a - t))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+284)
		tmp = fma(t_1, Float64(z - t), x);
	elseif (t_2 <= -2e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(Float64(z - t) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+284], N[(t$95$1 * N[(z - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, -2e-294], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], t$95$2, N[(x + N[(N[(z - t), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000008e284

   1. Initial program 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-*l/ 88.2%

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

      3. fma-def 88.3%

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

   3. Simplified 88.3%

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

   if -1.00000000000000008e284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000003e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.0000000000000001e299

   1. Initial program 96.9%

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

   if -2.00000000000000003e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 4.6%

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

   3. Simplified 4.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. distribute-lft-out-- 99.8%

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

      3. div-sub 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 1.0000000000000001e299 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 29.3%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 10^{+299}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 -2e+289)
     t_1
     (if (<= t_2 -2e-294)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 1e+299) 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) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+289) {
		tmp = t_1;
	} else if (t_2 <= -2e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 1e+299) {
		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) * (t - z)) / (a - t))
    if (t_2 <= (-2d+289)) then
        tmp = t_1
    else if (t_2 <= (-2d-294)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t_2 <= 1d+299) 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) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+289) {
		tmp = t_1;
	} else if (t_2 <= -2e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 1e+299) {
		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) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -2e+289:
		tmp = t_1
	elif t_2 <= -2e-294:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 1e+299:
		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(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e+289)
		tmp = t_1;
	elseif (t_2 <= -2e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 1e+299)
		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) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e+289)
		tmp = t_1;
	elseif (t_2 <= -2e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 1e+299)
		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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+289], t$95$1, If[LessEqual[t$95$2, -2e-294], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], 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))) < -2.0000000000000001e289 or 1.0000000000000001e299 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.7%

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

      1. associate-*l/ 85.9%

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

   3. Simplified 85.9%

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

   if -2.0000000000000001e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000003e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.0000000000000001e299

   1. Initial program 96.9%

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

   if -2.00000000000000003e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 4.6%

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

   3. Simplified 4.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. distribute-lft-out-- 99.8%

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

      3. div-sub 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{+289}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 10^{+299}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -6.2e+179)
     y
     (if (<= t -3.7e+70)
       (/ z (/ t x))
       (if (<= t -7.4e+31)
         (+ x y)
         (if (<= t 4.2e-275)
           t_1
           (if (<= t 8e-131)
             (+ x (/ y (/ a z)))
             (if (<= t 2.1e-36)
               t_1
               (if (<= t 1.95e-11)
                 (* y (/ z (- a t)))
                 (if (<= t 6.6e+129) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6.2e+179) {
		tmp = y;
	} else if (t <= -3.7e+70) {
		tmp = z / (t / x);
	} else if (t <= -7.4e+31) {
		tmp = x + y;
	} else if (t <= 4.2e-275) {
		tmp = t_1;
	} else if (t <= 8e-131) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 1.95e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.6e+129) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-6.2d+179)) then
        tmp = y
    else if (t <= (-3.7d+70)) then
        tmp = z / (t / x)
    else if (t <= (-7.4d+31)) then
        tmp = x + y
    else if (t <= 4.2d-275) then
        tmp = t_1
    else if (t <= 8d-131) then
        tmp = x + (y / (a / z))
    else if (t <= 2.1d-36) then
        tmp = t_1
    else if (t <= 1.95d-11) then
        tmp = y * (z / (a - t))
    else if (t <= 6.6d+129) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6.2e+179) {
		tmp = y;
	} else if (t <= -3.7e+70) {
		tmp = z / (t / x);
	} else if (t <= -7.4e+31) {
		tmp = x + y;
	} else if (t <= 4.2e-275) {
		tmp = t_1;
	} else if (t <= 8e-131) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 1.95e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.6e+129) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -6.2e+179:
		tmp = y
	elif t <= -3.7e+70:
		tmp = z / (t / x)
	elif t <= -7.4e+31:
		tmp = x + y
	elif t <= 4.2e-275:
		tmp = t_1
	elif t <= 8e-131:
		tmp = x + (y / (a / z))
	elif t <= 2.1e-36:
		tmp = t_1
	elif t <= 1.95e-11:
		tmp = y * (z / (a - t))
	elif t <= 6.6e+129:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = y;
	elseif (t <= -3.7e+70)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -7.4e+31)
		tmp = Float64(x + y);
	elseif (t <= 4.2e-275)
		tmp = t_1;
	elseif (t <= 8e-131)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 1.95e-11)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 6.6e+129)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -6.2e+179)
		tmp = y;
	elseif (t <= -3.7e+70)
		tmp = z / (t / x);
	elseif (t <= -7.4e+31)
		tmp = x + y;
	elseif (t <= 4.2e-275)
		tmp = t_1;
	elseif (t <= 8e-131)
		tmp = x + (y / (a / z));
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 1.95e-11)
		tmp = y * (z / (a - t));
	elseif (t <= 6.6e+129)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+179], y, If[LessEqual[t, -3.7e+70], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.4e+31], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.2e-275], t$95$1, If[LessEqual[t, 8e-131], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-36], t$95$1, If[LessEqual[t, 1.95e-11], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+129], t$95$1, y]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.2e179 or 6.5999999999999998e129 < 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/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in t around inf 61.5%

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

   if -6.2e179 < t < -3.69999999999999989e70

   1. Initial program 46.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. unsub-neg 30.5%

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

      3. associate-/l* 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 32.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 26.7%

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

       1. *-commutative 26.7%

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

       2. associate-/l* 41.6%

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

   13. Simplified 41.6%

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

   if -3.69999999999999989e70 < t < -7.3999999999999996e31

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

      1. fma-udef 78.6%

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

      2. *-commutative 78.6%

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

      3. clear-num 78.6%

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

      4. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 78.5%

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

   8. Taylor expanded in t around inf 57.1%

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

   if -7.3999999999999996e31 < t < 4.19999999999999976e-275 or 7.9999999999999999e-131 < t < 2.09999999999999991e-36 or 1.95000000000000005e-11 < t < 6.5999999999999998e129

   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/ 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. Add Preprocessing

   5. Taylor expanded in t around 0 58.8%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   8. Simplified 59.2%

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

   if 4.19999999999999976e-275 < t < 7.9999999999999999e-131

   1. Initial program 96.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 81.2%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 74.4%

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

   8. Simplified 74.4%

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

   if 2.09999999999999991e-36 < t < 1.95000000000000005e-11

   1. Initial program 71.3%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 80.4%

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

      1. div-sub 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in z around inf 70.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+180}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.6e+180)
     y
     (if (<= t -7.2e+70)
       (/ z (/ t x))
       (if (<= t -5.3e+35)
         (+ x y)
         (if (<= t 2.1e-275)
           (- x (/ x (/ a z)))
           (if (<= t 3.4e-130)
             (+ x (/ y (/ a z)))
             (if (<= t 2.1e-36)
               t_1
               (if (<= t 2.5e-11)
                 (* y (/ z (- a t)))
                 (if (<= t 4.5e+131) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.6e+180) {
		tmp = y;
	} else if (t <= -7.2e+70) {
		tmp = z / (t / x);
	} else if (t <= -5.3e+35) {
		tmp = x + y;
	} else if (t <= 2.1e-275) {
		tmp = x - (x / (a / z));
	} else if (t <= 3.4e-130) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 2.5e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.5e+131) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.6d+180)) then
        tmp = y
    else if (t <= (-7.2d+70)) then
        tmp = z / (t / x)
    else if (t <= (-5.3d+35)) then
        tmp = x + y
    else if (t <= 2.1d-275) then
        tmp = x - (x / (a / z))
    else if (t <= 3.4d-130) then
        tmp = x + (y / (a / z))
    else if (t <= 2.1d-36) then
        tmp = t_1
    else if (t <= 2.5d-11) then
        tmp = y * (z / (a - t))
    else if (t <= 4.5d+131) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.6e+180) {
		tmp = y;
	} else if (t <= -7.2e+70) {
		tmp = z / (t / x);
	} else if (t <= -5.3e+35) {
		tmp = x + y;
	} else if (t <= 2.1e-275) {
		tmp = x - (x / (a / z));
	} else if (t <= 3.4e-130) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 2.5e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.5e+131) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.6e+180:
		tmp = y
	elif t <= -7.2e+70:
		tmp = z / (t / x)
	elif t <= -5.3e+35:
		tmp = x + y
	elif t <= 2.1e-275:
		tmp = x - (x / (a / z))
	elif t <= 3.4e-130:
		tmp = x + (y / (a / z))
	elif t <= 2.1e-36:
		tmp = t_1
	elif t <= 2.5e-11:
		tmp = y * (z / (a - t))
	elif t <= 4.5e+131:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.6e+180)
		tmp = y;
	elseif (t <= -7.2e+70)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -5.3e+35)
		tmp = Float64(x + y);
	elseif (t <= 2.1e-275)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 3.4e-130)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 2.5e-11)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4.5e+131)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.6e+180)
		tmp = y;
	elseif (t <= -7.2e+70)
		tmp = z / (t / x);
	elseif (t <= -5.3e+35)
		tmp = x + y;
	elseif (t <= 2.1e-275)
		tmp = x - (x / (a / z));
	elseif (t <= 3.4e-130)
		tmp = x + (y / (a / z));
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 2.5e-11)
		tmp = y * (z / (a - t));
	elseif (t <= 4.5e+131)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+180], y, If[LessEqual[t, -7.2e+70], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.3e+35], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.1e-275], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-130], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-36], t$95$1, If[LessEqual[t, 2.5e-11], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+131], t$95$1, y]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.6000000000000002e180 or 4.5000000000000002e131 < 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/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in t around inf 61.5%

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

   if -3.6000000000000002e180 < t < -7.1999999999999999e70

   1. Initial program 46.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. unsub-neg 30.5%

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

      3. associate-/l* 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 32.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 26.7%

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

       1. *-commutative 26.7%

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

       2. associate-/l* 41.6%

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

   13. Simplified 41.6%

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

   if -7.1999999999999999e70 < t < -5.30000000000000009e35

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

      1. fma-udef 78.6%

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

      2. *-commutative 78.6%

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

      3. clear-num 78.6%

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

      4. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 78.5%

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

   8. Taylor expanded in t around inf 57.1%

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

   if -5.30000000000000009e35 < t < 2.09999999999999988e-275

   1. Initial program 86.2%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 63.9%

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

   6. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.4%

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

      2. sub-neg 53.4%

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

      3. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if 2.09999999999999988e-275 < t < 3.40000000000000005e-130

   1. Initial program 96.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 81.2%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 74.4%

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

   8. Simplified 74.4%

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

   if 3.40000000000000005e-130 < t < 2.09999999999999991e-36 or 2.50000000000000009e-11 < t < 4.5000000000000002e131

   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/ 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in t around 0 50.2%

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

   6. Taylor expanded in x around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

   8. Simplified 53.7%

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

   if 2.09999999999999991e-36 < t < 2.50000000000000009e-11

   1. Initial program 71.3%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 80.4%

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

      1. div-sub 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in z around inf 70.5%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a - t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+180}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+131}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.75e+181)
   y
   (if (<= t -2.6e+69)
     (/ z (/ t x))
     (if (<= t -4.1e+30)
       (+ x y)
       (if (<= t 4.1e-277)
         (- x (/ x (/ a z)))
         (if (<= t 5.1e-135)
           (+ x (/ y (/ a z)))
           (if (<= t 1.3e-36)
             (* x (- 1.0 (/ z a)))
             (if (<= t 7.8e-6)
               (* y (/ z (- a t)))
               (if (<= t 7e+131) (/ (* x (- z a)) t) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e+181) {
		tmp = y;
	} else if (t <= -2.6e+69) {
		tmp = z / (t / x);
	} else if (t <= -4.1e+30) {
		tmp = x + y;
	} else if (t <= 4.1e-277) {
		tmp = x - (x / (a / z));
	} else if (t <= 5.1e-135) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.3e-36) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 7.8e-6) {
		tmp = y * (z / (a - t));
	} else if (t <= 7e+131) {
		tmp = (x * (z - a)) / 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 <= (-1.75d+181)) then
        tmp = y
    else if (t <= (-2.6d+69)) then
        tmp = z / (t / x)
    else if (t <= (-4.1d+30)) then
        tmp = x + y
    else if (t <= 4.1d-277) then
        tmp = x - (x / (a / z))
    else if (t <= 5.1d-135) then
        tmp = x + (y / (a / z))
    else if (t <= 1.3d-36) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 7.8d-6) then
        tmp = y * (z / (a - t))
    else if (t <= 7d+131) then
        tmp = (x * (z - a)) / 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 <= -1.75e+181) {
		tmp = y;
	} else if (t <= -2.6e+69) {
		tmp = z / (t / x);
	} else if (t <= -4.1e+30) {
		tmp = x + y;
	} else if (t <= 4.1e-277) {
		tmp = x - (x / (a / z));
	} else if (t <= 5.1e-135) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.3e-36) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 7.8e-6) {
		tmp = y * (z / (a - t));
	} else if (t <= 7e+131) {
		tmp = (x * (z - a)) / t;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.75e+181:
		tmp = y
	elif t <= -2.6e+69:
		tmp = z / (t / x)
	elif t <= -4.1e+30:
		tmp = x + y
	elif t <= 4.1e-277:
		tmp = x - (x / (a / z))
	elif t <= 5.1e-135:
		tmp = x + (y / (a / z))
	elif t <= 1.3e-36:
		tmp = x * (1.0 - (z / a))
	elif t <= 7.8e-6:
		tmp = y * (z / (a - t))
	elif t <= 7e+131:
		tmp = (x * (z - a)) / t
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.75e+181)
		tmp = y;
	elseif (t <= -2.6e+69)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -4.1e+30)
		tmp = Float64(x + y);
	elseif (t <= 4.1e-277)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 5.1e-135)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.3e-36)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 7.8e-6)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 7e+131)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.75e+181)
		tmp = y;
	elseif (t <= -2.6e+69)
		tmp = z / (t / x);
	elseif (t <= -4.1e+30)
		tmp = x + y;
	elseif (t <= 4.1e-277)
		tmp = x - (x / (a / z));
	elseif (t <= 5.1e-135)
		tmp = x + (y / (a / z));
	elseif (t <= 1.3e-36)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 7.8e-6)
		tmp = y * (z / (a - t));
	elseif (t <= 7e+131)
		tmp = (x * (z - a)) / t;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.75e+181], y, If[LessEqual[t, -2.6e+69], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e+30], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.1e-277], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-135], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-36], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-6], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+131], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], y]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.75000000000000004e181 or 6.9999999999999998e131 < 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/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in t around inf 61.5%

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

   if -1.75000000000000004e181 < t < -2.6000000000000002e69

   1. Initial program 46.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. unsub-neg 30.5%

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

      3. associate-/l* 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 32.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 26.7%

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

       1. *-commutative 26.7%

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

       2. associate-/l* 41.6%

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

   13. Simplified 41.6%

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

   if -2.6000000000000002e69 < t < -4.10000000000000005e30

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

      1. fma-udef 78.6%

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

      2. *-commutative 78.6%

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

      3. clear-num 78.6%

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

      4. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 78.5%

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

   8. Taylor expanded in t around inf 57.1%

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

   if -4.10000000000000005e30 < t < 4.09999999999999989e-277

   1. Initial program 86.2%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 63.9%

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

   6. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.4%

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

      2. sub-neg 53.4%

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

      3. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if 4.09999999999999989e-277 < t < 5.1000000000000001e-135

   1. Initial program 96.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 81.2%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 74.4%

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

   8. Simplified 74.4%

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

   if 5.1000000000000001e-135 < t < 1.3e-36

   1. Initial program 78.9%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around 0 57.3%

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

   6. Taylor expanded in x around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   8. Simplified 65.9%

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

   if 1.3e-36 < t < 7.7999999999999999e-6

   1. Initial program 73.9%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around inf 73.4%

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

      1. div-sub 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around inf 64.5%

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

   if 7.7999999999999999e-6 < t < 6.9999999999999998e131

   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/ 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in y around 0 47.8%

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

      1. mul-1-neg 47.8%

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

      2. unsub-neg 47.8%

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

      3. associate-/l* 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in t around inf 37.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 37.6%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 37.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 37.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 37.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 37.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 37.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 37.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 37.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in t around inf 48.1%

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

       1. distribute-lft-out-- 48.1%

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

       2. mul-1-neg 48.1%

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

       3. *-commutative 48.1%

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

       4. distribute-lft-out-- 48.1%

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

   13. Simplified 48.1%

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

   14. Taylor expanded in x around inf 48.1%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+30}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+131}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -1.8e+163)
     t_2
     (if (<= a -1.9e-38)
       (- x (/ x (/ a z)))
       (if (<= a -2.3e-208)
         t_1
         (if (<= a -2.8e-262)
           (/ x (/ t z))
           (if (<= a 3.2e-239)
             t_1
             (if (<= a 2.7e-185)
               (/ (* x (- z a)) t)
               (if (<= a 3e+25) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.8e+163) {
		tmp = t_2;
	} else if (a <= -1.9e-38) {
		tmp = x - (x / (a / z));
	} else if (a <= -2.3e-208) {
		tmp = t_1;
	} else if (a <= -2.8e-262) {
		tmp = x / (t / z);
	} else if (a <= 3.2e-239) {
		tmp = t_1;
	} else if (a <= 2.7e-185) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 3e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = y * ((t - z) / t)
    t_2 = x + (y / (a / z))
    if (a <= (-1.8d+163)) then
        tmp = t_2
    else if (a <= (-1.9d-38)) then
        tmp = x - (x / (a / z))
    else if (a <= (-2.3d-208)) then
        tmp = t_1
    else if (a <= (-2.8d-262)) then
        tmp = x / (t / z)
    else if (a <= 3.2d-239) then
        tmp = t_1
    else if (a <= 2.7d-185) then
        tmp = (x * (z - a)) / t
    else if (a <= 3d+25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -1.8e+163) {
		tmp = t_2;
	} else if (a <= -1.9e-38) {
		tmp = x - (x / (a / z));
	} else if (a <= -2.3e-208) {
		tmp = t_1;
	} else if (a <= -2.8e-262) {
		tmp = x / (t / z);
	} else if (a <= 3.2e-239) {
		tmp = t_1;
	} else if (a <= 2.7e-185) {
		tmp = (x * (z - a)) / t;
	} else if (a <= 3e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -1.8e+163:
		tmp = t_2
	elif a <= -1.9e-38:
		tmp = x - (x / (a / z))
	elif a <= -2.3e-208:
		tmp = t_1
	elif a <= -2.8e-262:
		tmp = x / (t / z)
	elif a <= 3.2e-239:
		tmp = t_1
	elif a <= 2.7e-185:
		tmp = (x * (z - a)) / t
	elif a <= 3e+25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.8e+163)
		tmp = t_2;
	elseif (a <= -1.9e-38)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (a <= -2.3e-208)
		tmp = t_1;
	elseif (a <= -2.8e-262)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 3.2e-239)
		tmp = t_1;
	elseif (a <= 2.7e-185)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (a <= 3e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -1.8e+163)
		tmp = t_2;
	elseif (a <= -1.9e-38)
		tmp = x - (x / (a / z));
	elseif (a <= -2.3e-208)
		tmp = t_1;
	elseif (a <= -2.8e-262)
		tmp = x / (t / z);
	elseif (a <= 3.2e-239)
		tmp = t_1;
	elseif (a <= 2.7e-185)
		tmp = (x * (z - a)) / t;
	elseif (a <= 3e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+163], t$95$2, If[LessEqual[a, -1.9e-38], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-208], t$95$1, If[LessEqual[a, -2.8e-262], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-239], t$95$1, If[LessEqual[a, 2.7e-185], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 3e+25], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.79999999999999989e163 or 3.00000000000000006e25 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 63.4%

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

   6. Taylor expanded in y around inf 60.5%

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

      1. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   if -1.79999999999999989e163 < a < -1.9e-38

   1. Initial program 68.5%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 52.5%

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

   6. Taylor expanded in y around 0 44.2%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.2%

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

      2. sub-neg 44.2%

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

      3. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

   if -1.9e-38 < a < -2.29999999999999997e-208 or -2.79999999999999975e-262 < a < 3.1999999999999999e-239 or 2.69999999999999988e-185 < a < 3.00000000000000006e25

   1. Initial program 59.1%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in y around inf 58.8%

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

      1. div-sub 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in a around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. neg-mul-1 55.6%

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

   10. Simplified 55.6%

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

   if -2.29999999999999997e-208 < a < -2.79999999999999975e-262

   1. Initial program 51.7%

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

      1. associate-*l/ 43.1%

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

   3. Simplified 43.1%

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

   5. Taylor expanded in y around 0 33.1%

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

      1. mul-1-neg 33.1%

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

      2. unsub-neg 33.1%

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

      3. associate-/l* 23.5%

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

   7. Simplified 23.5%

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

   8. Taylor expanded in t around inf 50.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 50.2%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 50.2%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 50.2%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 50.2%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 50.2%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 50.2%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 50.2%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 50.2%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in t around inf 70.6%

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

       1. distribute-lft-out-- 70.6%

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

       2. mul-1-neg 70.6%

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

       3. *-commutative 70.6%

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

       4. distribute-lft-out-- 70.6%

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

   13. Simplified 70.6%

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

   14. Taylor expanded in a around 0 70.6%

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

       1. associate-/l* 71.0%

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

   16. Simplified 71.0%

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

   if 3.1999999999999999e-239 < a < 2.69999999999999988e-185

   1. Initial program 66.7%

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

   5. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

      3. associate-/l* 51.8%

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

   7. Simplified 51.8%

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

   8. Taylor expanded in t around inf 67.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 67.0%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 67.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 67.0%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 67.0%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 67.0%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 67.0%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 67.0%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in t around inf 67.1%

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

       1. distribute-lft-out-- 67.1%

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

       2. mul-1-neg 67.1%

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

       3. *-commutative 67.1%

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

       4. distribute-lft-out-- 67.3%

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

   13. Simplified 67.3%

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

   14. Taylor expanded in x around inf 67.3%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ t_3 := \frac{z \cdot \left(-x\right)}{a - t}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t)))
        (t_2 (+ x (/ y (/ a z))))
        (t_3 (/ (* z (- x)) (- a t))))
   (if (<= a -2e+164)
     t_2
     (if (<= a -2.1e-43)
       (- x (/ x (/ a z)))
       (if (<= a -1.25e-207)
         t_1
         (if (<= a -2.6e-262)
           t_3
           (if (<= a 4.4e-239)
             t_1
             (if (<= a 2.1e-158) t_3 (if (<= a 2e+26) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y / (a / z));
	double t_3 = (z * -x) / (a - t);
	double tmp;
	if (a <= -2e+164) {
		tmp = t_2;
	} else if (a <= -2.1e-43) {
		tmp = x - (x / (a / z));
	} else if (a <= -1.25e-207) {
		tmp = t_1;
	} else if (a <= -2.6e-262) {
		tmp = t_3;
	} else if (a <= 4.4e-239) {
		tmp = t_1;
	} else if (a <= 2.1e-158) {
		tmp = t_3;
	} else if (a <= 2e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x + (y / (a / z))
    t_3 = (z * -x) / (a - t)
    if (a <= (-2d+164)) then
        tmp = t_2
    else if (a <= (-2.1d-43)) then
        tmp = x - (x / (a / z))
    else if (a <= (-1.25d-207)) then
        tmp = t_1
    else if (a <= (-2.6d-262)) then
        tmp = t_3
    else if (a <= 4.4d-239) then
        tmp = t_1
    else if (a <= 2.1d-158) then
        tmp = t_3
    else if (a <= 2d+26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x + (y / (a / z));
	double t_3 = (z * -x) / (a - t);
	double tmp;
	if (a <= -2e+164) {
		tmp = t_2;
	} else if (a <= -2.1e-43) {
		tmp = x - (x / (a / z));
	} else if (a <= -1.25e-207) {
		tmp = t_1;
	} else if (a <= -2.6e-262) {
		tmp = t_3;
	} else if (a <= 4.4e-239) {
		tmp = t_1;
	} else if (a <= 2.1e-158) {
		tmp = t_3;
	} else if (a <= 2e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x + (y / (a / z))
	t_3 = (z * -x) / (a - t)
	tmp = 0
	if a <= -2e+164:
		tmp = t_2
	elif a <= -2.1e-43:
		tmp = x - (x / (a / z))
	elif a <= -1.25e-207:
		tmp = t_1
	elif a <= -2.6e-262:
		tmp = t_3
	elif a <= 4.4e-239:
		tmp = t_1
	elif a <= 2.1e-158:
		tmp = t_3
	elif a <= 2e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	t_3 = Float64(Float64(z * Float64(-x)) / Float64(a - t))
	tmp = 0.0
	if (a <= -2e+164)
		tmp = t_2;
	elseif (a <= -2.1e-43)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (a <= -1.25e-207)
		tmp = t_1;
	elseif (a <= -2.6e-262)
		tmp = t_3;
	elseif (a <= 4.4e-239)
		tmp = t_1;
	elseif (a <= 2.1e-158)
		tmp = t_3;
	elseif (a <= 2e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x + (y / (a / z));
	t_3 = (z * -x) / (a - t);
	tmp = 0.0;
	if (a <= -2e+164)
		tmp = t_2;
	elseif (a <= -2.1e-43)
		tmp = x - (x / (a / z));
	elseif (a <= -1.25e-207)
		tmp = t_1;
	elseif (a <= -2.6e-262)
		tmp = t_3;
	elseif (a <= 4.4e-239)
		tmp = t_1;
	elseif (a <= 2.1e-158)
		tmp = t_3;
	elseif (a <= 2e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * (-x)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+164], t$95$2, If[LessEqual[a, -2.1e-43], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-207], t$95$1, If[LessEqual[a, -2.6e-262], t$95$3, If[LessEqual[a, 4.4e-239], t$95$1, If[LessEqual[a, 2.1e-158], t$95$3, If[LessEqual[a, 2e+26], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2e164 or 2.0000000000000001e26 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 63.4%

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

   6. Taylor expanded in y around inf 60.5%

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

      1. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   if -2e164 < a < -2.1000000000000001e-43

   1. Initial program 68.5%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 52.5%

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

   6. Taylor expanded in y around 0 44.2%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.2%

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

      2. sub-neg 44.2%

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

      3. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

   if -2.1000000000000001e-43 < a < -1.25000000000000004e-207 or -2.5999999999999999e-262 < a < 4.39999999999999965e-239 or 2.09999999999999991e-158 < a < 2.0000000000000001e26

   1. Initial program 59.0%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around inf 59.7%

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

      1. div-sub 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in a around 0 56.2%

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

      1. associate-*r/ 56.2%

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

      2. neg-mul-1 56.2%

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

   10. Simplified 56.2%

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

   if -1.25000000000000004e-207 < a < -2.5999999999999999e-262 or 4.39999999999999965e-239 < a < 2.09999999999999991e-158

   1. Initial program 60.2%

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

      1. associate-*l/ 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

      3. associate-/l* 36.0%

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

   7. Simplified 36.0%

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

   8. Taylor expanded in z around inf 71.3%

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

      1. associate-*r/ 71.3%

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

      2. associate-*r* 71.3%

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

      3. neg-mul-1 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{a - t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{a - t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+45} \lor \neg \left(t \leq 3.2 \cdot 10^{+127}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.2e-60)
     t_1
     (if (<= t 2.25e-277)
       (- x (/ x (/ a z)))
       (if (<= t 5.5e-127)
         (+ x (/ y (/ a z)))
         (if (<= t 1.22e-36)
           (* x (- 1.0 (/ z a)))
           (if (or (<= t 4.8e+45) (not (<= t 3.2e+127)))
             t_1
             (/ (* x (- z a)) t))))))))

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 <= -3.2e-60) {
		tmp = t_1;
	} else if (t <= 2.25e-277) {
		tmp = x - (x / (a / z));
	} else if (t <= 5.5e-127) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.22e-36) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 4.8e+45) || !(t <= 3.2e+127)) {
		tmp = t_1;
	} else {
		tmp = (x * (z - 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 = y * ((z - t) / (a - t))
    if (t <= (-3.2d-60)) then
        tmp = t_1
    else if (t <= 2.25d-277) then
        tmp = x - (x / (a / z))
    else if (t <= 5.5d-127) then
        tmp = x + (y / (a / z))
    else if (t <= 1.22d-36) then
        tmp = x * (1.0d0 - (z / a))
    else if ((t <= 4.8d+45) .or. (.not. (t <= 3.2d+127))) then
        tmp = t_1
    else
        tmp = (x * (z - 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.2e-60) {
		tmp = t_1;
	} else if (t <= 2.25e-277) {
		tmp = x - (x / (a / z));
	} else if (t <= 5.5e-127) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.22e-36) {
		tmp = x * (1.0 - (z / a));
	} else if ((t <= 4.8e+45) || !(t <= 3.2e+127)) {
		tmp = t_1;
	} else {
		tmp = (x * (z - a)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.2e-60:
		tmp = t_1
	elif t <= 2.25e-277:
		tmp = x - (x / (a / z))
	elif t <= 5.5e-127:
		tmp = x + (y / (a / z))
	elif t <= 1.22e-36:
		tmp = x * (1.0 - (z / a))
	elif (t <= 4.8e+45) or not (t <= 3.2e+127):
		tmp = t_1
	else:
		tmp = (x * (z - a)) / t
	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 <= -3.2e-60)
		tmp = t_1;
	elseif (t <= 2.25e-277)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 5.5e-127)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.22e-36)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((t <= 4.8e+45) || !(t <= 3.2e+127))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	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 <= -3.2e-60)
		tmp = t_1;
	elseif (t <= 2.25e-277)
		tmp = x - (x / (a / z));
	elseif (t <= 5.5e-127)
		tmp = x + (y / (a / z));
	elseif (t <= 1.22e-36)
		tmp = x * (1.0 - (z / a));
	elseif ((t <= 4.8e+45) || ~((t <= 3.2e+127)))
		tmp = t_1;
	else
		tmp = (x * (z - a)) / t;
	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, -3.2e-60], t$95$1, If[LessEqual[t, 2.25e-277], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-127], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-36], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.8e+45], N[Not[LessEqual[t, 3.2e+127]], $MachinePrecision]], t$95$1, N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2000000000000001e-60 or 1.2200000000000001e-36 < t < 4.79999999999999979e45 or 3.19999999999999976e127 < t

   1. Initial program 51.3%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. div-sub 58.3%

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

   7. Simplified 58.3%

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

   if -3.2000000000000001e-60 < t < 2.24999999999999996e-277

   1. Initial program 87.9%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 74.1%

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

   6. Taylor expanded in y around 0 65.2%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   7. Step-by-step derivation

      1. mul-1-neg 65.2%

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

      2. sub-neg 65.2%

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

      3. associate-/l* 74.5%

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

   8. Simplified 74.5%

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

   if 2.24999999999999996e-277 < t < 5.50000000000000036e-127

   1. Initial program 96.5%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 78.4%

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

   6. Taylor expanded in y around inf 64.8%

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

      1. associate-/l* 71.8%

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

   8. Simplified 71.8%

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

   if 5.50000000000000036e-127 < t < 1.2200000000000001e-36

   1. Initial program 77.7%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 60.4%

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

   6. Taylor expanded in x around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

   8. Simplified 69.5%

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

   if 4.79999999999999979e45 < t < 3.19999999999999976e127

   1. Initial program 65.7%

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

      1. associate-*l/ 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in y around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. unsub-neg 59.1%

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

      3. associate-/l* 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in t around inf 43.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 43.6%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 43.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 43.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 43.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 43.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 43.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 43.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in t around inf 59.2%

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

       1. distribute-lft-out-- 59.2%

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

       2. mul-1-neg 59.2%

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

       3. *-commutative 59.2%

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

       4. distribute-lft-out-- 59.2%

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

   13. Simplified 59.2%

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

   14. Taylor expanded in x around inf 59.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+45} \lor \neg \left(t \leq 3.2 \cdot 10^{+127}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-165}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ (- y x) a)))))
   (if (<= a -1.2e-36)
     t_2
     (if (<= a -1.8e-156)
       t_1
       (if (<= a 8e-165)
         (* (- y x) (/ z (- a t)))
         (if (<= a 1.8e-111)
           t_1
           (if (<= a 4e-51) (* z (/ (- y x) (- a t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * ((y - x) / a));
	double tmp;
	if (a <= -1.2e-36) {
		tmp = t_2;
	} else if (a <= -1.8e-156) {
		tmp = t_1;
	} else if (a <= 8e-165) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.8e-111) {
		tmp = t_1;
	} else if (a <= 4e-51) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_2;
	}
	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 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * ((y - x) / a))
    if (a <= (-1.2d-36)) then
        tmp = t_2
    else if (a <= (-1.8d-156)) then
        tmp = t_1
    else if (a <= 8d-165) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.8d-111) then
        tmp = t_1
    else if (a <= 4d-51) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * ((y - x) / a));
	double tmp;
	if (a <= -1.2e-36) {
		tmp = t_2;
	} else if (a <= -1.8e-156) {
		tmp = t_1;
	} else if (a <= 8e-165) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.8e-111) {
		tmp = t_1;
	} else if (a <= 4e-51) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * ((y - x) / a))
	tmp = 0
	if a <= -1.2e-36:
		tmp = t_2
	elif a <= -1.8e-156:
		tmp = t_1
	elif a <= 8e-165:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.8e-111:
		tmp = t_1
	elif a <= 4e-51:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -1.2e-36)
		tmp = t_2;
	elseif (a <= -1.8e-156)
		tmp = t_1;
	elseif (a <= 8e-165)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.8e-111)
		tmp = t_1;
	elseif (a <= 4e-51)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * ((y - x) / a));
	tmp = 0.0;
	if (a <= -1.2e-36)
		tmp = t_2;
	elseif (a <= -1.8e-156)
		tmp = t_1;
	elseif (a <= 8e-165)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.8e-111)
		tmp = t_1;
	elseif (a <= 4e-51)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-36], t$95$2, If[LessEqual[a, -1.8e-156], t$95$1, If[LessEqual[a, 8e-165], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-111], t$95$1, If[LessEqual[a, 4e-51], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2e-36 or 4e-51 < a

   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/ 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 75.1%

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

   if -1.2e-36 < a < -1.79999999999999999e-156 or 8.0000000000000001e-165 < a < 1.80000000000000005e-111

   1. Initial program 58.3%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   7. Simplified 71.5%

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

   if -1.79999999999999999e-156 < a < 8.0000000000000001e-165

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-*l/ 68.2%

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

      3. fma-def 68.1%

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

   3. Simplified 68.1%

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

      1. fma-udef 68.2%

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

      2. *-commutative 68.2%

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

      3. clear-num 68.0%

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

      4. un-div-inv 68.2%

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

   6. Applied egg-rr 68.2%

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

   7. Taylor expanded in z around -inf 66.2%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in z around 0 66.2%

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

       1. associate-*l/ 70.6%

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

   12. Simplified 70.6%

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

   if 1.80000000000000005e-111 < a < 4e-51

   1. Initial program 34.5%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 70.8%

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

      1. div-sub 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-36}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-165}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{-135} \lor \neg \left(a \leq 1.45 \cdot 10^{-134} \lor \neg \left(a \leq 2.1 \cdot 10^{-34}\right) \land a \leq 7.5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.6e-135)
         (not (or (<= a 1.45e-134) (and (not (<= a 2.1e-34)) (<= a 7.5e+43)))))
   (+ x (* (- z t) (/ (- y x) (- a t))))
   (+ y (/ (* (- y x) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.6e-135) || !((a <= 1.45e-134) || (!(a <= 2.1e-34) && (a <= 7.5e+43)))) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / 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) :: tmp
    if ((a <= (-9.6d-135)) .or. (.not. (a <= 1.45d-134) .or. (.not. (a <= 2.1d-34)) .and. (a <= 7.5d+43))) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    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 <= -9.6e-135) || !((a <= 1.45e-134) || (!(a <= 2.1e-34) && (a <= 7.5e+43)))) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.6e-135) or not ((a <= 1.45e-134) or (not (a <= 2.1e-34) and (a <= 7.5e+43))):
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.6e-135) || !((a <= 1.45e-134) || (!(a <= 2.1e-34) && (a <= 7.5e+43))))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.6e-135) || ~(((a <= 1.45e-134) || (~((a <= 2.1e-34)) && (a <= 7.5e+43)))))
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.6e-135], N[Not[Or[LessEqual[a, 1.45e-134], And[N[Not[LessEqual[a, 2.1e-34]], $MachinePrecision], LessEqual[a, 7.5e+43]]]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.5999999999999994e-135 or 1.44999999999999997e-134 < a < 2.1000000000000001e-34 or 7.49999999999999967e43 < a

   1. Initial program 67.6%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   if -9.5999999999999994e-135 < a < 1.44999999999999997e-134 or 2.1000000000000001e-34 < a < 7.49999999999999967e43

   1. Initial program 61.8%

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

      1. associate-*l/ 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in t around inf 84.3%

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

      1. associate--l+ 84.3%

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

      2. distribute-lft-out-- 84.3%

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

      3. div-sub 84.3%

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

      4. mul-1-neg 84.3%

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

      5. unsub-neg 84.3%

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

      6. distribute-rgt-out-- 84.3%

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

   7. Simplified 84.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{-135} \lor \neg \left(a \leq 1.45 \cdot 10^{-134} \lor \neg \left(a \leq 2.1 \cdot 10^{-34}\right) \land a \leq 7.5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.8e+179)
     y
     (if (<= t -1.32e+70)
       (/ z (/ t x))
       (if (<= t -1.75e+35)
         (+ x y)
         (if (<= t 2.1e-36)
           t_1
           (if (<= t 4.2e-11)
             (* y (/ z (- a t)))
             (if (<= t 4.8e+130) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.8e+179) {
		tmp = y;
	} else if (t <= -1.32e+70) {
		tmp = z / (t / x);
	} else if (t <= -1.75e+35) {
		tmp = x + y;
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 4.2e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.8e+130) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-7.8d+179)) then
        tmp = y
    else if (t <= (-1.32d+70)) then
        tmp = z / (t / x)
    else if (t <= (-1.75d+35)) then
        tmp = x + y
    else if (t <= 2.1d-36) then
        tmp = t_1
    else if (t <= 4.2d-11) then
        tmp = y * (z / (a - t))
    else if (t <= 4.8d+130) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.8e+179) {
		tmp = y;
	} else if (t <= -1.32e+70) {
		tmp = z / (t / x);
	} else if (t <= -1.75e+35) {
		tmp = x + y;
	} else if (t <= 2.1e-36) {
		tmp = t_1;
	} else if (t <= 4.2e-11) {
		tmp = y * (z / (a - t));
	} else if (t <= 4.8e+130) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -7.8e+179:
		tmp = y
	elif t <= -1.32e+70:
		tmp = z / (t / x)
	elif t <= -1.75e+35:
		tmp = x + y
	elif t <= 2.1e-36:
		tmp = t_1
	elif t <= 4.2e-11:
		tmp = y * (z / (a - t))
	elif t <= 4.8e+130:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -7.8e+179)
		tmp = y;
	elseif (t <= -1.32e+70)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -1.75e+35)
		tmp = Float64(x + y);
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 4.2e-11)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4.8e+130)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -7.8e+179)
		tmp = y;
	elseif (t <= -1.32e+70)
		tmp = z / (t / x);
	elseif (t <= -1.75e+35)
		tmp = x + y;
	elseif (t <= 2.1e-36)
		tmp = t_1;
	elseif (t <= 4.2e-11)
		tmp = y * (z / (a - t));
	elseif (t <= 4.8e+130)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+179], y, If[LessEqual[t, -1.32e+70], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e+35], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.1e-36], t$95$1, If[LessEqual[t, 4.2e-11], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+130], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.79999999999999947e179 or 4.80000000000000048e130 < 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/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in t around inf 61.5%

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

   if -7.79999999999999947e179 < t < -1.3199999999999999e70

   1. Initial program 46.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. unsub-neg 30.5%

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

      3. associate-/l* 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 32.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 26.7%

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

       1. *-commutative 26.7%

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

       2. associate-/l* 41.6%

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

   13. Simplified 41.6%

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

   if -1.3199999999999999e70 < t < -1.75e35

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

      1. fma-udef 78.6%

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

      2. *-commutative 78.6%

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

      3. clear-num 78.6%

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

      4. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 78.5%

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

   8. Taylor expanded in t around inf 57.1%

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

   if -1.75e35 < t < 2.09999999999999991e-36 or 4.1999999999999997e-11 < t < 4.80000000000000048e130

   1. Initial program 83.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in t around 0 63.1%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   8. Simplified 59.2%

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

   if 2.09999999999999991e-36 < t < 4.1999999999999997e-11

   1. Initial program 71.3%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 80.4%

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

      1. div-sub 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in z around inf 70.5%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -9.7 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+140}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -9.7e+179)
     t_1
     (if (<= t -6.2e+74)
       (* z (/ (- y x) (- a t)))
       (if (<= t -1.7e-46)
         t_1
         (if (<= t 2.15e-36)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 1.3e+140) (* (- y x) (/ z (- a t))) t_1)))))))

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 <= -9.7e+179) {
		tmp = t_1;
	} else if (t <= -6.2e+74) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.7e-46) {
		tmp = t_1;
	} else if (t <= 2.15e-36) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.3e+140) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-9.7d+179)) then
        tmp = t_1
    else if (t <= (-6.2d+74)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-1.7d-46)) then
        tmp = t_1
    else if (t <= 2.15d-36) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 1.3d+140) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -9.7e+179) {
		tmp = t_1;
	} else if (t <= -6.2e+74) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.7e-46) {
		tmp = t_1;
	} else if (t <= 2.15e-36) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.3e+140) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -9.7e+179:
		tmp = t_1
	elif t <= -6.2e+74:
		tmp = z * ((y - x) / (a - t))
	elif t <= -1.7e-46:
		tmp = t_1
	elif t <= 2.15e-36:
		tmp = x + (z / (a / (y - x)))
	elif t <= 1.3e+140:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	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 <= -9.7e+179)
		tmp = t_1;
	elseif (t <= -6.2e+74)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -1.7e-46)
		tmp = t_1;
	elseif (t <= 2.15e-36)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 1.3e+140)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	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 <= -9.7e+179)
		tmp = t_1;
	elseif (t <= -6.2e+74)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -1.7e-46)
		tmp = t_1;
	elseif (t <= 2.15e-36)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 1.3e+140)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_1;
	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, -9.7e+179], t$95$1, If[LessEqual[t, -6.2e+74], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-46], t$95$1, If[LessEqual[t, 2.15e-36], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+140], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.69999999999999954e179 or -6.20000000000000043e74 < t < -1.69999999999999998e-46 or 1.3000000000000001e140 < t

   1. Initial program 47.1%

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

   5. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   7. Simplified 65.6%

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

   if -9.69999999999999954e179 < t < -6.20000000000000043e74

   1. Initial program 48.5%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 51.6%

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

      1. div-sub 51.6%

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

   7. Simplified 51.6%

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

   if -1.69999999999999998e-46 < t < 2.1500000000000001e-36

   1. Initial program 85.9%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around 0 69.1%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if 2.1500000000000001e-36 < t < 1.3000000000000001e140

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.6%

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

   3. Simplified 73.6%

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

      1. fma-udef 73.2%

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

      2. *-commutative 73.2%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.0%

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

   6. Applied egg-rr 73.0%

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

   7. Taylor expanded in z around -inf 57.0%

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

      1. associate-/l* 64.4%

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

   9. Simplified 64.4%

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

   10. Taylor expanded in z around 0 57.0%

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

       1. associate-*l/ 67.2%

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

   12. Simplified 67.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+140}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-165}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -6e-37)
     (+ x (/ z (/ a (- y x))))
     (if (<= a -2.7e-156)
       t_1
       (if (<= a 7e-165)
         (* (- y x) (/ z (- a t)))
         (if (<= a 1.25e-108)
           t_1
           (if (<= a 1.4e+26)
             (* z (/ (- y x) (- a t)))
             (+ x (/ y (/ a (- z t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6e-37) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.7e-156) {
		tmp = t_1;
	} else if (a <= 7e-165) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.25e-108) {
		tmp = t_1;
	} else if (a <= 1.4e+26) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / (a / (z - 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 = y * ((z - t) / (a - t))
    if (a <= (-6d-37)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-2.7d-156)) then
        tmp = t_1
    else if (a <= 7d-165) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.25d-108) then
        tmp = t_1
    else if (a <= 1.4d+26) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (y / (a / (z - 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 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -6e-37) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.7e-156) {
		tmp = t_1;
	} else if (a <= 7e-165) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.25e-108) {
		tmp = t_1;
	} else if (a <= 1.4e+26) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -6e-37:
		tmp = x + (z / (a / (y - x)))
	elif a <= -2.7e-156:
		tmp = t_1
	elif a <= 7e-165:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.25e-108:
		tmp = t_1
	elif a <= 1.4e+26:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (y / (a / (z - t)))
	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 (a <= -6e-37)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -2.7e-156)
		tmp = t_1;
	elseif (a <= 7e-165)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.25e-108)
		tmp = t_1;
	elseif (a <= 1.4e+26)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	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 (a <= -6e-37)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -2.7e-156)
		tmp = t_1;
	elseif (a <= 7e-165)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.25e-108)
		tmp = t_1;
	elseif (a <= 1.4e+26)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (y / (a / (z - t)));
	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[a, -6e-37], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-156], t$95$1, If[LessEqual[a, 7e-165], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-108], t$95$1, If[LessEqual[a, 1.4e+26], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6e-37

   1. Initial program 70.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around 0 59.9%

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

      1. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   if -6e-37 < a < -2.70000000000000012e-156 or 7.0000000000000003e-165 < a < 1.25e-108

   1. Initial program 58.3%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   7. Simplified 71.5%

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

   if -2.70000000000000012e-156 < a < 7.0000000000000003e-165

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-*l/ 68.2%

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

      3. fma-def 68.1%

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

   3. Simplified 68.1%

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

      1. fma-udef 68.2%

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

      2. *-commutative 68.2%

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

      3. clear-num 68.0%

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

      4. un-div-inv 68.2%

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

   6. Applied egg-rr 68.2%

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

   7. Taylor expanded in z around -inf 66.2%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in z around 0 66.2%

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

       1. associate-*l/ 70.6%

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

   12. Simplified 70.6%

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

   if 1.25e-108 < a < 1.4e26

   1. Initial program 51.5%

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

      1. associate-*l/ 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in z around inf 51.9%

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

      1. div-sub 51.9%

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

   7. Simplified 51.9%

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

   if 1.4e26 < a

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-*l/ 86.7%

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

      3. fma-def 86.9%

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

   3. Simplified 86.9%

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

      1. fma-udef 86.7%

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

      2. *-commutative 86.7%

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

      3. clear-num 86.5%

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

      4. un-div-inv 86.5%

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

   6. Applied egg-rr 86.5%

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

   7. Taylor expanded in y around inf 79.6%

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

   8. Taylor expanded in a around inf 68.4%

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

      1. associate-/l* 71.4%

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

   10. Simplified 71.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-165}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-163}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -1.35e-36)
     (+ x (/ z (/ a (- y x))))
     (if (<= a -2.05e-156)
       t_1
       (if (<= a 8.5e-163)
         (* (- y x) (/ z (- a t)))
         (if (<= a 4.5e-113)
           t_1
           (if (<= a 2.15e+26)
             (* z (/ (- y x) (- a t)))
             (+ x (/ (- z t) (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.35e-36) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.05e-156) {
		tmp = t_1;
	} else if (a <= 8.5e-163) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4.5e-113) {
		tmp = t_1;
	} else if (a <= 2.15e+26) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + ((z - t) / (a / 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-1.35d-36)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-2.05d-156)) then
        tmp = t_1
    else if (a <= 8.5d-163) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 4.5d-113) then
        tmp = t_1
    else if (a <= 2.15d+26) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + ((z - t) / (a / y))
    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 (a <= -1.35e-36) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -2.05e-156) {
		tmp = t_1;
	} else if (a <= 8.5e-163) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4.5e-113) {
		tmp = t_1;
	} else if (a <= 2.15e+26) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -1.35e-36:
		tmp = x + (z / (a / (y - x)))
	elif a <= -2.05e-156:
		tmp = t_1
	elif a <= 8.5e-163:
		tmp = (y - x) * (z / (a - t))
	elif a <= 4.5e-113:
		tmp = t_1
	elif a <= 2.15e+26:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + ((z - t) / (a / y))
	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 (a <= -1.35e-36)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -2.05e-156)
		tmp = t_1;
	elseif (a <= 8.5e-163)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 4.5e-113)
		tmp = t_1;
	elseif (a <= 2.15e+26)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	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 (a <= -1.35e-36)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -2.05e-156)
		tmp = t_1;
	elseif (a <= 8.5e-163)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 4.5e-113)
		tmp = t_1;
	elseif (a <= 2.15e+26)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + ((z - t) / (a / y));
	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[a, -1.35e-36], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-156], t$95$1, If[LessEqual[a, 8.5e-163], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-113], t$95$1, If[LessEqual[a, 2.15e+26], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35000000000000004e-36

   1. Initial program 70.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around 0 59.9%

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

      1. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   if -1.35000000000000004e-36 < a < -2.0500000000000001e-156 or 8.5e-163 < a < 4.5000000000000001e-113

   1. Initial program 58.3%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   7. Simplified 71.5%

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

   if -2.0500000000000001e-156 < a < 8.5e-163

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-*l/ 68.2%

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

      3. fma-def 68.1%

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

   3. Simplified 68.1%

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

      1. fma-udef 68.2%

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

      2. *-commutative 68.2%

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

      3. clear-num 68.0%

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

      4. un-div-inv 68.2%

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

   6. Applied egg-rr 68.2%

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

   7. Taylor expanded in z around -inf 66.2%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in z around 0 66.2%

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

       1. associate-*l/ 70.6%

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

   12. Simplified 70.6%

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

   if 4.5000000000000001e-113 < a < 2.1499999999999999e26

   1. Initial program 51.5%

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

      1. associate-*l/ 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in z around inf 51.9%

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

      1. div-sub 51.9%

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

   7. Simplified 51.9%

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

   if 2.1499999999999999e26 < a

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. associate-*l/ 86.7%

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

      3. fma-def 86.9%

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

   3. Simplified 86.9%

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

      1. fma-udef 86.7%

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

      2. *-commutative 86.7%

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

      3. clear-num 86.5%

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

      4. un-div-inv 86.5%

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

   6. Applied egg-rr 86.5%

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

   7. Taylor expanded in y around inf 79.6%

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

   8. Taylor expanded in a around inf 73.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-163}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* (- y x) (- a z)) t))))
   (if (<= a -3.9e-56)
     (+ x (/ (- y x) (/ a (- z t))))
     (if (<= a 6.4e-109)
       t_1
       (if (<= a 2.2e-34)
         (* z (/ (- y x) (- a t)))
         (if (<= a 8e+43) t_1 (- x (/ (- t z) (/ (- a t) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (a <= -3.9e-56) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (a <= 6.4e-109) {
		tmp = t_1;
	} else if (a <= 2.2e-34) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 8e+43) {
		tmp = t_1;
	} else {
		tmp = x - ((t - z) / ((a - t) / 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) :: t_1
    real(8) :: tmp
    t_1 = y + (((y - x) * (a - z)) / t)
    if (a <= (-3.9d-56)) then
        tmp = x + ((y - x) / (a / (z - t)))
    else if (a <= 6.4d-109) then
        tmp = t_1
    else if (a <= 2.2d-34) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 8d+43) then
        tmp = t_1
    else
        tmp = x - ((t - z) / ((a - t) / y))
    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 + (((y - x) * (a - z)) / t);
	double tmp;
	if (a <= -3.9e-56) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (a <= 6.4e-109) {
		tmp = t_1;
	} else if (a <= 2.2e-34) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 8e+43) {
		tmp = t_1;
	} else {
		tmp = x - ((t - z) / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) * (a - z)) / t)
	tmp = 0
	if a <= -3.9e-56:
		tmp = x + ((y - x) / (a / (z - t)))
	elif a <= 6.4e-109:
		tmp = t_1
	elif a <= 2.2e-34:
		tmp = z * ((y - x) / (a - t))
	elif a <= 8e+43:
		tmp = t_1
	else:
		tmp = x - ((t - z) / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t))
	tmp = 0.0
	if (a <= -3.9e-56)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	elseif (a <= 6.4e-109)
		tmp = t_1;
	elseif (a <= 2.2e-34)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 8e+43)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) * (a - z)) / t);
	tmp = 0.0;
	if (a <= -3.9e-56)
		tmp = x + ((y - x) / (a / (z - t)));
	elseif (a <= 6.4e-109)
		tmp = t_1;
	elseif (a <= 2.2e-34)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 8e+43)
		tmp = t_1;
	else
		tmp = x - ((t - z) / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e-56], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-109], t$95$1, If[LessEqual[a, 2.2e-34], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+43], t$95$1, N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.9e-56

   1. Initial program 68.3%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in a around inf 63.8%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if -3.9e-56 < a < 6.4000000000000003e-109 or 2.1999999999999999e-34 < a < 8.00000000000000011e43

   1. Initial program 61.7%

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

      1. associate-*l/ 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in t around inf 81.4%

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

      1. associate--l+ 81.4%

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

      2. distribute-lft-out-- 81.4%

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

      3. div-sub 81.4%

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

      4. mul-1-neg 81.4%

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

      5. unsub-neg 81.4%

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

      6. distribute-rgt-out-- 81.4%

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

   7. Simplified 81.4%

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

   if 6.4000000000000003e-109 < a < 2.1999999999999999e-34

   1. Initial program 53.0%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around inf 63.8%

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

      1. div-sub 63.8%

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

   7. Simplified 63.8%

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

   if 8.00000000000000011e43 < a

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-*l/ 90.4%

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

      3. fma-def 90.7%

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

   3. Simplified 90.7%

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

      1. fma-udef 90.4%

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

      2. *-commutative 90.4%

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

      3. clear-num 90.2%

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

      4. un-div-inv 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 84.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-109}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+43}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+139}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -8.8e+177)
     t_1
     (if (<= t -1.25e-48)
       (- x (/ (- t z) (/ (- a t) y)))
       (if (<= t 2.15e-36)
         (+ x (/ (- y x) (/ a (- z t))))
         (if (<= t 9.4e+139) (* (- y x) (/ z (- a t))) t_1))))))

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 <= -8.8e+177) {
		tmp = t_1;
	} else if (t <= -1.25e-48) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if (t <= 2.15e-36) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 9.4e+139) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-8.8d+177)) then
        tmp = t_1
    else if (t <= (-1.25d-48)) then
        tmp = x - ((t - z) / ((a - t) / y))
    else if (t <= 2.15d-36) then
        tmp = x + ((y - x) / (a / (z - t)))
    else if (t <= 9.4d+139) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.8e+177) {
		tmp = t_1;
	} else if (t <= -1.25e-48) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if (t <= 2.15e-36) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 9.4e+139) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -8.8e+177:
		tmp = t_1
	elif t <= -1.25e-48:
		tmp = x - ((t - z) / ((a - t) / y))
	elif t <= 2.15e-36:
		tmp = x + ((y - x) / (a / (z - t)))
	elif t <= 9.4e+139:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	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 <= -8.8e+177)
		tmp = t_1;
	elseif (t <= -1.25e-48)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	elseif (t <= 2.15e-36)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	elseif (t <= 9.4e+139)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	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 <= -8.8e+177)
		tmp = t_1;
	elseif (t <= -1.25e-48)
		tmp = x - ((t - z) / ((a - t) / y));
	elseif (t <= 2.15e-36)
		tmp = x + ((y - x) / (a / (z - t)));
	elseif (t <= 9.4e+139)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_1;
	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, -8.8e+177], t$95$1, If[LessEqual[t, -1.25e-48], N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-36], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.4e+139], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.7999999999999992e177 or 9.4000000000000002e139 < t

   1. Initial program 34.0%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. div-sub 68.0%

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

   7. Simplified 68.0%

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

   if -8.7999999999999992e177 < t < -1.25e-48

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-*l/ 82.8%

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

      3. fma-def 82.7%

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

   3. Simplified 82.7%

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

      1. fma-udef 82.8%

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

      2. *-commutative 82.8%

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

      3. clear-num 82.6%

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

      4. un-div-inv 82.5%

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

   6. Applied egg-rr 82.5%

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

   7. Taylor expanded in y around inf 66.8%

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

   if -1.25e-48 < t < 2.1500000000000001e-36

   1. Initial program 85.9%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 75.2%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 2.1500000000000001e-36 < t < 9.4000000000000002e139

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.6%

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

   3. Simplified 73.6%

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

      1. fma-udef 73.2%

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

      2. *-commutative 73.2%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.0%

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

   6. Applied egg-rr 73.0%

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

   7. Taylor expanded in z around -inf 57.0%

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

      1. associate-/l* 64.4%

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

   9. Simplified 64.4%

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

   10. Taylor expanded in z around 0 57.0%

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

       1. associate-*l/ 67.2%

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

   12. Simplified 67.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+139}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+180}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.95e+180)
   y
   (if (<= t -4.8e+69)
     (/ z (/ t x))
     (if (<= t -5.6e+33)
       (+ x y)
       (if (<= t 3.3e+131) (* x (- 1.0 (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.95e+180) {
		tmp = y;
	} else if (t <= -4.8e+69) {
		tmp = z / (t / x);
	} else if (t <= -5.6e+33) {
		tmp = x + y;
	} else if (t <= 3.3e+131) {
		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 <= (-2.95d+180)) then
        tmp = y
    else if (t <= (-4.8d+69)) then
        tmp = z / (t / x)
    else if (t <= (-5.6d+33)) then
        tmp = x + y
    else if (t <= 3.3d+131) 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 <= -2.95e+180) {
		tmp = y;
	} else if (t <= -4.8e+69) {
		tmp = z / (t / x);
	} else if (t <= -5.6e+33) {
		tmp = x + y;
	} else if (t <= 3.3e+131) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.95e+180:
		tmp = y
	elif t <= -4.8e+69:
		tmp = z / (t / x)
	elif t <= -5.6e+33:
		tmp = x + y
	elif t <= 3.3e+131:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.95e+180)
		tmp = y;
	elseif (t <= -4.8e+69)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -5.6e+33)
		tmp = Float64(x + y);
	elseif (t <= 3.3e+131)
		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 <= -2.95e+180)
		tmp = y;
	elseif (t <= -4.8e+69)
		tmp = z / (t / x);
	elseif (t <= -5.6e+33)
		tmp = x + y;
	elseif (t <= 3.3e+131)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.95e+180], y, If[LessEqual[t, -4.8e+69], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e+33], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.3e+131], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9500000000000001e180 or 3.2999999999999998e131 < 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/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in t around inf 61.5%

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

   if -2.9500000000000001e180 < t < -4.8000000000000003e69

   1. Initial program 46.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. unsub-neg 30.5%

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

      3. associate-/l* 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 32.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 32.7%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 26.7%

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

       1. *-commutative 26.7%

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

       2. associate-/l* 41.6%

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

   13. Simplified 41.6%

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

   if -4.8000000000000003e69 < t < -5.6000000000000002e33

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

      1. fma-udef 78.6%

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

      2. *-commutative 78.6%

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

      3. clear-num 78.6%

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

      4. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 78.5%

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

   8. Taylor expanded in t around inf 57.1%

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

   if -5.6000000000000002e33 < t < 3.2999999999999998e131

   1. Initial program 82.4%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in t around 0 61.6%

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

   6. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   8. Simplified 55.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+180}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.9:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -2.05e-54)
     t_1
     (if (<= z -4.2e-191)
       (+ x y)
       (if (<= z 4.9) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.05e-54) {
		tmp = t_1;
	} else if (z <= -4.2e-191) {
		tmp = x + y;
	} else if (z <= 4.9) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (z <= (-2.05d-54)) then
        tmp = t_1
    else if (z <= (-4.2d-191)) then
        tmp = x + y
    else if (z <= 4.9d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.05e-54) {
		tmp = t_1;
	} else if (z <= -4.2e-191) {
		tmp = x + y;
	} else if (z <= 4.9) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -2.05e-54:
		tmp = t_1
	elif z <= -4.2e-191:
		tmp = x + y
	elif z <= 4.9:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.05e-54)
		tmp = t_1;
	elseif (z <= -4.2e-191)
		tmp = Float64(x + y);
	elseif (z <= 4.9)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -2.05e-54)
		tmp = t_1;
	elseif (z <= -4.2e-191)
		tmp = x + y;
	elseif (z <= 4.9)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e-54], t$95$1, If[LessEqual[z, -4.2e-191], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.9], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e-54 or 4.9000000000000004 < z

   1. Initial program 63.3%

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

      1. associate-*l/ 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. div-sub 66.8%

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

   7. Simplified 66.8%

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

   if -2.05e-54 < z < -4.19999999999999971e-191

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-*l/ 80.5%

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

      3. fma-def 80.5%

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

   3. Simplified 80.5%

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

      1. fma-udef 80.5%

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

      2. *-commutative 80.5%

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

      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 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in y around inf 79.4%

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

   8. Taylor expanded in t around inf 63.7%

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

   if -4.19999999999999971e-191 < z < 4.9000000000000004

   1. Initial program 66.6%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. div-sub 50.5%

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

   7. Simplified 50.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.9:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.92:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z (- a t)))))
   (if (<= z -2.05e-54)
     t_1
     (if (<= z -1.18e-191)
       (+ x y)
       (if (<= z 1.92) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double tmp;
	if (z <= -2.05e-54) {
		tmp = t_1;
	} else if (z <= -1.18e-191) {
		tmp = x + y;
	} else if (z <= 1.92) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (z / (a - t))
    if (z <= (-2.05d-54)) then
        tmp = t_1
    else if (z <= (-1.18d-191)) then
        tmp = x + y
    else if (z <= 1.92d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double tmp;
	if (z <= -2.05e-54) {
		tmp = t_1;
	} else if (z <= -1.18e-191) {
		tmp = x + y;
	} else if (z <= 1.92) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z / (a - t))
	tmp = 0
	if z <= -2.05e-54:
		tmp = t_1
	elif z <= -1.18e-191:
		tmp = x + y
	elif z <= 1.92:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.05e-54)
		tmp = t_1;
	elseif (z <= -1.18e-191)
		tmp = Float64(x + y);
	elseif (z <= 1.92)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z / (a - t));
	tmp = 0.0;
	if (z <= -2.05e-54)
		tmp = t_1;
	elseif (z <= -1.18e-191)
		tmp = x + y;
	elseif (z <= 1.92)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e-54], t$95$1, If[LessEqual[z, -1.18e-191], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.92], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e-54 or 1.9199999999999999 < z

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. associate-*l/ 84.5%

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

      3. fma-def 84.6%

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

   3. Simplified 84.6%

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

      1. fma-udef 84.5%

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

      2. *-commutative 84.5%

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

      3. clear-num 84.4%

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

      4. un-div-inv 84.3%

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

   6. Applied egg-rr 84.3%

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

   7. Taylor expanded in z around -inf 54.5%

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

      1. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   10. Taylor expanded in z around 0 54.5%

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

       1. associate-*l/ 68.8%

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

   12. Simplified 68.8%

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

   if -2.05e-54 < z < -1.1799999999999999e-191

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-*l/ 80.5%

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

      3. fma-def 80.5%

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

   3. Simplified 80.5%

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

      1. fma-udef 80.5%

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

      2. *-commutative 80.5%

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

      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 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in y around inf 79.4%

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

   8. Taylor expanded in t around inf 63.7%

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

   if -1.1799999999999999e-191 < z < 1.9199999999999999

   1. Initial program 66.6%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. div-sub 50.5%

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

   7. Simplified 50.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-54}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.92:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+139}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.5e+93)
     t_1
     (if (<= t 2.15e-36)
       (+ x (/ (- y x) (/ a (- z t))))
       (if (<= t 9.2e+139) (* (- y x) (/ z (- a t))) t_1)))))

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 <= -2.5e+93) {
		tmp = t_1;
	} else if (t <= 2.15e-36) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 9.2e+139) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.5d+93)) then
        tmp = t_1
    else if (t <= 2.15d-36) then
        tmp = x + ((y - x) / (a / (z - t)))
    else if (t <= 9.2d+139) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+93) {
		tmp = t_1;
	} else if (t <= 2.15e-36) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 9.2e+139) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.5e+93:
		tmp = t_1
	elif t <= 2.15e-36:
		tmp = x + ((y - x) / (a / (z - t)))
	elif t <= 9.2e+139:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	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 <= -2.5e+93)
		tmp = t_1;
	elseif (t <= 2.15e-36)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	elseif (t <= 9.2e+139)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	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 <= -2.5e+93)
		tmp = t_1;
	elseif (t <= 2.15e-36)
		tmp = x + ((y - x) / (a / (z - t)));
	elseif (t <= 9.2e+139)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_1;
	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, -2.5e+93], t$95$1, If[LessEqual[t, 2.15e-36], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+139], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5000000000000001e93 or 9.2e139 < t

   1. Initial program 35.9%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in y around inf 63.1%

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

      1. div-sub 63.1%

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

   7. Simplified 63.1%

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

   if -2.5000000000000001e93 < t < 2.1500000000000001e-36

   1. Initial program 83.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

   if 2.1500000000000001e-36 < t < 9.2e139

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.6%

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

   3. Simplified 73.6%

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

      1. fma-udef 73.2%

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

      2. *-commutative 73.2%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.0%

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

   6. Applied egg-rr 73.0%

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

   7. Taylor expanded in z around -inf 57.0%

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

      1. associate-/l* 64.4%

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

   9. Simplified 64.4%

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

   10. Taylor expanded in z around 0 57.0%

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

       1. associate-*l/ 67.2%

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

   12. Simplified 67.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+139}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.22e+27)
   x
   (if (<= a -2.8e-156)
     y
     (if (<= a 5.6e-157) (/ x (/ t z)) (if (<= a 1.1e+90) (+ x y) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.22e+27) {
		tmp = x;
	} else if (a <= -2.8e-156) {
		tmp = y;
	} else if (a <= 5.6e-157) {
		tmp = x / (t / z);
	} else if (a <= 1.1e+90) {
		tmp = x + 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 <= (-1.22d+27)) then
        tmp = x
    else if (a <= (-2.8d-156)) then
        tmp = y
    else if (a <= 5.6d-157) then
        tmp = x / (t / z)
    else if (a <= 1.1d+90) then
        tmp = x + 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 <= -1.22e+27) {
		tmp = x;
	} else if (a <= -2.8e-156) {
		tmp = y;
	} else if (a <= 5.6e-157) {
		tmp = x / (t / z);
	} else if (a <= 1.1e+90) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.22e+27:
		tmp = x
	elif a <= -2.8e-156:
		tmp = y
	elif a <= 5.6e-157:
		tmp = x / (t / z)
	elif a <= 1.1e+90:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.22e+27)
		tmp = x;
	elseif (a <= -2.8e-156)
		tmp = y;
	elseif (a <= 5.6e-157)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 1.1e+90)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.22e+27)
		tmp = x;
	elseif (a <= -2.8e-156)
		tmp = y;
	elseif (a <= 5.6e-157)
		tmp = x / (t / z);
	elseif (a <= 1.1e+90)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.22e+27], x, If[LessEqual[a, -2.8e-156], y, If[LessEqual[a, 5.6e-157], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+90], N[(x + y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2200000000000001e27 or 1.09999999999999995e90 < a

   1. Initial program 70.4%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 52.0%

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

   if -1.2200000000000001e27 < a < -2.8000000000000002e-156

   1. Initial program 62.6%

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

      1. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t around inf 45.3%

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

   if -2.8000000000000002e-156 < a < 5.6000000000000002e-157

   1. Initial program 63.9%

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

   5. Taylor expanded in y around 0 32.1%

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

      1. mul-1-neg 32.1%

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

      2. unsub-neg 32.1%

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

      3. associate-/l* 32.1%

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

   7. Simplified 32.1%

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

   8. Taylor expanded in t around inf 37.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 37.3%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 37.3%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 36.1%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in t around inf 46.9%

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

       1. distribute-lft-out-- 46.9%

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

       2. mul-1-neg 46.9%

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

       3. *-commutative 46.9%

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

       4. distribute-lft-out-- 46.9%

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

   13. Simplified 46.9%

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

   14. Taylor expanded in a around 0 45.7%

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

       1. associate-/l* 45.7%

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

   16. Simplified 45.7%

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

   if 5.6000000000000002e-157 < a < 1.09999999999999995e90

   1. Initial program 60.7%

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

      1. +-commutative 60.7%

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

      2. associate-*l/ 73.1%

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

      3. fma-def 73.0%

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

   3. Simplified 73.0%

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

      1. fma-udef 73.1%

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

      2. *-commutative 73.1%

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

      3. clear-num 72.8%

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

      4. un-div-inv 72.9%

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

   6. Applied egg-rr 72.9%

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

   7. Taylor expanded in y around inf 50.4%

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

   8. Taylor expanded in t around inf 37.7%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+26)
   x
   (if (<= a -1.6e-156)
     y
     (if (<= a 3e-157) (/ z (/ t x)) (if (<= a 7.8e+90) (+ x y) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+26) {
		tmp = x;
	} else if (a <= -1.6e-156) {
		tmp = y;
	} else if (a <= 3e-157) {
		tmp = z / (t / x);
	} else if (a <= 7.8e+90) {
		tmp = x + 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 <= (-8.5d+26)) then
        tmp = x
    else if (a <= (-1.6d-156)) then
        tmp = y
    else if (a <= 3d-157) then
        tmp = z / (t / x)
    else if (a <= 7.8d+90) then
        tmp = x + 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 <= -8.5e+26) {
		tmp = x;
	} else if (a <= -1.6e-156) {
		tmp = y;
	} else if (a <= 3e-157) {
		tmp = z / (t / x);
	} else if (a <= 7.8e+90) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+26:
		tmp = x
	elif a <= -1.6e-156:
		tmp = y
	elif a <= 3e-157:
		tmp = z / (t / x)
	elif a <= 7.8e+90:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+26)
		tmp = x;
	elseif (a <= -1.6e-156)
		tmp = y;
	elseif (a <= 3e-157)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 7.8e+90)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+26)
		tmp = x;
	elseif (a <= -1.6e-156)
		tmp = y;
	elseif (a <= 3e-157)
		tmp = z / (t / x);
	elseif (a <= 7.8e+90)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+26], x, If[LessEqual[a, -1.6e-156], y, If[LessEqual[a, 3e-157], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+90], N[(x + y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.5e26 or 7.8000000000000004e90 < a

   1. Initial program 70.4%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 52.0%

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

   if -8.5e26 < a < -1.59999999999999991e-156

   1. Initial program 62.6%

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

      1. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t around inf 45.3%

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

   if -1.59999999999999991e-156 < a < 3e-157

   1. Initial program 63.9%

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

   5. Taylor expanded in y around 0 32.1%

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

      1. mul-1-neg 32.1%

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

      2. unsub-neg 32.1%

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

      3. associate-/l* 32.1%

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

   7. Simplified 32.1%

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

   8. Taylor expanded in t around inf 37.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{a \cdot x}{t} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 37.3%

         \[\leadsto \color{blue}{-1 \cdot \left(\frac{a \cdot x}{t} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right)} - -1 \cdot \frac{x \cdot z}{t} \]

      2. associate-/l* 37.3%

         \[\leadsto -1 \cdot \left(\color{blue}{\frac{a}{\frac{t}{x}}} + \frac{a \cdot \left(-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      3. associate-/l* 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \color{blue}{\frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z\right) - -1 \cdot \left(a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      4. distribute-lft-out-- 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{\color{blue}{-1 \cdot \left(x \cdot z - a \cdot x\right)}}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      5. *-commutative 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - \color{blue}{x \cdot a}\right)}}\right) - -1 \cdot \frac{x \cdot z}{t} \]

      6. associate-*r/ 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      7. mul-1-neg 36.1%

         \[\leadsto -1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{\color{blue}{-x \cdot z}}{t} \]

   10. Simplified 36.1%

       \[\leadsto \color{blue}{-1 \cdot \left(\frac{a}{\frac{t}{x}} + \frac{a}{\frac{{t}^{2}}{-1 \cdot \left(x \cdot z - x \cdot a\right)}}\right) - \frac{-x \cdot z}{t}} \]

   11. Taylor expanded in a around 0 45.7%

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

       1. *-commutative 45.7%

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

       2. associate-/l* 46.0%

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

   13. Simplified 46.0%

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

   if 3e-157 < a < 7.8000000000000004e90

   1. Initial program 60.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 73.1%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 73.1%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. *-commutative 73.1%

         \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} + x \]

      3. clear-num 72.8%

         \[\leadsto \left(z - t\right) \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} + x \]

      4. un-div-inv 72.9%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} + x \]

   6. Applied egg-rr 72.9%

      \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y - x}} + x} \]

   7. Taylor expanded in y around inf 50.4%

      \[\leadsto \frac{z - t}{\color{blue}{\frac{a - t}{y}}} + x \]

   8. Taylor expanded in t around inf 37.7%

      \[\leadsto \color{blue}{y} + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-156}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+26) x (if (<= a 1.9e+26) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+26) {
		tmp = x;
	} else if (a <= 1.9e+26) {
		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 <= (-5.5d+26)) then
        tmp = x
    else if (a <= 1.9d+26) 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 <= -5.5e+26) {
		tmp = x;
	} else if (a <= 1.9e+26) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+26:
		tmp = x
	elif a <= 1.9e+26:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+26)
		tmp = x;
	elseif (a <= 1.9e+26)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e+26)
		tmp = x;
	elseif (a <= 1.9e+26)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+26], x, If[LessEqual[a, 1.9e+26], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999997e26 or 1.9000000000000001e26 < a

   1. Initial program 70.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 49.1%

      \[\leadsto \color{blue}{x} \]

   if -5.4999999999999997e26 < a < 1.9000000000000001e26

   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/ 72.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 72.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 35.5%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.3% 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 65.5%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 79.8%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 79.8%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 25.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 25.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.6% 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 2024010 
(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))))