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

Percentage Accurate: 68.0% → 88.6%

Time: 21.4s

Alternatives: 22

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: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + \left(x + x \cdot \frac{t - z}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-248}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 -1e-197)
     (+ (* y (/ (- z t) (- a t))) (+ x (* x (/ (- t z) (- a t)))))
     (if (<= t_1 2e-248)
       (+ y (/ (* (- y x) (- a z)) t))
       (+ x (/ (- y x) (/ (- a t) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -1e-197) {
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - t))));
	} else if (t_1 <= 2e-248) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (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 = x - (((y - x) * (t - z)) / (a - t))
    if (t_1 <= (-1d-197)) then
        tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - t))))
    else if (t_1 <= 2d-248) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = x + ((y - x) / ((a - t) / (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 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -1e-197) {
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - t))));
	} else if (t_1 <= 2e-248) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -1e-197:
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - t))))
	elif t_1 <= 2e-248:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-197)
		tmp = Float64(Float64(y * Float64(Float64(z - t) / Float64(a - t))) + Float64(x + Float64(x * Float64(Float64(t - z) / Float64(a - t)))));
	elseif (t_1 <= 2e-248)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-197)
		tmp = (y * ((z - t) / (a - t))) + (x + (x * ((t - z) / (a - t))));
	elseif (t_1 <= 2e-248)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-197], N[(N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(x * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-248], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999999e-198

   1. Initial program 68.6%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/r/ 88.4%

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

      3. div-sub 86.7%

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

      4. associate-+l- 93.7%

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

      5. div-inv 92.8%

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

      6. clear-num 92.8%

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

      7. div-inv 92.8%

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

      8. clear-num 92.8%

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

   5. Applied egg-rr 92.8%

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

   if -9.9999999999999999e-198 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999996e-248

   1. Initial program 8.3%

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

      1. associate-*l/ 8.4%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. div-sub 99.6%

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

      5. distribute-lft-out-- 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-neg-frac 99.6%

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

      8. unsub-neg 99.6%

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

      9. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

   if 1.99999999999999996e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.9%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + \left(x + x \cdot \frac{t - z}{a - t}\right)\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{-248}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 2: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-248}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ (- x y) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-197)
       t_2
       (if (<= t_2 2e-248)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 2e+307) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-197) {
		tmp = t_2;
	} else if (t_2 <= 2e-248) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+307) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-197) {
		tmp = t_2;
	} else if (t_2 <= 2e-248) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+307) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * ((x - y) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-197:
		tmp = t_2
	elif t_2 <= 2e-248:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 2e+307:
		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(x - y) / Float64(a - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-197)
		tmp = t_2;
	elseif (t_2 <= 2e-248)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 2e+307)
		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) * ((x - y) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-197)
		tmp = t_2;
	elseif (t_2 <= 2e-248)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 2e+307)
		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[(x - y), $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, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-197], t$95$2, If[LessEqual[t$95$2, 2e-248], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+307], 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))) < -inf.0 or 1.99999999999999997e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 37.3%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999999e-198 or 1.99999999999999996e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 97.7%

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

   if -9.9999999999999999e-198 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999996e-248

   1. Initial program 8.3%

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

      1. associate-*l/ 8.4%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. div-sub 99.6%

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

      5. distribute-lft-out-- 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-neg-frac 99.6%

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

      8. unsub-neg 99.6%

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

      9. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-197}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{-248}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-197} \lor \neg \left(t_1 \leq 2 \cdot 10^{-248}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-197) (not (<= t_1 2e-248)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-197) || !(t_1 <= 2e-248)) {
		tmp = x + ((y - x) / ((a - t) / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-1d-197)) .or. (.not. (t_1 <= 2d-248))) then
        tmp = x + ((y - x) / ((a - t) / (z - 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 t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-197) || !(t_1 <= 2e-248)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-197) or not (t_1 <= 2e-248):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-197) || !(t_1 <= 2e-248))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - 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)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-197) || ~((t_1 <= 2e-248)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-197], N[Not[LessEqual[t$95$1, 2e-248]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - 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 (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999999e-198 or 1.99999999999999996e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   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* 88.7%

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

   3. Simplified 88.7%

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

   if -9.9999999999999999e-198 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999996e-248

   1. Initial program 8.3%

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

      1. associate-*l/ 8.4%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. div-sub 99.6%

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

      5. distribute-lft-out-- 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-neg-frac 99.6%

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

      8. unsub-neg 99.6%

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

      9. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-197} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{-248}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 4: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -2.8e-10)
     t_1
     (if (<= a -4.5e-148)
       (/ 1.0 (/ (/ (- a t) z) (- y x)))
       (if (<= a -2.4e-214)
         (* y (/ (- z t) (- a t)))
         (if (<= a 9.5e-124)
           (+ y (/ (* (- y x) (- a z)) t))
           (if (<= a 2.2e-28)
             (* z (/ (- y x) (- a t)))
             (if (<= a 1.1e-8) y t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -2.8e-10) {
		tmp = t_1;
	} else if (a <= -4.5e-148) {
		tmp = 1.0 / (((a - t) / z) / (y - x));
	} else if (a <= -2.4e-214) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.5e-124) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 2.2e-28) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.1e-8) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (a <= (-2.8d-10)) then
        tmp = t_1
    else if (a <= (-4.5d-148)) then
        tmp = 1.0d0 / (((a - t) / z) / (y - x))
    else if (a <= (-2.4d-214)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 9.5d-124) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (a <= 2.2d-28) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.1d-8) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -2.8e-10) {
		tmp = t_1;
	} else if (a <= -4.5e-148) {
		tmp = 1.0 / (((a - t) / z) / (y - x));
	} else if (a <= -2.4e-214) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.5e-124) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 2.2e-28) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.1e-8) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -2.8e-10:
		tmp = t_1
	elif a <= -4.5e-148:
		tmp = 1.0 / (((a - t) / z) / (y - x))
	elif a <= -2.4e-214:
		tmp = y * ((z - t) / (a - t))
	elif a <= 9.5e-124:
		tmp = y + (((y - x) * (a - z)) / t)
	elif a <= 2.2e-28:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.1e-8:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -2.8e-10)
		tmp = t_1;
	elseif (a <= -4.5e-148)
		tmp = Float64(1.0 / Float64(Float64(Float64(a - t) / z) / Float64(y - x)));
	elseif (a <= -2.4e-214)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 9.5e-124)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (a <= 2.2e-28)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.1e-8)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -2.8e-10)
		tmp = t_1;
	elseif (a <= -4.5e-148)
		tmp = 1.0 / (((a - t) / z) / (y - x));
	elseif (a <= -2.4e-214)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 9.5e-124)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (a <= 2.2e-28)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.1e-8)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-10], t$95$1, If[LessEqual[a, -4.5e-148], N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-214], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-124], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-28], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-8], y, t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.80000000000000015e-10 or 1.0999999999999999e-8 < a

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 83.2%

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

   if -2.80000000000000015e-10 < a < -4.50000000000000015e-148

   1. Initial program 71.1%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around -inf 61.8%

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

      1. clear-num 61.8%

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

      2. inv-pow 61.8%

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

   6. Applied egg-rr 61.8%

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

      1. unpow-1 61.8%

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

      2. associate-/r* 68.2%

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

   8. Simplified 68.2%

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

   if -4.50000000000000015e-148 < a < -2.4000000000000002e-214

   1. Initial program 67.5%

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

      1. associate-/l* 67.6%

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

   3. Simplified 67.6%

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

      1. clear-num 67.4%

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

      2. inv-pow 67.4%

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

   5. Applied egg-rr 67.4%

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

      1. unpow-1 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in x around 0 74.1%

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

      1. associate-*r/ 80.4%

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

   10. Simplified 80.4%

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

   if -2.4000000000000002e-214 < a < 9.49999999999999989e-124

   1. Initial program 67.8%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. associate-*r/ 85.8%

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

      3. associate-*r/ 85.8%

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

      4. div-sub 85.8%

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

      5. distribute-lft-out-- 85.8%

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

      6. mul-1-neg 85.8%

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

      7. distribute-neg-frac 85.8%

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

      8. unsub-neg 85.8%

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

      9. distribute-rgt-out-- 85.8%

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

   6. Simplified 85.8%

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

   if 9.49999999999999989e-124 < a < 2.19999999999999996e-28

   1. Initial program 69.0%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   6. Simplified 79.8%

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

   if 2.19999999999999996e-28 < a < 1.0999999999999999e-8

   1. Initial program 43.7%

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

      1. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.072:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -9.5e-14)
     t_2
     (if (<= z -6.8e-220)
       t_1
       (if (<= z -3.5e-300)
         x
         (if (<= z 1.8e-228)
           t_1
           (if (<= z 1.9e-152) x (if (<= z 0.072) t_1 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 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -9.5e-14) {
		tmp = t_2;
	} else if (z <= -6.8e-220) {
		tmp = t_1;
	} else if (z <= -3.5e-300) {
		tmp = x;
	} else if (z <= 1.8e-228) {
		tmp = t_1;
	} else if (z <= 1.9e-152) {
		tmp = x;
	} else if (z <= 0.072) {
		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 * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-9.5d-14)) then
        tmp = t_2
    else if (z <= (-6.8d-220)) then
        tmp = t_1
    else if (z <= (-3.5d-300)) then
        tmp = x
    else if (z <= 1.8d-228) then
        tmp = t_1
    else if (z <= 1.9d-152) then
        tmp = x
    else if (z <= 0.072d0) 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 * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -9.5e-14) {
		tmp = t_2;
	} else if (z <= -6.8e-220) {
		tmp = t_1;
	} else if (z <= -3.5e-300) {
		tmp = x;
	} else if (z <= 1.8e-228) {
		tmp = t_1;
	} else if (z <= 1.9e-152) {
		tmp = x;
	} else if (z <= 0.072) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -9.5e-14:
		tmp = t_2
	elif z <= -6.8e-220:
		tmp = t_1
	elif z <= -3.5e-300:
		tmp = x
	elif z <= 1.8e-228:
		tmp = t_1
	elif z <= 1.9e-152:
		tmp = x
	elif z <= 0.072:
		tmp = t_1
	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(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -9.5e-14)
		tmp = t_2;
	elseif (z <= -6.8e-220)
		tmp = t_1;
	elseif (z <= -3.5e-300)
		tmp = x;
	elseif (z <= 1.8e-228)
		tmp = t_1;
	elseif (z <= 1.9e-152)
		tmp = x;
	elseif (z <= 0.072)
		tmp = t_1;
	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 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -9.5e-14)
		tmp = t_2;
	elseif (z <= -6.8e-220)
		tmp = t_1;
	elseif (z <= -3.5e-300)
		tmp = x;
	elseif (z <= 1.8e-228)
		tmp = t_1;
	elseif (z <= 1.9e-152)
		tmp = x;
	elseif (z <= 0.072)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-14], t$95$2, If[LessEqual[z, -6.8e-220], t$95$1, If[LessEqual[z, -3.5e-300], x, If[LessEqual[z, 1.8e-228], t$95$1, If[LessEqual[z, 1.9e-152], x, If[LessEqual[z, 0.072], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999999e-14 or 0.0719999999999999946 < z

   1. Initial program 69.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in z around inf 73.3%

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

      1. div-sub 74.1%

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

   6. Simplified 74.1%

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

   if -9.4999999999999999e-14 < z < -6.79999999999999987e-220 or -3.5000000000000002e-300 < z < 1.8000000000000001e-228 or 1.90000000000000006e-152 < z < 0.0719999999999999946

   1. Initial program 64.8%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

      1. clear-num 77.6%

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

      2. inv-pow 77.6%

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

   5. Applied egg-rr 77.6%

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

      1. unpow-1 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in x around 0 49.6%

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

      1. associate-*r/ 61.4%

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

   10. Simplified 61.4%

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

   if -6.79999999999999987e-220 < z < -3.5000000000000002e-300 or 1.8000000000000001e-228 < z < 1.90000000000000006e-152

   1. Initial program 64.2%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in a around inf 59.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.072:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 6: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0033:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= z -5.2e-9)
     (* z (/ (- y x) (- a t)))
     (if (<= z -4.6e-219)
       t_1
       (if (<= z -2.3e-300)
         x
         (if (<= z 4.6e-228)
           t_1
           (if (<= z 1.46e-152)
             x
             (if (<= z 0.0033) t_1 (* (- y 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 (z <= -5.2e-9) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -4.6e-219) {
		tmp = t_1;
	} else if (z <= -2.3e-300) {
		tmp = x;
	} else if (z <= 4.6e-228) {
		tmp = t_1;
	} else if (z <= 1.46e-152) {
		tmp = x;
	} else if (z <= 0.0033) {
		tmp = t_1;
	} else {
		tmp = (y - 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 (z <= (-5.2d-9)) then
        tmp = z * ((y - x) / (a - t))
    else if (z <= (-4.6d-219)) then
        tmp = t_1
    else if (z <= (-2.3d-300)) then
        tmp = x
    else if (z <= 4.6d-228) then
        tmp = t_1
    else if (z <= 1.46d-152) then
        tmp = x
    else if (z <= 0.0033d0) then
        tmp = t_1
    else
        tmp = (y - 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 (z <= -5.2e-9) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -4.6e-219) {
		tmp = t_1;
	} else if (z <= -2.3e-300) {
		tmp = x;
	} else if (z <= 4.6e-228) {
		tmp = t_1;
	} else if (z <= 1.46e-152) {
		tmp = x;
	} else if (z <= 0.0033) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if z <= -5.2e-9:
		tmp = z * ((y - x) / (a - t))
	elif z <= -4.6e-219:
		tmp = t_1
	elif z <= -2.3e-300:
		tmp = x
	elif z <= 4.6e-228:
		tmp = t_1
	elif z <= 1.46e-152:
		tmp = x
	elif z <= 0.0033:
		tmp = t_1
	else:
		tmp = (y - 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 (z <= -5.2e-9)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (z <= -4.6e-219)
		tmp = t_1;
	elseif (z <= -2.3e-300)
		tmp = x;
	elseif (z <= 4.6e-228)
		tmp = t_1;
	elseif (z <= 1.46e-152)
		tmp = x;
	elseif (z <= 0.0033)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - x) * Float64(z / Float64(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 (z <= -5.2e-9)
		tmp = z * ((y - x) / (a - t));
	elseif (z <= -4.6e-219)
		tmp = t_1;
	elseif (z <= -2.3e-300)
		tmp = x;
	elseif (z <= 4.6e-228)
		tmp = t_1;
	elseif (z <= 1.46e-152)
		tmp = x;
	elseif (z <= 0.0033)
		tmp = t_1;
	else
		tmp = (y - 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[z, -5.2e-9], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-219], t$95$1, If[LessEqual[z, -2.3e-300], x, If[LessEqual[z, 4.6e-228], t$95$1, If[LessEqual[z, 1.46e-152], x, If[LessEqual[z, 0.0033], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2000000000000002e-9

   1. Initial program 68.6%

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

      1. associate-*l/ 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in z around inf 67.2%

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

      1. div-sub 67.2%

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

   6. Simplified 67.2%

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

   if -5.2000000000000002e-9 < z < -4.59999999999999977e-219 or -2.30000000000000001e-300 < z < 4.5999999999999998e-228 or 1.46000000000000001e-152 < z < 0.0033

   1. Initial program 64.8%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

      1. clear-num 77.6%

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

      2. inv-pow 77.6%

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

   5. Applied egg-rr 77.6%

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

      1. unpow-1 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in x around 0 49.6%

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

      1. associate-*r/ 61.4%

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

   10. Simplified 61.4%

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

   if -4.59999999999999977e-219 < z < -2.30000000000000001e-300 or 4.5999999999999998e-228 < z < 1.46000000000000001e-152

   1. Initial program 64.2%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in a around inf 59.3%

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

   if 0.0033 < z

   1. Initial program 70.8%

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

      1. +-commutative 88.8%

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

      2. associate-*l/ 70.8%

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

      3. div-inv 70.7%

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

      4. fma-def 70.7%

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

   5. Applied egg-rr 70.7%

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

   6. Taylor expanded in z around -inf 66.6%

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

      1. associate-/l* 80.1%

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

      2. associate-/r/ 81.6%

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

   8. Simplified 81.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0033:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y - x}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+214} \lor \neg \left(t \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;y + \left(\frac{a}{t_1} - \frac{z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- y x))))
   (if (or (<= t -3.1e+214) (not (<= t 2.6e+109)))
     (+ y (- (/ a t_1) (/ z t_1)))
     (+ x (/ (- y x) (/ (- a t) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (y - x);
	double tmp;
	if ((t <= -3.1e+214) || !(t <= 2.6e+109)) {
		tmp = y + ((a / t_1) - (z / t_1));
	} else {
		tmp = x + ((y - x) / ((a - t) / (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 = t / (y - x)
    if ((t <= (-3.1d+214)) .or. (.not. (t <= 2.6d+109))) then
        tmp = y + ((a / t_1) - (z / t_1))
    else
        tmp = x + ((y - x) / ((a - t) / (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 = t / (y - x);
	double tmp;
	if ((t <= -3.1e+214) || !(t <= 2.6e+109)) {
		tmp = y + ((a / t_1) - (z / t_1));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (y - x)
	tmp = 0
	if (t <= -3.1e+214) or not (t <= 2.6e+109):
		tmp = y + ((a / t_1) - (z / t_1))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(y - x))
	tmp = 0.0
	if ((t <= -3.1e+214) || !(t <= 2.6e+109))
		tmp = Float64(y + Float64(Float64(a / t_1) - Float64(z / t_1)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (y - x);
	tmp = 0.0;
	if ((t <= -3.1e+214) || ~((t <= 2.6e+109)))
		tmp = y + ((a / t_1) - (z / t_1));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -3.1e+214], N[Not[LessEqual[t, 2.6e+109]], $MachinePrecision]], N[(y + N[(N[(a / t$95$1), $MachinePrecision] - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.09999999999999979e214 or 2.5999999999999998e109 < t

   1. Initial program 22.6%

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

      1. associate-*l/ 47.8%

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

   3. Simplified 47.8%

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

      1. +-commutative 47.8%

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

      2. associate-*l/ 22.6%

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

      3. div-inv 22.6%

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

      4. fma-def 22.7%

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

   5. Applied egg-rr 22.7%

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

   6. Taylor expanded in t around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/l* 75.1%

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

      5. associate-/l* 85.3%

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

   8. Simplified 85.3%

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

   if -3.09999999999999979e214 < t < 2.5999999999999998e109

   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* 92.1%

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

   3. Simplified 92.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+214} \lor \neg \left(t \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;y + \left(\frac{a}{\frac{t}{y - x}} - \frac{z}{\frac{t}{y - x}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 8: 40.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-225}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2800:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= a -1.7e+97)
     x
     (if (<= a -3e-174)
       t_1
       (if (<= a -4e-225)
         y
         (if (<= a 3.9e-233)
           t_1
           (if (<= a 2.2e-106)
             y
             (if (<= a 2.95e-30) t_1 (if (<= a 2800.0) y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -1.7e+97) {
		tmp = x;
	} else if (a <= -3e-174) {
		tmp = t_1;
	} else if (a <= -4e-225) {
		tmp = y;
	} else if (a <= 3.9e-233) {
		tmp = t_1;
	} else if (a <= 2.2e-106) {
		tmp = y;
	} else if (a <= 2.95e-30) {
		tmp = t_1;
	} else if (a <= 2800.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (a <= (-1.7d+97)) then
        tmp = x
    else if (a <= (-3d-174)) then
        tmp = t_1
    else if (a <= (-4d-225)) then
        tmp = y
    else if (a <= 3.9d-233) then
        tmp = t_1
    else if (a <= 2.2d-106) then
        tmp = y
    else if (a <= 2.95d-30) then
        tmp = t_1
    else if (a <= 2800.0d0) 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 t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -1.7e+97) {
		tmp = x;
	} else if (a <= -3e-174) {
		tmp = t_1;
	} else if (a <= -4e-225) {
		tmp = y;
	} else if (a <= 3.9e-233) {
		tmp = t_1;
	} else if (a <= 2.2e-106) {
		tmp = y;
	} else if (a <= 2.95e-30) {
		tmp = t_1;
	} else if (a <= 2800.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if a <= -1.7e+97:
		tmp = x
	elif a <= -3e-174:
		tmp = t_1
	elif a <= -4e-225:
		tmp = y
	elif a <= 3.9e-233:
		tmp = t_1
	elif a <= 2.2e-106:
		tmp = y
	elif a <= 2.95e-30:
		tmp = t_1
	elif a <= 2800.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -1.7e+97)
		tmp = x;
	elseif (a <= -3e-174)
		tmp = t_1;
	elseif (a <= -4e-225)
		tmp = y;
	elseif (a <= 3.9e-233)
		tmp = t_1;
	elseif (a <= 2.2e-106)
		tmp = y;
	elseif (a <= 2.95e-30)
		tmp = t_1;
	elseif (a <= 2800.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (a <= -1.7e+97)
		tmp = x;
	elseif (a <= -3e-174)
		tmp = t_1;
	elseif (a <= -4e-225)
		tmp = y;
	elseif (a <= 3.9e-233)
		tmp = t_1;
	elseif (a <= 2.2e-106)
		tmp = y;
	elseif (a <= 2.95e-30)
		tmp = t_1;
	elseif (a <= 2800.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+97], x, If[LessEqual[a, -3e-174], t$95$1, If[LessEqual[a, -4e-225], y, If[LessEqual[a, 3.9e-233], t$95$1, If[LessEqual[a, 2.2e-106], y, If[LessEqual[a, 2.95e-30], t$95$1, If[LessEqual[a, 2800.0], y, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000005e97 or 2800 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.6%

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

   if -1.70000000000000005e97 < a < -3.00000000000000021e-174 or -3.9999999999999998e-225 < a < 3.9000000000000001e-233 or 2.19999999999999994e-106 < a < 2.9499999999999999e-30

   1. Initial program 69.3%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in a around 0 54.1%

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

      1. associate-*r/ 54.1%

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

      2. neg-mul-1 54.1%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in z around inf 50.1%

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

      1. div-sub 50.1%

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

   9. Simplified 50.1%

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

   if -3.00000000000000021e-174 < a < -3.9999999999999998e-225 or 3.9000000000000001e-233 < a < 2.19999999999999994e-106 or 2.9499999999999999e-30 < a < 2800

   1. Initial program 64.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in t around inf 54.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-174}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-225}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2800:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+272}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.65e+53)
     t_1
     (if (<= t 1.35e-145)
       (+ x (/ (- y x) (/ (- a t) z)))
       (if (<= t 2.95e+109)
         (- x (* (/ y (- a t)) (- t z)))
         (if (<= t 3.5e+170)
           (* z (/ (- x y) t))
           (if (<= t 1.35e+272) t_1 (+ y (/ a (/ t (- y x)))))))))))

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 <= -1.65e+53) {
		tmp = t_1;
	} else if (t <= 1.35e-145) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.95e+109) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 3.5e+170) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.35e+272) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-1.65d+53)) then
        tmp = t_1
    else if (t <= 1.35d-145) then
        tmp = x + ((y - x) / ((a - t) / z))
    else if (t <= 2.95d+109) then
        tmp = x - ((y / (a - t)) * (t - z))
    else if (t <= 3.5d+170) then
        tmp = z * ((x - y) / t)
    else if (t <= 1.35d+272) then
        tmp = t_1
    else
        tmp = y + (a / (t / (y - x)))
    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 <= -1.65e+53) {
		tmp = t_1;
	} else if (t <= 1.35e-145) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.95e+109) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 3.5e+170) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.35e+272) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.65e+53:
		tmp = t_1
	elif t <= 1.35e-145:
		tmp = x + ((y - x) / ((a - t) / z))
	elif t <= 2.95e+109:
		tmp = x - ((y / (a - t)) * (t - z))
	elif t <= 3.5e+170:
		tmp = z * ((x - y) / t)
	elif t <= 1.35e+272:
		tmp = t_1
	else:
		tmp = y + (a / (t / (y - x)))
	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 <= -1.65e+53)
		tmp = t_1;
	elseif (t <= 1.35e-145)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	elseif (t <= 2.95e+109)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (t <= 3.5e+170)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 1.35e+272)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	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 <= -1.65e+53)
		tmp = t_1;
	elseif (t <= 1.35e-145)
		tmp = x + ((y - x) / ((a - t) / z));
	elseif (t <= 2.95e+109)
		tmp = x - ((y / (a - t)) * (t - z));
	elseif (t <= 3.5e+170)
		tmp = z * ((x - y) / t);
	elseif (t <= 1.35e+272)
		tmp = t_1;
	else
		tmp = y + (a / (t / (y - x)));
	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, -1.65e+53], t$95$1, If[LessEqual[t, 1.35e-145], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+109], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+170], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+272], t$95$1, N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.6500000000000001e53 or 3.50000000000000005e170 < t < 1.35000000000000006e272

   1. Initial program 31.1%

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

      1. associate-/l* 66.3%

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

   3. Simplified 66.3%

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

      1. clear-num 66.2%

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

      2. inv-pow 66.2%

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

   5. Applied egg-rr 66.2%

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

      1. unpow-1 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in x around 0 41.3%

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

      1. associate-*r/ 69.5%

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

   10. Simplified 69.5%

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

   if -1.6500000000000001e53 < t < 1.35e-145

   1. Initial program 92.4%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 85.5%

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

   if 1.35e-145 < t < 2.9499999999999999e109

   1. Initial program 75.7%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around inf 80.5%

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

   if 2.9499999999999999e109 < t < 3.50000000000000005e170

   1. Initial program 44.8%

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

      1. associate-*l/ 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in a around 0 30.4%

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

      1. associate-*r/ 30.4%

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

      2. neg-mul-1 30.4%

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

   6. Simplified 30.4%

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

   7. Taylor expanded in z around inf 58.9%

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

      1. div-sub 58.9%

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

   9. Simplified 58.9%

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

   if 1.35000000000000006e272 < t

   1. Initial program 10.9%

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

      1. associate-/l* 16.9%

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

   3. Simplified 16.9%

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

   4. Taylor expanded in z around 0 16.7%

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

      1. associate-*r/ 16.7%

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

      2. neg-mul-1 16.7%

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

   6. Simplified 16.7%

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

   7. Taylor expanded in a around 0 80.1%

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

      1. associate-/l* 88.1%

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

   9. Simplified 88.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+272}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 10: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -3.6e-14)
     t_1
     (if (<= a 9.5e-124)
       (+ y (/ (* (- y x) (- a z)) t))
       (if (<= a 3.4e-28)
         (* z (/ (- y x) (- a t)))
         (if (<= a 1.1e-8) y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.6e-14) {
		tmp = t_1;
	} else if (a <= 9.5e-124) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 3.4e-28) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.1e-8) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (a <= (-3.6d-14)) then
        tmp = t_1
    else if (a <= 9.5d-124) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (a <= 3.4d-28) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.1d-8) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -3.6e-14) {
		tmp = t_1;
	} else if (a <= 9.5e-124) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 3.4e-28) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.1e-8) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -3.6e-14:
		tmp = t_1
	elif a <= 9.5e-124:
		tmp = y + (((y - x) * (a - z)) / t)
	elif a <= 3.4e-28:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.1e-8:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -3.6e-14)
		tmp = t_1;
	elseif (a <= 9.5e-124)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (a <= 3.4e-28)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.1e-8)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -3.6e-14)
		tmp = t_1;
	elseif (a <= 9.5e-124)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (a <= 3.4e-28)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.1e-8)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e-14], t$95$1, If[LessEqual[a, 9.5e-124], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-28], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-8], y, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5999999999999998e-14 or 1.0999999999999999e-8 < a

   1. Initial program 66.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 82.5%

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

   if -3.5999999999999998e-14 < a < 9.49999999999999989e-124

   1. Initial program 68.4%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in t around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-*r/ 77.1%

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

      3. associate-*r/ 77.1%

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

      4. div-sub 77.1%

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

      5. distribute-lft-out-- 77.1%

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

      6. mul-1-neg 77.1%

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

      7. distribute-neg-frac 77.1%

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

      8. unsub-neg 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   6. Simplified 77.1%

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

   if 9.49999999999999989e-124 < a < 3.4000000000000001e-28

   1. Initial program 69.0%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in z around inf 79.8%

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

      1. div-sub 79.8%

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

   6. Simplified 79.8%

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

   if 3.4000000000000001e-28 < a < 1.0999999999999999e-8

   1. Initial program 43.7%

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

      1. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in t around inf 100.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 11: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -8.3 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-266}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t z))))
   (if (<= a -8.3e+96)
     x
     (if (<= a -2.3e-148)
       t_1
       (if (<= a -2.65e-266)
         y
         (if (<= a 1.25e-231)
           t_1
           (if (<= a 2.2e-108)
             y
             (if (<= a 9.2e-32) (* z (/ x t)) (if (<= a 5.7e-6) y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / z);
	double tmp;
	if (a <= -8.3e+96) {
		tmp = x;
	} else if (a <= -2.3e-148) {
		tmp = t_1;
	} else if (a <= -2.65e-266) {
		tmp = y;
	} else if (a <= 1.25e-231) {
		tmp = t_1;
	} else if (a <= 2.2e-108) {
		tmp = y;
	} else if (a <= 9.2e-32) {
		tmp = z * (x / t);
	} else if (a <= 5.7e-6) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x / (t / z)
    if (a <= (-8.3d+96)) then
        tmp = x
    else if (a <= (-2.3d-148)) then
        tmp = t_1
    else if (a <= (-2.65d-266)) then
        tmp = y
    else if (a <= 1.25d-231) then
        tmp = t_1
    else if (a <= 2.2d-108) then
        tmp = y
    else if (a <= 9.2d-32) then
        tmp = z * (x / t)
    else if (a <= 5.7d-6) 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 t_1 = x / (t / z);
	double tmp;
	if (a <= -8.3e+96) {
		tmp = x;
	} else if (a <= -2.3e-148) {
		tmp = t_1;
	} else if (a <= -2.65e-266) {
		tmp = y;
	} else if (a <= 1.25e-231) {
		tmp = t_1;
	} else if (a <= 2.2e-108) {
		tmp = y;
	} else if (a <= 9.2e-32) {
		tmp = z * (x / t);
	} else if (a <= 5.7e-6) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / z)
	tmp = 0
	if a <= -8.3e+96:
		tmp = x
	elif a <= -2.3e-148:
		tmp = t_1
	elif a <= -2.65e-266:
		tmp = y
	elif a <= 1.25e-231:
		tmp = t_1
	elif a <= 2.2e-108:
		tmp = y
	elif a <= 9.2e-32:
		tmp = z * (x / t)
	elif a <= 5.7e-6:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / z))
	tmp = 0.0
	if (a <= -8.3e+96)
		tmp = x;
	elseif (a <= -2.3e-148)
		tmp = t_1;
	elseif (a <= -2.65e-266)
		tmp = y;
	elseif (a <= 1.25e-231)
		tmp = t_1;
	elseif (a <= 2.2e-108)
		tmp = y;
	elseif (a <= 9.2e-32)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= 5.7e-6)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / z);
	tmp = 0.0;
	if (a <= -8.3e+96)
		tmp = x;
	elseif (a <= -2.3e-148)
		tmp = t_1;
	elseif (a <= -2.65e-266)
		tmp = y;
	elseif (a <= 1.25e-231)
		tmp = t_1;
	elseif (a <= 2.2e-108)
		tmp = y;
	elseif (a <= 9.2e-32)
		tmp = z * (x / t);
	elseif (a <= 5.7e-6)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.3e+96], x, If[LessEqual[a, -2.3e-148], t$95$1, If[LessEqual[a, -2.65e-266], y, If[LessEqual[a, 1.25e-231], t$95$1, If[LessEqual[a, 2.2e-108], y, If[LessEqual[a, 9.2e-32], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e-6], y, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2999999999999997e96 or 5.6999999999999996e-6 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.6%

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

   if -8.2999999999999997e96 < a < -2.29999999999999997e-148 or -2.6500000000000001e-266 < a < 1.25000000000000006e-231

   1. Initial program 71.5%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in a around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in x around inf 39.7%

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

      1. associate-/l* 41.2%

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

   9. Simplified 41.2%

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

   if -2.29999999999999997e-148 < a < -2.6500000000000001e-266 or 1.25000000000000006e-231 < a < 2.2000000000000001e-108 or 9.2000000000000002e-32 < a < 5.6999999999999996e-6

   1. Initial program 65.4%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in t around inf 50.1%

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

   if 2.2000000000000001e-108 < a < 9.2000000000000002e-32

   1. Initial program 63.2%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in a around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in z around inf 57.8%

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

      1. div-sub 57.8%

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

   9. Simplified 57.8%

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

   10. Taylor expanded in x around inf 44.9%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.3 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-266}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= x -4.2e+233)
     (* z (/ x t))
     (if (<= x -6.8e+45)
       t_1
       (if (<= x -3.8e-18) (* z (/ (- x y) t)) (if (<= x 1.35e+123) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (x <= -4.2e+233) {
		tmp = z * (x / t);
	} else if (x <= -6.8e+45) {
		tmp = t_1;
	} else if (x <= -3.8e-18) {
		tmp = z * ((x - y) / t);
	} else if (x <= 1.35e+123) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (x <= (-4.2d+233)) then
        tmp = z * (x / t)
    else if (x <= (-6.8d+45)) then
        tmp = t_1
    else if (x <= (-3.8d-18)) then
        tmp = z * ((x - y) / t)
    else if (x <= 1.35d+123) then
        tmp = t_1
    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 t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (x <= -4.2e+233) {
		tmp = z * (x / t);
	} else if (x <= -6.8e+45) {
		tmp = t_1;
	} else if (x <= -3.8e-18) {
		tmp = z * ((x - y) / t);
	} else if (x <= 1.35e+123) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if x <= -4.2e+233:
		tmp = z * (x / t)
	elif x <= -6.8e+45:
		tmp = t_1
	elif x <= -3.8e-18:
		tmp = z * ((x - y) / t)
	elif x <= 1.35e+123:
		tmp = t_1
	else:
		tmp = x
	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 (x <= -4.2e+233)
		tmp = Float64(z * Float64(x / t));
	elseif (x <= -6.8e+45)
		tmp = t_1;
	elseif (x <= -3.8e-18)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (x <= 1.35e+123)
		tmp = t_1;
	else
		tmp = x;
	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 (x <= -4.2e+233)
		tmp = z * (x / t);
	elseif (x <= -6.8e+45)
		tmp = t_1;
	elseif (x <= -3.8e-18)
		tmp = z * ((x - y) / t);
	elseif (x <= 1.35e+123)
		tmp = t_1;
	else
		tmp = x;
	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[x, -4.2e+233], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e+45], t$95$1, If[LessEqual[x, -3.8e-18], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+123], t$95$1, x]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.19999999999999993e233

   1. Initial program 63.7%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in a around 0 30.8%

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

      1. associate-*r/ 30.8%

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

      2. neg-mul-1 30.8%

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

   6. Simplified 30.8%

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

   7. Taylor expanded in z around inf 39.9%

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

      1. div-sub 39.9%

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

   9. Simplified 39.9%

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

   10. Taylor expanded in x around inf 40.2%

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

   if -4.19999999999999993e233 < x < -6.8e45 or -3.7999999999999998e-18 < x < 1.35000000000000007e123

   1. Initial program 69.1%

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

      1. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

      1. clear-num 83.8%

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

      2. inv-pow 83.8%

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

   5. Applied egg-rr 83.8%

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

      1. unpow-1 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 70.1%

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

   10. Simplified 70.1%

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

   if -6.8e45 < x < -3.7999999999999998e-18

   1. Initial program 74.4%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in a around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. neg-mul-1 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in z around inf 39.8%

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

      1. div-sub 39.7%

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

   9. Simplified 39.7%

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

   if 1.35000000000000007e123 < x

   1. Initial program 57.7%

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

      1. associate-*l/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in a around inf 46.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+54)
   (* y (/ (- z t) (- a t)))
   (if (<= t -1.4e-79)
     (* (- y x) (/ z (- a t)))
     (if (<= t 1.35e+54)
       (- x (/ (- x y) (/ a z)))
       (if (<= t 2.4e+170)
         (* z (/ (- y x) (- a t)))
         (+ y (/ a (/ t (- y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+54) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.4e-79) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.35e+54) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 2.4e+170) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+54)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-1.4d-79)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 1.35d+54) then
        tmp = x - ((x - y) / (a / z))
    else if (t <= 2.4d+170) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+54) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.4e-79) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.35e+54) {
		tmp = x - ((x - y) / (a / z));
	} else if (t <= 2.4e+170) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+54:
		tmp = y * ((z - t) / (a - t))
	elif t <= -1.4e-79:
		tmp = (y - x) * (z / (a - t))
	elif t <= 1.35e+54:
		tmp = x - ((x - y) / (a / z))
	elif t <= 2.4e+170:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+54)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -1.4e-79)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 1.35e+54)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	elseif (t <= 2.4e+170)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+54)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -1.4e-79)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 1.35e+54)
		tmp = x - ((x - y) / (a / z));
	elseif (t <= 2.4e+170)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+54], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-79], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+54], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+170], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.50000000000000003e54

   1. Initial program 36.8%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

      1. clear-num 62.1%

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

      2. inv-pow 62.1%

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

   5. Applied egg-rr 62.1%

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

      1. unpow-1 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in x around 0 48.2%

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

      1. associate-*r/ 68.1%

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

   10. Simplified 68.1%

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

   if -2.50000000000000003e54 < t < -1.40000000000000006e-79

   1. Initial program 91.4%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-*l/ 91.4%

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

      3. div-inv 91.4%

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

      4. fma-def 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in z around -inf 67.9%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 70.6%

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

   8. Simplified 70.6%

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

   if -1.40000000000000006e-79 < t < 1.35000000000000005e54

   1. Initial program 89.8%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 73.7%

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

   if 1.35000000000000005e54 < t < 2.4e170

   1. Initial program 50.4%

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

      1. associate-*l/ 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in z around inf 55.2%

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

      1. div-sub 55.2%

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

   6. Simplified 55.2%

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

   if 2.4e170 < t

   1. Initial program 14.4%

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

      1. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   4. Taylor expanded in z around 0 44.5%

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

      1. associate-*r/ 44.5%

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

      2. neg-mul-1 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in a around 0 61.6%

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

      1. associate-/l* 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 14: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+214}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+206}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.9e+214)
   (+ y (/ (* (- y x) (- a z)) t))
   (if (<= t 1.8e+206)
     (- x (* (- z t) (/ (- x y) (- a t))))
     (+ y (/ a (/ t (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e+214) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.8e+206) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.9d+214)) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t <= 1.8d+206) then
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e+214) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.8e+206) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.9e+214:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t <= 1.8e+206:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.9e+214)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t <= 1.8e+206)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.9e+214)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t <= 1.8e+206)
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.9e+214], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+206], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.89999999999999976e214

   1. Initial program 22.6%

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

      1. associate-*l/ 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in t around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. mul-1-neg 72.6%

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

      7. distribute-neg-frac 72.6%

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

      8. unsub-neg 72.6%

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

      9. distribute-rgt-out-- 76.6%

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

   6. Simplified 76.6%

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

   if -6.89999999999999976e214 < t < 1.80000000000000014e206

   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/ 84.9%

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

   3. Simplified 84.9%

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

   if 1.80000000000000014e206 < t

   1. Initial program 12.9%

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

      1. associate-/l* 47.9%

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

   3. Simplified 47.9%

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

   4. Taylor expanded in z around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. neg-mul-1 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in a around 0 71.9%

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

      1. associate-/l* 85.4%

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

   9. Simplified 85.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+214}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+206}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 15: 44.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.4:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= a -4.2e+96)
     x
     (if (<= a -1.95e-146)
       t_1
       (if (<= a 9.5e-124)
         (- y (/ y (/ t z)))
         (if (<= a 1.65e-30) t_1 (if (<= a 9.4) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -4.2e+96) {
		tmp = x;
	} else if (a <= -1.95e-146) {
		tmp = t_1;
	} else if (a <= 9.5e-124) {
		tmp = y - (y / (t / z));
	} else if (a <= 1.65e-30) {
		tmp = t_1;
	} else if (a <= 9.4) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (a <= (-4.2d+96)) then
        tmp = x
    else if (a <= (-1.95d-146)) then
        tmp = t_1
    else if (a <= 9.5d-124) then
        tmp = y - (y / (t / z))
    else if (a <= 1.65d-30) then
        tmp = t_1
    else if (a <= 9.4d0) 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 t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -4.2e+96) {
		tmp = x;
	} else if (a <= -1.95e-146) {
		tmp = t_1;
	} else if (a <= 9.5e-124) {
		tmp = y - (y / (t / z));
	} else if (a <= 1.65e-30) {
		tmp = t_1;
	} else if (a <= 9.4) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if a <= -4.2e+96:
		tmp = x
	elif a <= -1.95e-146:
		tmp = t_1
	elif a <= 9.5e-124:
		tmp = y - (y / (t / z))
	elif a <= 1.65e-30:
		tmp = t_1
	elif a <= 9.4:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -4.2e+96)
		tmp = x;
	elseif (a <= -1.95e-146)
		tmp = t_1;
	elseif (a <= 9.5e-124)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	elseif (a <= 1.65e-30)
		tmp = t_1;
	elseif (a <= 9.4)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (a <= -4.2e+96)
		tmp = x;
	elseif (a <= -1.95e-146)
		tmp = t_1;
	elseif (a <= 9.5e-124)
		tmp = y - (y / (t / z));
	elseif (a <= 1.65e-30)
		tmp = t_1;
	elseif (a <= 9.4)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+96], x, If[LessEqual[a, -1.95e-146], t$95$1, If[LessEqual[a, 9.5e-124], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-30], t$95$1, If[LessEqual[a, 9.4], y, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2000000000000002e96 or 9.40000000000000036 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.6%

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

   if -4.2000000000000002e96 < a < -1.95000000000000001e-146 or 9.49999999999999989e-124 < a < 1.6500000000000001e-30

   1. Initial program 69.1%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in a around 0 46.8%

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

      1. associate-*r/ 46.8%

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

      2. neg-mul-1 46.8%

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

   6. Simplified 46.8%

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

   7. Taylor expanded in z around inf 46.0%

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

      1. div-sub 46.0%

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

   9. Simplified 46.0%

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

   if -1.95000000000000001e-146 < a < 9.49999999999999989e-124

   1. Initial program 67.7%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 62.1%

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

   5. Taylor expanded in a around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-/l* 62.5%

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

      3. distribute-neg-frac 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

      3. associate-/l* 62.5%

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

   10. Simplified 62.5%

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

   if 1.6500000000000001e-30 < a < 9.40000000000000036

   1. Initial program 59.6%

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

      1. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in t around inf 73.0%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-124}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 9.4:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 44.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 6000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e+96)
   x
   (if (<= a -1.95e-146)
     (/ z (/ t (- x y)))
     (if (<= a 7.5e-124)
       (- y (/ y (/ t z)))
       (if (<= a 5.7e-31) (* z (/ (- x y) t)) (if (<= a 6000.0) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+96) {
		tmp = x;
	} else if (a <= -1.95e-146) {
		tmp = z / (t / (x - y));
	} else if (a <= 7.5e-124) {
		tmp = y - (y / (t / z));
	} else if (a <= 5.7e-31) {
		tmp = z * ((x - y) / t);
	} else if (a <= 6000.0) {
		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 <= (-3.9d+96)) then
        tmp = x
    else if (a <= (-1.95d-146)) then
        tmp = z / (t / (x - y))
    else if (a <= 7.5d-124) then
        tmp = y - (y / (t / z))
    else if (a <= 5.7d-31) then
        tmp = z * ((x - y) / t)
    else if (a <= 6000.0d0) 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 <= -3.9e+96) {
		tmp = x;
	} else if (a <= -1.95e-146) {
		tmp = z / (t / (x - y));
	} else if (a <= 7.5e-124) {
		tmp = y - (y / (t / z));
	} else if (a <= 5.7e-31) {
		tmp = z * ((x - y) / t);
	} else if (a <= 6000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e+96:
		tmp = x
	elif a <= -1.95e-146:
		tmp = z / (t / (x - y))
	elif a <= 7.5e-124:
		tmp = y - (y / (t / z))
	elif a <= 5.7e-31:
		tmp = z * ((x - y) / t)
	elif a <= 6000.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e+96)
		tmp = x;
	elseif (a <= -1.95e-146)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 7.5e-124)
		tmp = Float64(y - Float64(y / Float64(t / z)));
	elseif (a <= 5.7e-31)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 6000.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e+96)
		tmp = x;
	elseif (a <= -1.95e-146)
		tmp = z / (t / (x - y));
	elseif (a <= 7.5e-124)
		tmp = y - (y / (t / z));
	elseif (a <= 5.7e-31)
		tmp = z * ((x - y) / t);
	elseif (a <= 6000.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e+96], x, If[LessEqual[a, -1.95e-146], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-124], N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e-31], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6000.0], y, x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.9e96 or 6e3 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.6%

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

   if -3.9e96 < a < -1.95000000000000001e-146

   1. Initial program 69.8%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in a around 0 45.9%

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

      1. associate-*r/ 45.9%

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

      2. neg-mul-1 45.9%

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

   6. Simplified 45.9%

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

   7. Taylor expanded in t around 0 39.0%

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

      1. associate-/l* 42.0%

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

   9. Simplified 42.0%

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

   if -1.95000000000000001e-146 < a < 7.4999999999999996e-124

   1. Initial program 67.7%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 62.1%

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

   5. Taylor expanded in a around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-/l* 62.5%

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

      3. distribute-neg-frac 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

      3. associate-/l* 62.5%

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

   10. Simplified 62.5%

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

   if 7.4999999999999996e-124 < a < 5.69999999999999995e-31

   1. Initial program 67.3%

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

      1. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in a around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   6. Simplified 48.8%

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

   7. Taylor expanded in z around inf 56.9%

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

      1. div-sub 56.9%

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

   9. Simplified 56.9%

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

   if 5.69999999999999995e-31 < a < 6e3

   1. Initial program 59.6%

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

      1. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in t around inf 73.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-124}:\\ \;\;\;\;y - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 6000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-85}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 10^{+47}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.2e+48)
     t_1
     (if (<= t -8.8e-85)
       (* (- y x) (/ z (- a t)))
       (if (<= t 1e+47) (+ x (/ z (/ a (- y x)))) 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 <= -2.2e+48) {
		tmp = t_1;
	} else if (t <= -8.8e-85) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1e+47) {
		tmp = x + (z / (a / (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 = y * ((z - t) / (a - t))
    if (t <= (-2.2d+48)) then
        tmp = t_1
    else if (t <= (-8.8d-85)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 1d+47) then
        tmp = x + (z / (a / (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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.2e+48) {
		tmp = t_1;
	} else if (t <= -8.8e-85) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1e+47) {
		tmp = x + (z / (a / (y - x)));
	} 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 <= -2.2e+48:
		tmp = t_1
	elif t <= -8.8e-85:
		tmp = (y - x) * (z / (a - t))
	elif t <= 1e+47:
		tmp = x + (z / (a / (y - x)))
	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 <= -2.2e+48)
		tmp = t_1;
	elseif (t <= -8.8e-85)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 1e+47)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	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 <= -2.2e+48)
		tmp = t_1;
	elseif (t <= -8.8e-85)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 1e+47)
		tmp = x + (z / (a / (y - x)));
	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, -2.2e+48], t$95$1, If[LessEqual[t, -8.8e-85], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+47], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e48 or 1e47 < t

   1. Initial program 33.4%

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

      1. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

      1. clear-num 60.7%

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

      2. inv-pow 60.7%

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

   5. Applied egg-rr 60.7%

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

      1. unpow-1 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in x around 0 39.3%

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

      1. associate-*r/ 60.5%

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

   10. Simplified 60.5%

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

   if -2.1999999999999999e48 < t < -8.8e-85

   1. Initial program 91.4%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-*l/ 91.4%

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

      3. div-inv 91.4%

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

      4. fma-def 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in z around -inf 67.9%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 70.6%

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

   8. Simplified 70.6%

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

   if -8.8e-85 < t < 1e47

   1. Initial program 92.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 69.9%

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

      1. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-85}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 10^{+47}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 18: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-77}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.4e+47)
     t_1
     (if (<= t -2.7e-77)
       (* (- y x) (/ z (- a t)))
       (if (<= t 1.4e+47) (- x (/ (- x y) (/ a z))) 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 <= -1.4e+47) {
		tmp = t_1;
	} else if (t <= -2.7e-77) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.4e+47) {
		tmp = x - ((x - y) / (a / z));
	} 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 <= (-1.4d+47)) then
        tmp = t_1
    else if (t <= (-2.7d-77)) then
        tmp = (y - x) * (z / (a - t))
    else if (t <= 1.4d+47) then
        tmp = x - ((x - y) / (a / z))
    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 <= -1.4e+47) {
		tmp = t_1;
	} else if (t <= -2.7e-77) {
		tmp = (y - x) * (z / (a - t));
	} else if (t <= 1.4e+47) {
		tmp = x - ((x - y) / (a / z));
	} 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 <= -1.4e+47:
		tmp = t_1
	elif t <= -2.7e-77:
		tmp = (y - x) * (z / (a - t))
	elif t <= 1.4e+47:
		tmp = x - ((x - y) / (a / z))
	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 <= -1.4e+47)
		tmp = t_1;
	elseif (t <= -2.7e-77)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (t <= 1.4e+47)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	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 <= -1.4e+47)
		tmp = t_1;
	elseif (t <= -2.7e-77)
		tmp = (y - x) * (z / (a - t));
	elseif (t <= 1.4e+47)
		tmp = x - ((x - y) / (a / z));
	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, -1.4e+47], t$95$1, If[LessEqual[t, -2.7e-77], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+47], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999994e47 or 1.39999999999999994e47 < t

   1. Initial program 33.4%

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

      1. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

      1. clear-num 60.7%

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

      2. inv-pow 60.7%

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

   5. Applied egg-rr 60.7%

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

      1. unpow-1 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in x around 0 39.3%

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

      1. associate-*r/ 60.5%

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

   10. Simplified 60.5%

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

   if -1.39999999999999994e47 < t < -2.7e-77

   1. Initial program 91.4%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-*l/ 91.4%

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

      3. div-inv 91.4%

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

      4. fma-def 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in z around -inf 67.9%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 70.6%

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

   8. Simplified 70.6%

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

   if -2.7e-77 < t < 1.39999999999999994e47

   1. Initial program 92.1%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around 0 75.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-77}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 19: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e-6)
   (/ z (/ (- a t) (- y x)))
   (if (<= z 5.8e-5)
     (- x (* (/ y (- a t)) (- t z)))
     (* (- y x) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e-6) {
		tmp = z / ((a - t) / (y - x));
	} else if (z <= 5.8e-5) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = (y - 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) :: tmp
    if (z <= (-4d-6)) then
        tmp = z / ((a - t) / (y - x))
    else if (z <= 5.8d-5) then
        tmp = x - ((y / (a - t)) * (t - z))
    else
        tmp = (y - 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 tmp;
	if (z <= -4e-6) {
		tmp = z / ((a - t) / (y - x));
	} else if (z <= 5.8e-5) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e-6:
		tmp = z / ((a - t) / (y - x))
	elif z <= 5.8e-5:
		tmp = x - ((y / (a - t)) * (t - z))
	else:
		tmp = (y - x) * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e-6)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (z <= 5.8e-5)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e-6)
		tmp = z / ((a - t) / (y - x));
	elseif (z <= 5.8e-5)
		tmp = x - ((y / (a - t)) * (t - z));
	else
		tmp = (y - x) * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e-6], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-5], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999982e-6

   1. Initial program 67.4%

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

      1. associate-*l/ 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in z around inf 69.4%

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

      1. div-sub 69.4%

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

      2. associate-*r/ 62.4%

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

      3. associate-/l* 69.5%

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

   6. Simplified 69.5%

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

   if -3.99999999999999982e-6 < z < 5.8e-5

   1. Initial program 65.1%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in y around inf 70.2%

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

   if 5.8e-5 < z

   1. Initial program 70.8%

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

      1. +-commutative 88.8%

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

      2. associate-*l/ 70.8%

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

      3. div-inv 70.7%

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

      4. fma-def 70.7%

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

   5. Applied egg-rr 70.7%

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

   6. Taylor expanded in z around -inf 66.6%

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

      1. associate-/l* 80.1%

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

      2. associate-/r/ 81.6%

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

   8. Simplified 81.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 20: 36.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 245:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ x t))))
   (if (<= a -3.9e+96)
     x
     (if (<= a -6.1e-151)
       t_1
       (if (<= a 3.2e-114) y (if (<= a 7e-32) t_1 (if (<= a 245.0) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (x / t);
	double tmp;
	if (a <= -3.9e+96) {
		tmp = x;
	} else if (a <= -6.1e-151) {
		tmp = t_1;
	} else if (a <= 3.2e-114) {
		tmp = y;
	} else if (a <= 7e-32) {
		tmp = t_1;
	} else if (a <= 245.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (x / t)
    if (a <= (-3.9d+96)) then
        tmp = x
    else if (a <= (-6.1d-151)) then
        tmp = t_1
    else if (a <= 3.2d-114) then
        tmp = y
    else if (a <= 7d-32) then
        tmp = t_1
    else if (a <= 245.0d0) 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 t_1 = z * (x / t);
	double tmp;
	if (a <= -3.9e+96) {
		tmp = x;
	} else if (a <= -6.1e-151) {
		tmp = t_1;
	} else if (a <= 3.2e-114) {
		tmp = y;
	} else if (a <= 7e-32) {
		tmp = t_1;
	} else if (a <= 245.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (x / t)
	tmp = 0
	if a <= -3.9e+96:
		tmp = x
	elif a <= -6.1e-151:
		tmp = t_1
	elif a <= 3.2e-114:
		tmp = y
	elif a <= 7e-32:
		tmp = t_1
	elif a <= 245.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(x / t))
	tmp = 0.0
	if (a <= -3.9e+96)
		tmp = x;
	elseif (a <= -6.1e-151)
		tmp = t_1;
	elseif (a <= 3.2e-114)
		tmp = y;
	elseif (a <= 7e-32)
		tmp = t_1;
	elseif (a <= 245.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (x / t);
	tmp = 0.0;
	if (a <= -3.9e+96)
		tmp = x;
	elseif (a <= -6.1e-151)
		tmp = t_1;
	elseif (a <= 3.2e-114)
		tmp = y;
	elseif (a <= 7e-32)
		tmp = t_1;
	elseif (a <= 245.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+96], x, If[LessEqual[a, -6.1e-151], t$95$1, If[LessEqual[a, 3.2e-114], y, If[LessEqual[a, 7e-32], t$95$1, If[LessEqual[a, 245.0], y, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9e96 or 245 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.6%

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

   if -3.9e96 < a < -6.1e-151 or 3.2000000000000002e-114 < a < 6.9999999999999997e-32

   1. Initial program 68.0%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in a around 0 46.6%

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

      1. associate-*r/ 46.6%

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

      2. neg-mul-1 46.6%

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

   6. Simplified 46.6%

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

   7. Taylor expanded in z around inf 45.9%

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

      1. div-sub 45.8%

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

   9. Simplified 45.8%

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

   10. Taylor expanded in x around inf 37.1%

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

   if -6.1e-151 < a < 3.2000000000000002e-114 or 6.9999999999999997e-32 < a < 245

   1. Initial program 67.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-151}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 245:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 37.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1420:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.9e+92) x (if (<= a 1420.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.9e+92) {
		tmp = x;
	} else if (a <= 1420.0) {
		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 <= (-4.9d+92)) then
        tmp = x
    else if (a <= 1420.0d0) 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 <= -4.9e+92) {
		tmp = x;
	} else if (a <= 1420.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.9e+92:
		tmp = x
	elif a <= 1420.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.9e+92)
		tmp = x;
	elseif (a <= 1420.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.9e+92)
		tmp = x;
	elseif (a <= 1420.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.9e+92], x, If[LessEqual[a, 1420.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9000000000000002e92 or 1420 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 51.2%

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

   if -4.9000000000000002e92 < a < 1420

   1. Initial program 67.7%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in t around inf 33.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1420:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 25.0% 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 67.0%

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

   1. associate-*l/ 77.6%

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

3. Simplified 77.6%

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

4. Taylor expanded in a around inf 25.3%

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

5. Final simplification 25.3%

   \[\leadsto x \]

Developer target: 86.7% 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 2023293 
(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))))