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

Percentage Accurate: 68.2% → 91.5%

Time: 16.7s

Alternatives: 16

Speedup: 0.6×

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: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-304} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -4e-304) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (* (- z a) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-304) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -4e-304) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-304], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $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))) < -3.99999999999999988e-304 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-/l* 93.0%

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

      3. fma-define 92.9%

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

   3. Simplified 92.9%

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

   if -3.99999999999999988e-304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-304} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \frac{y}{x} + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* x (+ (* (/ (- z t) (- a t)) (/ y x)) (/ (- z t) (- t a)))))
     (if (<= t_1 -4e-304)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_1 5e+286)
           (+ x (/ (+ (* y (- z t)) (* x (- t z))) (- a t)))
           (+ x (* z (/ (- y x) (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (x * ((((z - t) / (a - t)) * (y / x)) + ((z - t) / (t - a))));
	} else if (t_1 <= -4e-304) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 5e+286) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (x * ((((z - t) / (a - t)) * (y / x)) + ((z - t) / (t - a))));
	} else if (t_1 <= -4e-304) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 5e+286) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (x * ((((z - t) / (a - t)) * (y / x)) + ((z - t) / (t - a))))
	elif t_1 <= -4e-304:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_1 <= 5e+286:
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(x * Float64(Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(y / x)) + Float64(Float64(z - t) / Float64(t - a)))));
	elseif (t_1 <= -4e-304)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_1 <= 5e+286)
		tmp = Float64(x + Float64(Float64(Float64(y * Float64(z - t)) + Float64(x * Float64(t - z))) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (x * ((((z - t) / (a - t)) * (y / x)) + ((z - t) / (t - a))));
	elseif (t_1 <= -4e-304)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_1 <= 5e+286)
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(x * N[(N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-304], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], N[(x + N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 42.2%

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

   3. Taylor expanded in x around -inf 51.5%

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

      1. associate-*r* 51.5%

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

      2. neg-mul-1 51.5%

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

      3. associate--l+ 51.5%

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

      4. mul-1-neg 51.5%

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

      5. times-frac 76.7%

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

      6. div-sub 76.7%

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

   5. Simplified 76.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999988e-304

   1. Initial program 98.6%

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

   if -3.99999999999999988e-304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000004e286

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. distribute-lft-in 98.4%

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

   4. Applied egg-rr 98.4%

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

   if 5.0000000000000004e286 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.4%

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

   3. Taylor expanded in z around inf 38.7%

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

      1. associate-/l* 62.4%

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

   5. Simplified 62.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \frac{y}{x} + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-304)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_2 5e+286)
           (+ x (/ (+ (* y (- z t)) (* x (- t z))) (- a t)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-304) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+286) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} 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 * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-304) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+286) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-304:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_2 <= 5e+286:
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-304)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 5e+286)
		tmp = Float64(x + Float64(Float64(Float64(y * Float64(z - t)) + Float64(x * Float64(t - z))) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-304)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_2 <= 5e+286)
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-304], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+286], N[(x + N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 5.0000000000000004e286 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 39.7%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. associate-/l* 66.3%

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

   5. Simplified 66.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999988e-304

   1. Initial program 98.6%

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

   if -3.99999999999999988e-304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000004e286

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. sub-neg 98.4%

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

      3. distribute-lft-in 98.4%

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

   4. Applied egg-rr 98.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-304)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_2 5e+286) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-304) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+286) {
		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 * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-304) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_2 <= 5e+286) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-304:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_2 <= 5e+286:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-304)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_2 <= 5e+286)
		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 * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-304)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_2 <= 5e+286)
		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[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-304], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+286], 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 5.0000000000000004e286 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 39.7%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. associate-/l* 66.3%

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

   5. Simplified 66.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999988e-304 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000004e286

   1. Initial program 98.5%

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

   if -3.99999999999999988e-304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-75}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* (- z a) (- x y)) t))))
   (if (<= t -8e+95)
     t_1
     (if (<= t 4.4e-75)
       (+ x (* z (/ (- y x) (- a t))))
       (if (<= t 1.3e-8) (+ x (/ (* y (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((z - a) * (x - y)) / t);
	double tmp;
	if (t <= -8e+95) {
		tmp = t_1;
	} else if (t <= 4.4e-75) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.3e-8) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (((z - a) * (x - y)) / t)
    if (t <= (-8d+95)) then
        tmp = t_1
    else if (t <= 4.4d-75) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 1.3d-8) then
        tmp = x + ((y * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((z - a) * (x - y)) / t);
	double tmp;
	if (t <= -8e+95) {
		tmp = t_1;
	} else if (t <= 4.4e-75) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.3e-8) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((z - a) * (x - y)) / t)
	tmp = 0
	if t <= -8e+95:
		tmp = t_1
	elif t <= 4.4e-75:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 1.3e-8:
		tmp = x + ((y * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t))
	tmp = 0.0
	if (t <= -8e+95)
		tmp = t_1;
	elseif (t <= 4.4e-75)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 1.3e-8)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((z - a) * (x - y)) / t);
	tmp = 0.0;
	if (t <= -8e+95)
		tmp = t_1;
	elseif (t <= 4.4e-75)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 1.3e-8)
		tmp = x + ((y * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+95], t$95$1, If[LessEqual[t, 4.4e-75], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-8], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000016e95 or 1.3000000000000001e-8 < t

   1. Initial program 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-/l* 65.4%

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

      3. fma-define 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in t around inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. associate-*r/ 69.5%

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

      3. associate-*r/ 69.5%

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

      4. mul-1-neg 69.5%

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

      5. div-sub 69.5%

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

      6. mul-1-neg 69.5%

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

      7. distribute-lft-out-- 69.5%

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

      8. associate-*r/ 69.5%

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

      9. mul-1-neg 69.5%

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

      10. unsub-neg 69.5%

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

      11. distribute-rgt-out-- 70.7%

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

   7. Simplified 70.7%

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

   if -8.00000000000000016e95 < t < 4.40000000000000011e-75

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 84.7%

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

      1. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   if 4.40000000000000011e-75 < t < 1.3000000000000001e-8

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   5. Simplified 94.1%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+95}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-75}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+52}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+97)
   (* y (- 1.0 (/ z t)))
   (if (<= t 2.5e-70)
     (+ x (* y (/ z (- a t))))
     (if (<= t 9e+52) (- x (* t (/ y (- a t)))) (- y (* y (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+97) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 2.5e-70) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 9e+52) {
		tmp = x - (t * (y / (a - t)));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.3d+97)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 2.5d-70) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= 9d+52) then
        tmp = x - (t * (y / (a - t)))
    else
        tmp = y - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+97) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 2.5e-70) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 9e+52) {
		tmp = x - (t * (y / (a - t)));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+97:
		tmp = y * (1.0 - (z / t))
	elif t <= 2.5e-70:
		tmp = x + (y * (z / (a - t)))
	elif t <= 9e+52:
		tmp = x - (t * (y / (a - t)))
	else:
		tmp = y - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+97)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 2.5e-70)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= 9e+52)
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+97)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 2.5e-70)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= 9e+52)
		tmp = x - (t * (y / (a - t)));
	else
		tmp = y - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+97], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-70], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+52], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3e97

   1. Initial program 40.6%

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

      1. +-commutative 40.6%

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

      2. associate-/l* 68.8%

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

      3. fma-define 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in a around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. associate-/l* 51.1%

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

      4. div-sub 51.1%

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

      5. sub-neg 51.1%

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

      6. *-inverses 51.1%

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

      7. metadata-eval 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in y around inf 63.3%

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

   if -1.3e97 < t < 2.4999999999999999e-70

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 70.6%

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

      1. associate-/l* 75.5%

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

   8. Simplified 75.5%

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

   if 2.4999999999999999e-70 < t < 8.9999999999999999e52

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-/l* 70.5%

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

   8. Simplified 70.5%

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

   if 8.9999999999999999e52 < t

   1. Initial program 38.9%

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

      1. +-commutative 38.9%

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

      2. associate-/l* 62.8%

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

      3. fma-define 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in a around 0 28.0%

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

      1. mul-1-neg 28.0%

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

      2. unsub-neg 28.0%

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

      3. associate-/l* 43.2%

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

      4. div-sub 43.2%

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

      5. sub-neg 43.2%

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

      6. *-inverses 43.2%

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

      7. metadata-eval 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in y around inf 46.2%

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

   9. Taylor expanded in z around 0 41.9%

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

       1. mul-1-neg 41.9%

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

       2. unsub-neg 41.9%

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

       3. associate-/l* 46.3%

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

   11. Simplified 46.3%

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

Alternative 7: 69.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-35} \lor \neg \left(z \leq 7 \cdot 10^{+33}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e-35) (not (<= z 7e+33)))
   (+ x (* z (/ (- y x) (- a t))))
   (+ x (/ (* y (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-35) || !(z <= 7e+33)) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = x + ((y * (z - t)) / (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 <= (-9.2d-35)) .or. (.not. (z <= 7d+33))) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = x + ((y * (z - t)) / (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 <= -9.2e-35) || !(z <= 7e+33)) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = x + ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e-35) or not (z <= 7e+33):
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = x + ((y * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e-35) || !(z <= 7e+33))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e-35) || ~((z <= 7e+33)))
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = x + ((y * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e-35], N[Not[LessEqual[z, 7e+33]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999996e-35 or 7.0000000000000002e33 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 70.1%

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

      1. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   if -9.1999999999999996e-35 < z < 7.0000000000000002e33

   1. Initial program 71.5%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-35} \lor \neg \left(z \leq 7 \cdot 10^{+33}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-60} \lor \neg \left(z \leq 4.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e-60) (not (<= z 4.2e-11)))
   (+ x (* z (/ (- y x) (- a t))))
   (- x (* t (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e-60) || !(z <= 4.2e-11)) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = x - (t * (y / (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 <= (-3.1d-60)) .or. (.not. (z <= 4.2d-11))) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = x - (t * (y / (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 <= -3.1e-60) || !(z <= 4.2e-11)) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = x - (t * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e-60) or not (z <= 4.2e-11):
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = x - (t * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e-60) || !(z <= 4.2e-11))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.1e-60) || ~((z <= 4.2e-11)))
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = x - (t * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.1e-60], N[Not[LessEqual[z, 4.2e-11]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999988e-60 or 4.1999999999999997e-11 < z

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   if -3.09999999999999988e-60 < z < 4.1999999999999997e-11

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. unsub-neg 63.6%

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

      3. associate-/l* 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-60} \lor \neg \left(z \leq 4.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+31} \lor \neg \left(a \leq 20000000000000\right):\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.45e+31) (not (<= a 20000000000000.0)))
   (- x (* z (/ (- x y) a)))
   (/ (* (- y x) z) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e+31) || !(a <= 20000000000000.0)) {
		tmp = x - (z * ((x - y) / a));
	} 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 ((a <= (-1.45d+31)) .or. (.not. (a <= 20000000000000.0d0))) then
        tmp = x - (z * ((x - y) / a))
    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 ((a <= -1.45e+31) || !(a <= 20000000000000.0)) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = ((y - x) * z) / (a - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.45e+31) or not (a <= 20000000000000.0):
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = ((y - x) * z) / (a - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.45e+31) || !(a <= 20000000000000.0))
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.45e+31) || ~((a <= 20000000000000.0)))
		tmp = x - (z * ((x - y) / a));
	else
		tmp = ((y - x) * z) / (a - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.45e+31], N[Not[LessEqual[a, 20000000000000.0]], $MachinePrecision]], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e31 or 2e13 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in t around 0 67.3%

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

      1. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   if -1.45e31 < a < 2e13

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 80.2%

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

      3. fma-define 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in z around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in z around inf 55.2%

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

      1. div-sub 56.0%

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

      2. associate-/l* 57.0%

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

   10. Simplified 57.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+31} \lor \neg \left(a \leq 20000000000000\right):\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+95)
   (* y (- 1.0 (/ z t)))
   (if (<= t 7.2e-17) (+ x (* y (/ z (- a t)))) (- y (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+95) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 7.2e-17) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d+95)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 7.2d-17) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+95) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 7.2e-17) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+95:
		tmp = y * (1.0 - (z / t))
	elif t <= 7.2e-17:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+95)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 7.2e-17)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+95)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 7.2e-17)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+95], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-17], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999978e95

   1. Initial program 40.6%

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

      1. +-commutative 40.6%

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

      2. associate-/l* 68.8%

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

      3. fma-define 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in a around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. unsub-neg 35.5%

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

      3. associate-/l* 51.1%

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

      4. div-sub 51.1%

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

      5. sub-neg 51.1%

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

      6. *-inverses 51.1%

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

      7. metadata-eval 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in y around inf 63.3%

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

   if -3.59999999999999978e95 < t < 7.1999999999999999e-17

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf 83.5%

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

      1. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

   if 7.1999999999999999e-17 < t

   1. Initial program 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-/l* 65.7%

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

      3. fma-define 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in a around 0 32.0%

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

      1. mul-1-neg 32.0%

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

      2. unsub-neg 32.0%

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

      3. associate-/l* 43.2%

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

      4. div-sub 43.2%

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

      5. sub-neg 43.2%

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

      6. *-inverses 43.2%

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

      7. metadata-eval 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in y around inf 45.5%

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

   9. Taylor expanded in z around 0 42.3%

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

       1. mul-1-neg 42.3%

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

       2. unsub-neg 42.3%

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

       3. associate-/l* 45.6%

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

   11. Simplified 45.6%

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

Alternative 11: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+29} \lor \neg \left(a \leq 22000000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.4e+29) (not (<= a 22000000000000.0)))
   (+ x (* y (/ z a)))
   (- y (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.4e+29) || !(a <= 22000000000000.0)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.4d+29)) .or. (.not. (a <= 22000000000000.0d0))) then
        tmp = x + (y * (z / a))
    else
        tmp = y - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.4e+29) || !(a <= 22000000000000.0)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.4e+29) or not (a <= 22000000000000.0):
		tmp = x + (y * (z / a))
	else:
		tmp = y - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.4e+29) || !(a <= 22000000000000.0))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.4e+29) || ~((a <= 22000000000000.0)))
		tmp = x + (y * (z / a));
	else
		tmp = y - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.4e+29], N[Not[LessEqual[a, 22000000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4e29 or 2.2e13 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-/l* 72.5%

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

   8. Simplified 72.5%

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

   if -5.4e29 < a < 2.2e13

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 80.2%

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

      3. fma-define 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in a around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

      3. associate-/l* 56.7%

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

      4. div-sub 56.8%

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

      5. sub-neg 56.8%

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

      6. *-inverses 56.8%

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

      7. metadata-eval 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in y around inf 53.2%

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

   9. Taylor expanded in z around 0 48.8%

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

       1. mul-1-neg 48.8%

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

       2. unsub-neg 48.8%

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

       3. associate-/l* 53.2%

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

   11. Simplified 53.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+29} \lor \neg \left(a \leq 22000000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+29} \lor \neg \left(a \leq 20000000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.05e+29) (not (<= a 20000000000000.0)))
   (+ x (* y (/ z a)))
   (* y (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.05e+29) || !(a <= 20000000000000.0)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.05d+29)) .or. (.not. (a <= 20000000000000.0d0))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.05e+29) || !(a <= 20000000000000.0)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.05e+29) or not (a <= 20000000000000.0):
		tmp = x + (y * (z / a))
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.05e+29) || !(a <= 20000000000000.0))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.05e+29) || ~((a <= 20000000000000.0)))
		tmp = x + (y * (z / a));
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.05e+29], N[Not[LessEqual[a, 20000000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0499999999999999e29 or 2e13 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-/l* 72.5%

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

   8. Simplified 72.5%

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

   if -3.0499999999999999e29 < a < 2e13

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 80.2%

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

      3. fma-define 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in a around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

      3. associate-/l* 56.7%

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

      4. div-sub 56.8%

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

      5. sub-neg 56.8%

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

      6. *-inverses 56.8%

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

      7. metadata-eval 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in y around inf 53.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+29} \lor \neg \left(a \leq 20000000000000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1100000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+106) x (if (<= a 1100000.0) (* y (- 1.0 (/ z t))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+106) {
		tmp = x;
	} else if (a <= 1100000.0) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.7d+106)) then
        tmp = x
    else if (a <= 1100000.0d0) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+106) {
		tmp = x;
	} else if (a <= 1100000.0) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+106:
		tmp = x
	elif a <= 1100000.0:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+106)
		tmp = x;
	elseif (a <= 1100000.0)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+106)
		tmp = x;
	elseif (a <= 1100000.0)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+106], x, If[LessEqual[a, 1100000.0], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999997e106 or 1.1e6 < a

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 92.2%

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

      3. fma-define 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in a around inf 57.3%

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

   if -1.69999999999999997e106 < a < 1.1e6

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 80.8%

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

      3. fma-define 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 54.4%

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

      4. div-sub 54.4%

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

      5. sub-neg 54.4%

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

      6. *-inverses 54.4%

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

      7. metadata-eval 54.4%

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

   7. Simplified 54.4%

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

   8. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 37.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 32000000000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.05e+29)
   x
   (if (<= a 3.3e-294) (* x (/ z t)) (if (<= a 32000000000000.0) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.05e+29) {
		tmp = x;
	} else if (a <= 3.3e-294) {
		tmp = x * (z / t);
	} else if (a <= 32000000000000.0) {
		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 <= (-3.05d+29)) then
        tmp = x
    else if (a <= 3.3d-294) then
        tmp = x * (z / t)
    else if (a <= 32000000000000.0d0) 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 <= -3.05e+29) {
		tmp = x;
	} else if (a <= 3.3e-294) {
		tmp = x * (z / t);
	} else if (a <= 32000000000000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.05e+29:
		tmp = x
	elif a <= 3.3e-294:
		tmp = x * (z / t)
	elif a <= 32000000000000.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.05e+29)
		tmp = x;
	elseif (a <= 3.3e-294)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 32000000000000.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.05e+29)
		tmp = x;
	elseif (a <= 3.3e-294)
		tmp = x * (z / t);
	elseif (a <= 32000000000000.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.05e+29], x, If[LessEqual[a, 3.3e-294], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 32000000000000.0], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.0499999999999999e29 or 3.2e13 < a

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-/l* 91.1%

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

      3. fma-define 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 53.0%

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

   if -3.0499999999999999e29 < a < 3.3e-294

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 76.5%

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

      3. fma-define 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unsub-neg 48.9%

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

      3. associate-/l* 52.9%

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

      4. div-sub 52.9%

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

      5. sub-neg 52.9%

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

      6. *-inverses 52.9%

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

      7. metadata-eval 52.9%

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

   7. Simplified 52.9%

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

   8. Taylor expanded in x around -inf 33.1%

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

      1. associate-/l* 37.1%

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

   10. Simplified 37.1%

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

   if 3.3e-294 < a < 3.2e13

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 84.7%

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

      3. fma-define 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in t around inf 36.5%

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

Alternative 15: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+96) y (if (<= t 7.5e-17) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+96) {
		tmp = y;
	} else if (t <= 7.5e-17) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+96)) then
        tmp = y
    else if (t <= 7.5d-17) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+96) {
		tmp = y;
	} else if (t <= 7.5e-17) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+96:
		tmp = y
	elif t <= 7.5e-17:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+96)
		tmp = y;
	elseif (t <= 7.5e-17)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+96)
		tmp = y;
	elseif (t <= 7.5e-17)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+96], y, If[LessEqual[t, 7.5e-17], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9000000000000001e96 or 7.49999999999999984e-17 < t

   1. Initial program 45.1%

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

      1. +-commutative 45.1%

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

      2. associate-/l* 66.9%

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

      3. fma-define 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in z around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in t around inf 44.8%

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

   if -1.9000000000000001e96 < t < 7.49999999999999984e-17

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in a around inf 42.1%

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

Alternative 16: 26.0% 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 72.0%

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

   1. +-commutative 72.0%

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

   2. associate-/l* 85.7%

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

   3. fma-define 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in a around inf 31.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 86.9% accurate, 0.5× 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 2024145 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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