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

Percentage Accurate: 67.5% → 89.9%

Time: 23.1s

Alternatives: 25

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: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-246} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -4e-246) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (* (/ (- y x) t) (- a z))))))

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-246) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	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-246) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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-246], 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[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999982e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 93.1%

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

      3. fma-define 93.1%

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

   3. Simplified 93.1%

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

   if -3.99999999999999982e-246 < (+.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. Add Preprocessing

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.7%

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

      2. distribute-lft-out-- 99.7%

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

      3. div-sub 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. div-sub 99.7%

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

      7. associate-/l* 99.9%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-246} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y - x}{a - t} + \frac{x + t \cdot \frac{y - x}{t - a}}{z}\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* z (+ (/ (- y x) (- a t)) (/ (+ x (* t (/ (- y x) (- t a)))) z)))
     (if (<= t_1 -4e-246)
       t_1
       (if (<= t_1 0.0)
         (+ y (* (/ (- y x) t) (- a z)))
         (if (<= t_1 1e+232)
           t_1
           (+ x (* y (* (+ (/ x y) -1.0) (/ (- z t) (- t a)))))))))))

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 = z * (((y - x) / (a - t)) + ((x + (t * ((y - x) / (t - a)))) / z));
	} else if (t_1 <= -4e-246) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= 1e+232) {
		tmp = t_1;
	} else {
		tmp = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))));
	}
	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 = z * (((y - x) / (a - t)) + ((x + (t * ((y - x) / (t - a)))) / z));
	} else if (t_1 <= -4e-246) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= 1e+232) {
		tmp = t_1;
	} else {
		tmp = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))));
	}
	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 = z * (((y - x) / (a - t)) + ((x + (t * ((y - x) / (t - a)))) / z))
	elif t_1 <= -4e-246:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) / t) * (a - z))
	elif t_1 <= 1e+232:
		tmp = t_1
	else:
		tmp = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))))
	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(z * Float64(Float64(Float64(y - x) / Float64(a - t)) + Float64(Float64(x + Float64(t * Float64(Float64(y - x) / Float64(t - a)))) / z)));
	elseif (t_1 <= -4e-246)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_1 <= 1e+232)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(x / y) + -1.0) * Float64(Float64(z - t) / Float64(t - a)))));
	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 = z * (((y - x) / (a - t)) + ((x + (t * ((y - x) / (t - a)))) / z));
	elseif (t_1 <= -4e-246)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t_1 <= 1e+232)
		tmp = t_1;
	else
		tmp = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))));
	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[(z * N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(N[(x + N[(t * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-246], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+232], t$95$1, N[(x + N[(y * N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 29.5%

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

   3. Taylor expanded in z around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. *-commutative 46.6%

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

      3. distribute-rgt-neg-in 46.6%

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

   5. Simplified 80.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999982e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.00000000000000006e232

   1. Initial program 98.7%

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

   if -3.99999999999999982e-246 < (+.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. Add Preprocessing

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.7%

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

      2. distribute-lft-out-- 99.7%

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

      3. div-sub 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. div-sub 99.7%

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

      7. associate-/l* 99.9%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

   if 1.00000000000000006e232 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 48.2%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. *-commutative 68.7%

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

      3. distribute-rgt-neg-in 68.7%

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

      4. +-commutative 68.7%

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

      5. times-frac 76.3%

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

      6. distribute-rgt-out 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y - x}{a - t} + \frac{x + t \cdot \frac{y - x}{t - a}}{z}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+232}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-246} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ 1.0 (/ (/ (- a t) z) (- y x))))
     (if (or (<= t_1 -4e-246) (and (not (<= t_1 0.0)) (<= t_1 5e+298)))
       t_1
       (+ y (* (/ (- y x) t) (- a z)))))))

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 + (1.0 / (((a - t) / z) / (y - x)));
	} else if ((t_1 <= -4e-246) || (!(t_1 <= 0.0) && (t_1 <= 5e+298))) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	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 + (1.0 / (((a - t) / z) / (y - x)));
	} else if ((t_1 <= -4e-246) || (!(t_1 <= 0.0) && (t_1 <= 5e+298))) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	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 + (1.0 / (((a - t) / z) / (y - x)))
	elif (t_1 <= -4e-246) or (not (t_1 <= 0.0) and (t_1 <= 5e+298)):
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * (a - z))
	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(1.0 / Float64(Float64(Float64(a - t) / z) / Float64(y - x))));
	elseif ((t_1 <= -4e-246) || (!(t_1 <= 0.0) && (t_1 <= 5e+298)))
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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 + (1.0 / (((a - t) / z) / (y - x)));
	elseif ((t_1 <= -4e-246) || (~((t_1 <= 0.0)) && (t_1 <= 5e+298)))
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * (a - z));
	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[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -4e-246], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+298]]], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 29.5%

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

      1. clear-num 29.5%

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

      2. inv-pow 29.5%

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

      3. *-commutative 29.5%

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

      4. associate-/r* 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. unpow-1 86.1%

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

      2. associate-/l/ 29.5%

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

      3. *-commutative 29.5%

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

   6. Simplified 29.5%

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

   7. Taylor expanded in z around inf 36.4%

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

      1. associate-/r* 66.6%

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

   9. Simplified 66.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999982e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000003e298

   1. Initial program 98.8%

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

   if -3.99999999999999982e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0 or 5.0000000000000003e298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 33.1%

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

   3. Taylor expanded in t around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. distribute-lft-out-- 63.1%

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

      3. div-sub 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

      6. div-sub 63.1%

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

      7. associate-/l* 73.5%

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

      8. associate-/l* 73.6%

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

      9. distribute-rgt-out-- 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-246} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right) \land x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-160}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 95000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= a -1.46e-26)
     x
     (if (<= a -3.8e-175)
       y
       (if (<= a -5e-231)
         t_1
         (if (<= a 4.1e-160)
           y
           (if (<= a 8e-81)
             t_1
             (if (<= a 95000000000.0)
               y
               (if (<= a 3.5e+49) (* x (/ z (- a))) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -1.46e-26) {
		tmp = x;
	} else if (a <= -3.8e-175) {
		tmp = y;
	} else if (a <= -5e-231) {
		tmp = t_1;
	} else if (a <= 4.1e-160) {
		tmp = y;
	} else if (a <= 8e-81) {
		tmp = t_1;
	} else if (a <= 95000000000.0) {
		tmp = y;
	} else if (a <= 3.5e+49) {
		tmp = x * (z / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (a <= (-1.46d-26)) then
        tmp = x
    else if (a <= (-3.8d-175)) then
        tmp = y
    else if (a <= (-5d-231)) then
        tmp = t_1
    else if (a <= 4.1d-160) then
        tmp = y
    else if (a <= 8d-81) then
        tmp = t_1
    else if (a <= 95000000000.0d0) then
        tmp = y
    else if (a <= 3.5d+49) then
        tmp = x * (z / -a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -1.46e-26) {
		tmp = x;
	} else if (a <= -3.8e-175) {
		tmp = y;
	} else if (a <= -5e-231) {
		tmp = t_1;
	} else if (a <= 4.1e-160) {
		tmp = y;
	} else if (a <= 8e-81) {
		tmp = t_1;
	} else if (a <= 95000000000.0) {
		tmp = y;
	} else if (a <= 3.5e+49) {
		tmp = x * (z / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if a <= -1.46e-26:
		tmp = x
	elif a <= -3.8e-175:
		tmp = y
	elif a <= -5e-231:
		tmp = t_1
	elif a <= 4.1e-160:
		tmp = y
	elif a <= 8e-81:
		tmp = t_1
	elif a <= 95000000000.0:
		tmp = y
	elif a <= 3.5e+49:
		tmp = x * (z / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (a <= -1.46e-26)
		tmp = x;
	elseif (a <= -3.8e-175)
		tmp = y;
	elseif (a <= -5e-231)
		tmp = t_1;
	elseif (a <= 4.1e-160)
		tmp = y;
	elseif (a <= 8e-81)
		tmp = t_1;
	elseif (a <= 95000000000.0)
		tmp = y;
	elseif (a <= 3.5e+49)
		tmp = Float64(x * Float64(z / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (a <= -1.46e-26)
		tmp = x;
	elseif (a <= -3.8e-175)
		tmp = y;
	elseif (a <= -5e-231)
		tmp = t_1;
	elseif (a <= 4.1e-160)
		tmp = y;
	elseif (a <= 8e-81)
		tmp = t_1;
	elseif (a <= 95000000000.0)
		tmp = y;
	elseif (a <= 3.5e+49)
		tmp = x * (z / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e-26], x, If[LessEqual[a, -3.8e-175], y, If[LessEqual[a, -5e-231], t$95$1, If[LessEqual[a, 4.1e-160], y, If[LessEqual[a, 8e-81], t$95$1, If[LessEqual[a, 95000000000.0], y, If[LessEqual[a, 3.5e+49], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.4599999999999999e-26 or 3.49999999999999975e49 < a

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf 47.8%

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

   if -1.4599999999999999e-26 < a < -3.8e-175 or -5.00000000000000023e-231 < a < 4.10000000000000002e-160 or 7.9999999999999997e-81 < a < 9.5e10

   1. Initial program 72.6%

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

   3. Taylor expanded in t around inf 39.3%

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

   if -3.8e-175 < a < -5.00000000000000023e-231 or 4.10000000000000002e-160 < a < 7.9999999999999997e-81

   1. Initial program 82.5%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in a around 0 56.8%

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

   if 9.5e10 < a < 3.49999999999999975e49

   1. Initial program 18.8%

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

   3. Taylor expanded in x around inf 26.7%

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

      1. mul-1-neg 26.7%

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

      2. unsub-neg 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in t around 0 25.7%

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

      1. *-commutative 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in z around inf 26.9%

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

       1. mul-1-neg 26.9%

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

   11. Simplified 26.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-160}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 95000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.5e+31)
     y
     (if (<= t -3.5e-118)
       t_1
       (if (<= t -1.55e-216)
         (+ x (/ (* y z) a))
         (if (<= t 9.5e-200)
           t_1
           (if (<= t 9.5e-179)
             (* y (/ (- z t) a))
             (if (<= t 8e+93) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.5e+31) {
		tmp = y;
	} else if (t <= -3.5e-118) {
		tmp = t_1;
	} else if (t <= -1.55e-216) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.5e-200) {
		tmp = t_1;
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 8e+93) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.5d+31)) then
        tmp = y
    else if (t <= (-3.5d-118)) then
        tmp = t_1
    else if (t <= (-1.55d-216)) then
        tmp = x + ((y * z) / a)
    else if (t <= 9.5d-200) then
        tmp = t_1
    else if (t <= 9.5d-179) then
        tmp = y * ((z - t) / a)
    else if (t <= 8d+93) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.5e+31) {
		tmp = y;
	} else if (t <= -3.5e-118) {
		tmp = t_1;
	} else if (t <= -1.55e-216) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.5e-200) {
		tmp = t_1;
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 8e+93) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.5e+31:
		tmp = y
	elif t <= -3.5e-118:
		tmp = t_1
	elif t <= -1.55e-216:
		tmp = x + ((y * z) / a)
	elif t <= 9.5e-200:
		tmp = t_1
	elif t <= 9.5e-179:
		tmp = y * ((z - t) / a)
	elif t <= 8e+93:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.5e+31)
		tmp = y;
	elseif (t <= -3.5e-118)
		tmp = t_1;
	elseif (t <= -1.55e-216)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 9.5e-200)
		tmp = t_1;
	elseif (t <= 9.5e-179)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 8e+93)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.5e+31)
		tmp = y;
	elseif (t <= -3.5e-118)
		tmp = t_1;
	elseif (t <= -1.55e-216)
		tmp = x + ((y * z) / a);
	elseif (t <= 9.5e-200)
		tmp = t_1;
	elseif (t <= 9.5e-179)
		tmp = y * ((z - t) / a);
	elseif (t <= 8e+93)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+31], y, If[LessEqual[t, -3.5e-118], t$95$1, If[LessEqual[t, -1.55e-216], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-200], t$95$1, If[LessEqual[t, 9.5e-179], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+93], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.5e31 or 8.00000000000000035e93 < t

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 45.3%

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

   if -3.5e31 < t < -3.5e-118 or -1.5500000000000001e-216 < t < 9.4999999999999995e-200 or 9.50000000000000037e-179 < t < 8.00000000000000035e93

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 58.7%

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

      1. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if -3.5e-118 < t < -1.5500000000000001e-216

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in t around 0 63.6%

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

   if 9.4999999999999995e-200 < t < 9.50000000000000037e-179

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate--l+ 99.7%

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

      3. fma-define 99.7%

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

      4. associate-/l* 99.7%

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

      5. *-commutative 99.7%

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

      6. div-sub 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 99.7%

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

      1. div-sub 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in a around inf 80.9%

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

       1. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -8.6e+32)
     y
     (if (<= t -2.05e-119)
       t_1
       (if (<= t -2.2e-213)
         (+ x (/ (* y z) a))
         (if (<= t 9.5e-200)
           (- x (* x (/ z a)))
           (if (<= t 9.5e-179)
             (* y (/ (- z t) a))
             (if (<= t 2.05e+93) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.6e+32) {
		tmp = y;
	} else if (t <= -2.05e-119) {
		tmp = t_1;
	} else if (t <= -2.2e-213) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.5e-200) {
		tmp = x - (x * (z / a));
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.05e+93) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-8.6d+32)) then
        tmp = y
    else if (t <= (-2.05d-119)) then
        tmp = t_1
    else if (t <= (-2.2d-213)) then
        tmp = x + ((y * z) / a)
    else if (t <= 9.5d-200) then
        tmp = x - (x * (z / a))
    else if (t <= 9.5d-179) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.05d+93) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.6e+32) {
		tmp = y;
	} else if (t <= -2.05e-119) {
		tmp = t_1;
	} else if (t <= -2.2e-213) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.5e-200) {
		tmp = x - (x * (z / a));
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.05e+93) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -8.6e+32:
		tmp = y
	elif t <= -2.05e-119:
		tmp = t_1
	elif t <= -2.2e-213:
		tmp = x + ((y * z) / a)
	elif t <= 9.5e-200:
		tmp = x - (x * (z / a))
	elif t <= 9.5e-179:
		tmp = y * ((z - t) / a)
	elif t <= 2.05e+93:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -8.6e+32)
		tmp = y;
	elseif (t <= -2.05e-119)
		tmp = t_1;
	elseif (t <= -2.2e-213)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 9.5e-200)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 9.5e-179)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.05e+93)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -8.6e+32)
		tmp = y;
	elseif (t <= -2.05e-119)
		tmp = t_1;
	elseif (t <= -2.2e-213)
		tmp = x + ((y * z) / a);
	elseif (t <= 9.5e-200)
		tmp = x - (x * (z / a));
	elseif (t <= 9.5e-179)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.05e+93)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+32], y, If[LessEqual[t, -2.05e-119], t$95$1, If[LessEqual[t, -2.2e-213], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-200], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-179], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+93], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.5999999999999994e32 or 2.0500000000000001e93 < t

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 45.3%

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

   if -8.5999999999999994e32 < t < -2.0500000000000001e-119 or 9.50000000000000037e-179 < t < 2.0500000000000001e93

   1. Initial program 84.2%

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

   3. Taylor expanded in x around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in t around 0 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -2.0500000000000001e-119 < t < -2.2000000000000001e-213

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in t around 0 63.6%

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

   if -2.2000000000000001e-213 < t < 9.4999999999999995e-200

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around 0 73.5%

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

      1. *-commutative 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in z around 0 64.5%

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

       1. mul-1-neg 64.5%

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

       2. unsub-neg 64.5%

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

       3. associate-/l* 73.5%

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

   11. Simplified 73.5%

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

   if 9.4999999999999995e-200 < t < 9.50000000000000037e-179

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate--l+ 99.7%

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

      3. fma-define 99.7%

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

      4. associate-/l* 99.7%

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

      5. *-commutative 99.7%

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

      6. div-sub 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 99.7%

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

      1. div-sub 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in a around inf 80.9%

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

       1. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ t_2 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 410:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ 1.0 (/ (/ (- a t) z) (- y x)))))
        (t_2 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -3.5e+45)
     t_2
     (if (<= t 5.4e-81)
       t_1
       (if (<= t 410.0)
         (* y (+ (/ (- z t) (- a t)) (/ x y)))
         (if (<= t 1.8e+93) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -3.5e+45) {
		tmp = t_2;
	} else if (t <= 5.4e-81) {
		tmp = t_1;
	} else if (t <= 410.0) {
		tmp = y * (((z - t) / (a - t)) + (x / y));
	} else if (t <= 1.8e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (1.0d0 / (((a - t) / z) / (y - x)))
    t_2 = y + (((y - x) / t) * (a - z))
    if (t <= (-3.5d+45)) then
        tmp = t_2
    else if (t <= 5.4d-81) then
        tmp = t_1
    else if (t <= 410.0d0) then
        tmp = y * (((z - t) / (a - t)) + (x / y))
    else if (t <= 1.8d+93) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -3.5e+45) {
		tmp = t_2;
	} else if (t <= 5.4e-81) {
		tmp = t_1;
	} else if (t <= 410.0) {
		tmp = y * (((z - t) / (a - t)) + (x / y));
	} else if (t <= 1.8e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)))
	t_2 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -3.5e+45:
		tmp = t_2
	elif t <= 5.4e-81:
		tmp = t_1
	elif t <= 410.0:
		tmp = y * (((z - t) / (a - t)) + (x / y))
	elif t <= 1.8e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / z) / Float64(y - x))))
	t_2 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -3.5e+45)
		tmp = t_2;
	elseif (t <= 5.4e-81)
		tmp = t_1;
	elseif (t <= 410.0)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(a - t)) + Float64(x / y)));
	elseif (t <= 1.8e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	t_2 = y + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -3.5e+45)
		tmp = t_2;
	elseif (t <= 5.4e-81)
		tmp = t_1;
	elseif (t <= 410.0)
		tmp = y * (((z - t) / (a - t)) + (x / y));
	elseif (t <= 1.8e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+45], t$95$2, If[LessEqual[t, 5.4e-81], t$95$1, If[LessEqual[t, 410.0], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+93], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000023e45 or 1.8e93 < t

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. distribute-lft-out-- 62.9%

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

      3. div-sub 62.9%

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

      4. mul-1-neg 62.9%

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

      5. unsub-neg 62.9%

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

      6. div-sub 62.9%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 84.2%

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

      9. distribute-rgt-out-- 84.2%

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

   5. Simplified 84.2%

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

   if -3.50000000000000023e45 < t < 5.39999999999999979e-81 or 410 < t < 1.8e93

   1. Initial program 86.2%

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

      1. clear-num 86.0%

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

      2. inv-pow 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-/r* 94.2%

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

   4. Applied egg-rr 94.2%

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

      1. unpow-1 94.2%

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

      2. associate-/l/ 86.0%

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

      3. *-commutative 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in z around inf 78.8%

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

      1. associate-/r* 87.0%

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

   9. Simplified 87.0%

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

   if 5.39999999999999979e-81 < t < 410

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 82.7%

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

      1. associate-+r+ 82.7%

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

      2. associate--l+ 82.7%

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

      3. fma-define 82.7%

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

      4. associate-/l* 95.5%

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

      5. *-commutative 95.5%

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

      6. div-sub 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in a around inf 87.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;t \leq 410:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-140}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.32e-80)
     t_2
     (if (<= x -9e-135)
       t_1
       (if (<= x -3.9e-140)
         (/ (* x z) (- t a))
         (if (<= x 6e-169)
           (* t (/ y (- t a)))
           (if (<= x 1.05e-9) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.32e-80) {
		tmp = t_2;
	} else if (x <= -9e-135) {
		tmp = t_1;
	} else if (x <= -3.9e-140) {
		tmp = (x * z) / (t - a);
	} else if (x <= 6e-169) {
		tmp = t * (y / (t - a));
	} else if (x <= 1.05e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (x <= (-1.32d-80)) then
        tmp = t_2
    else if (x <= (-9d-135)) then
        tmp = t_1
    else if (x <= (-3.9d-140)) then
        tmp = (x * z) / (t - a)
    else if (x <= 6d-169) then
        tmp = t * (y / (t - a))
    else if (x <= 1.05d-9) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.32e-80) {
		tmp = t_2;
	} else if (x <= -9e-135) {
		tmp = t_1;
	} else if (x <= -3.9e-140) {
		tmp = (x * z) / (t - a);
	} else if (x <= 6e-169) {
		tmp = t * (y / (t - a));
	} else if (x <= 1.05e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.32e-80:
		tmp = t_2
	elif x <= -9e-135:
		tmp = t_1
	elif x <= -3.9e-140:
		tmp = (x * z) / (t - a)
	elif x <= 6e-169:
		tmp = t * (y / (t - a))
	elif x <= 1.05e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.32e-80)
		tmp = t_2;
	elseif (x <= -9e-135)
		tmp = t_1;
	elseif (x <= -3.9e-140)
		tmp = Float64(Float64(x * z) / Float64(t - a));
	elseif (x <= 6e-169)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	elseif (x <= 1.05e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.32e-80)
		tmp = t_2;
	elseif (x <= -9e-135)
		tmp = t_1;
	elseif (x <= -3.9e-140)
		tmp = (x * z) / (t - a);
	elseif (x <= 6e-169)
		tmp = t * (y / (t - a));
	elseif (x <= 1.05e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.32e-80], t$95$2, If[LessEqual[x, -9e-135], t$95$1, If[LessEqual[x, -3.9e-140], N[(N[(x * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-169], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-9], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.31999999999999995e-80 or 1.0500000000000001e-9 < x

   1. Initial program 64.2%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in t around 0 55.4%

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

      1. *-commutative 55.4%

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

   8. Simplified 55.4%

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

   if -1.31999999999999995e-80 < x < -8.99999999999999975e-135 or 5.9999999999999998e-169 < x < 1.0500000000000001e-9

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. associate-+r+ 86.6%

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

      2. associate--l+ 86.6%

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

      3. fma-define 86.6%

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

      4. associate-/l* 89.4%

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

      5. *-commutative 89.4%

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

      6. div-sub 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around inf 70.5%

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

      1. div-sub 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in z around inf 42.3%

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

       1. associate-/l* 52.4%

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

   11. Simplified 52.4%

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

   if -8.99999999999999975e-135 < x < -3.90000000000000019e-140

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -3.90000000000000019e-140 < x < 5.9999999999999998e-169

   1. Initial program 80.9%

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

   3. Taylor expanded in z around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. associate-/l* 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in x around 0 43.8%

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

      1. mul-1-neg 43.8%

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

   8. Simplified 43.8%

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

      1. associate-*r/ 49.1%

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

      2. *-commutative 49.1%

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

   10. Applied egg-rr 49.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-140}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-172}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (* (+ (/ x y) -1.0) (/ (- z t) (- t a)))))))
   (if (<= y -7.6e-145)
     t_1
     (if (<= y -3.4e-172)
       (+ y (/ (+ (* (- y x) a) (* z (- x y))) t))
       (if (<= y 1.15e-193)
         (* x (+ (+ 1.0 (/ t (- a t))) (/ z (- t a))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))));
	double tmp;
	if (y <= -7.6e-145) {
		tmp = t_1;
	} else if (y <= -3.4e-172) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (y <= 1.15e-193) {
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	} 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 / y) + (-1.0d0)) * ((z - t) / (t - a))))
    if (y <= (-7.6d-145)) then
        tmp = t_1
    else if (y <= (-3.4d-172)) then
        tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
    else if (y <= 1.15d-193) then
        tmp = x * ((1.0d0 + (t / (a - t))) + (z / (t - a)))
    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 / y) + -1.0) * ((z - t) / (t - a))));
	double tmp;
	if (y <= -7.6e-145) {
		tmp = t_1;
	} else if (y <= -3.4e-172) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (y <= 1.15e-193) {
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))))
	tmp = 0
	if y <= -7.6e-145:
		tmp = t_1
	elif y <= -3.4e-172:
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
	elif y <= 1.15e-193:
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(Float64(x / y) + -1.0) * Float64(Float64(z - t) / Float64(t - a)))))
	tmp = 0.0
	if (y <= -7.6e-145)
		tmp = t_1;
	elseif (y <= -3.4e-172)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	elseif (y <= 1.15e-193)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) + Float64(z / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (((x / y) + -1.0) * ((z - t) / (t - a))));
	tmp = 0.0;
	if (y <= -7.6e-145)
		tmp = t_1;
	elseif (y <= -3.4e-172)
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	elseif (y <= 1.15e-193)
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e-145], t$95$1, If[LessEqual[y, -3.4e-172], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-193], N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000004e-145 or 1.15000000000000004e-193 < y

   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 y around -inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. *-commutative 82.7%

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

      3. distribute-rgt-neg-in 82.7%

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

      4. +-commutative 82.7%

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

      5. times-frac 87.8%

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

      6. distribute-rgt-out 89.9%

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

   5. Simplified 89.9%

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

   if -7.6000000000000004e-145 < y < -3.3999999999999999e-172

   1. Initial program 20.2%

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

   3. Taylor expanded in t around -inf 99.7%

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

   if -3.3999999999999999e-172 < y < 1.15000000000000004e-193

   1. Initial program 69.1%

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

   3. Taylor expanded in x around -inf 86.9%

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

      1. associate-*r* 86.9%

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

      2. neg-mul-1 86.9%

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

      3. +-commutative 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-145}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-172}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y - x}{t - a}\\ t_2 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 58:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ (- y x) (- t a)))))
        (t_2 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -1.6e+44)
     t_2
     (if (<= t 8e-79)
       t_1
       (if (<= t 58.0)
         (* y (+ (/ (- z t) (- a t)) (/ x y)))
         (if (<= t 2.05e+93) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * ((y - x) / (t - a)));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = t_2;
	} else if (t <= 8e-79) {
		tmp = t_1;
	} else if (t <= 58.0) {
		tmp = y * (((z - t) / (a - t)) + (x / y));
	} else if (t <= 2.05e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (z * ((y - x) / (t - a)))
    t_2 = y + (((y - x) / t) * (a - z))
    if (t <= (-1.6d+44)) then
        tmp = t_2
    else if (t <= 8d-79) then
        tmp = t_1
    else if (t <= 58.0d0) then
        tmp = y * (((z - t) / (a - t)) + (x / y))
    else if (t <= 2.05d+93) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * ((y - x) / (t - a)));
	double t_2 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = t_2;
	} else if (t <= 8e-79) {
		tmp = t_1;
	} else if (t <= 58.0) {
		tmp = y * (((z - t) / (a - t)) + (x / y));
	} else if (t <= 2.05e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * ((y - x) / (t - a)))
	t_2 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -1.6e+44:
		tmp = t_2
	elif t <= 8e-79:
		tmp = t_1
	elif t <= 58.0:
		tmp = y * (((z - t) / (a - t)) + (x / y))
	elif t <= 2.05e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))))
	t_2 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -1.6e+44)
		tmp = t_2;
	elseif (t <= 8e-79)
		tmp = t_1;
	elseif (t <= 58.0)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(a - t)) + Float64(x / y)));
	elseif (t <= 2.05e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * ((y - x) / (t - a)));
	t_2 = y + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -1.6e+44)
		tmp = t_2;
	elseif (t <= 8e-79)
		tmp = t_1;
	elseif (t <= 58.0)
		tmp = y * (((z - t) / (a - t)) + (x / y));
	elseif (t <= 2.05e+93)
		tmp = t_1;
	else
		tmp = t_2;
	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[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+44], t$95$2, If[LessEqual[t, 8e-79], t$95$1, If[LessEqual[t, 58.0], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+93], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000002e44 or 2.0500000000000001e93 < t

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. distribute-lft-out-- 62.9%

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

      3. div-sub 62.9%

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

      4. mul-1-neg 62.9%

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

      5. unsub-neg 62.9%

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

      6. div-sub 62.9%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 84.2%

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

      9. distribute-rgt-out-- 84.2%

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

   5. Simplified 84.2%

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

   if -1.60000000000000002e44 < t < 8e-79 or 58 < t < 2.0500000000000001e93

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. associate-/l* 84.5%

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

   5. Simplified 84.5%

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

   if 8e-79 < t < 58

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 82.7%

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

      1. associate-+r+ 82.7%

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

      2. associate--l+ 82.7%

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

      3. fma-define 82.7%

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

      4. associate-/l* 95.5%

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

      5. *-commutative 95.5%

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

      6. div-sub 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in a around inf 87.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 58:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-175}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-161}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= a -1.85e-22)
     x
     (if (<= a -5.5e-175)
       y
       (if (<= a -4.5e-240)
         t_1
         (if (<= a 7e-161) y (if (<= a 1.75e+61) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -1.85e-22) {
		tmp = x;
	} else if (a <= -5.5e-175) {
		tmp = y;
	} else if (a <= -4.5e-240) {
		tmp = t_1;
	} else if (a <= 7e-161) {
		tmp = y;
	} else if (a <= 1.75e+61) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (a <= (-1.85d-22)) then
        tmp = x
    else if (a <= (-5.5d-175)) then
        tmp = y
    else if (a <= (-4.5d-240)) then
        tmp = t_1
    else if (a <= 7d-161) then
        tmp = y
    else if (a <= 1.75d+61) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (a <= -1.85e-22) {
		tmp = x;
	} else if (a <= -5.5e-175) {
		tmp = y;
	} else if (a <= -4.5e-240) {
		tmp = t_1;
	} else if (a <= 7e-161) {
		tmp = y;
	} else if (a <= 1.75e+61) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if a <= -1.85e-22:
		tmp = x
	elif a <= -5.5e-175:
		tmp = y
	elif a <= -4.5e-240:
		tmp = t_1
	elif a <= 7e-161:
		tmp = y
	elif a <= 1.75e+61:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (a <= -1.85e-22)
		tmp = x;
	elseif (a <= -5.5e-175)
		tmp = y;
	elseif (a <= -4.5e-240)
		tmp = t_1;
	elseif (a <= 7e-161)
		tmp = y;
	elseif (a <= 1.75e+61)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (a <= -1.85e-22)
		tmp = x;
	elseif (a <= -5.5e-175)
		tmp = y;
	elseif (a <= -4.5e-240)
		tmp = t_1;
	elseif (a <= 7e-161)
		tmp = y;
	elseif (a <= 1.75e+61)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-22], x, If[LessEqual[a, -5.5e-175], y, If[LessEqual[a, -4.5e-240], t$95$1, If[LessEqual[a, 7e-161], y, If[LessEqual[a, 1.75e+61], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.85e-22 or 1.75000000000000009e61 < a

   1. Initial program 70.0%

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

   3. Taylor expanded in a around inf 48.2%

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

   if -1.85e-22 < a < -5.50000000000000054e-175 or -4.5000000000000001e-240 < a < 7.00000000000000039e-161

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf 41.9%

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

   if -5.50000000000000054e-175 < a < -4.5000000000000001e-240 or 7.00000000000000039e-161 < a < 1.75000000000000009e61

   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 x around inf 47.4%

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

      1. mul-1-neg 47.4%

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

      2. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in a around 0 36.6%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-175}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-161}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{t - a}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x \cdot \left(1 + t\_1\right)}{y}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- t a))))
   (if (<= y -1.5e-166)
     (* y (+ (/ (- z t) (- a t)) (/ (* x (+ 1.0 t_1)) y)))
     (if (<= y 1.35e-189)
       (* x (+ (+ 1.0 (/ t (- a t))) (/ z (- t a))))
       (+ x (* y (* (+ (/ x y) -1.0) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (t - a);
	double tmp;
	if (y <= -1.5e-166) {
		tmp = y * (((z - t) / (a - t)) + ((x * (1.0 + t_1)) / y));
	} else if (y <= 1.35e-189) {
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	} else {
		tmp = x + (y * (((x / y) + -1.0) * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (t - a)
    if (y <= (-1.5d-166)) then
        tmp = y * (((z - t) / (a - t)) + ((x * (1.0d0 + t_1)) / y))
    else if (y <= 1.35d-189) then
        tmp = x * ((1.0d0 + (t / (a - t))) + (z / (t - a)))
    else
        tmp = x + (y * (((x / y) + (-1.0d0)) * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (t - a);
	double tmp;
	if (y <= -1.5e-166) {
		tmp = y * (((z - t) / (a - t)) + ((x * (1.0 + t_1)) / y));
	} else if (y <= 1.35e-189) {
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	} else {
		tmp = x + (y * (((x / y) + -1.0) * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (t - a)
	tmp = 0
	if y <= -1.5e-166:
		tmp = y * (((z - t) / (a - t)) + ((x * (1.0 + t_1)) / y))
	elif y <= 1.35e-189:
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)))
	else:
		tmp = x + (y * (((x / y) + -1.0) * t_1))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(t - a))
	tmp = 0.0
	if (y <= -1.5e-166)
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(a - t)) + Float64(Float64(x * Float64(1.0 + t_1)) / y)));
	elseif (y <= 1.35e-189)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) + Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(x / y) + -1.0) * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (t - a);
	tmp = 0.0;
	if (y <= -1.5e-166)
		tmp = y * (((z - t) / (a - t)) + ((x * (1.0 + t_1)) / y));
	elseif (y <= 1.35e-189)
		tmp = x * ((1.0 + (t / (a - t))) + (z / (t - a)));
	else
		tmp = x + (y * (((x / y) + -1.0) * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-166], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-189], N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e-166

   1. Initial program 72.6%

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

   3. Taylor expanded in y around -inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. *-commutative 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

   5. Simplified 94.2%

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

   if -1.5000000000000001e-166 < y < 1.35e-189

   1. Initial program 66.8%

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

   3. Taylor expanded in x around -inf 84.0%

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

      1. associate-*r* 84.0%

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

      2. neg-mul-1 84.0%

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

      3. +-commutative 84.0%

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

   5. Simplified 84.0%

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

   if 1.35e-189 < y

   1. Initial program 71.8%

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

   3. Taylor expanded in y around -inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. *-commutative 79.7%

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

      3. distribute-rgt-neg-in 79.7%

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

      4. +-commutative 79.7%

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

      5. times-frac 83.3%

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

      6. distribute-rgt-out 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(\frac{z - t}{a - t} + \frac{x \cdot \left(1 + \frac{z - t}{t - a}\right)}{y}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \frac{z}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\frac{x}{y} + -1\right) \cdot \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+250}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 10000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.55e+250)
   y
   (if (<= y -1.05e+96)
     (* y (/ z a))
     (if (<= y -1.16e-147)
       x
       (if (<= y -2.7e-305) (* x (/ (- z a) t)) (if (<= y 10000000.0) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.55e+250) {
		tmp = y;
	} else if (y <= -1.05e+96) {
		tmp = y * (z / a);
	} else if (y <= -1.16e-147) {
		tmp = x;
	} else if (y <= -2.7e-305) {
		tmp = x * ((z - a) / t);
	} else if (y <= 10000000.0) {
		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 (y <= (-2.55d+250)) then
        tmp = y
    else if (y <= (-1.05d+96)) then
        tmp = y * (z / a)
    else if (y <= (-1.16d-147)) then
        tmp = x
    else if (y <= (-2.7d-305)) then
        tmp = x * ((z - a) / t)
    else if (y <= 10000000.0d0) 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 (y <= -2.55e+250) {
		tmp = y;
	} else if (y <= -1.05e+96) {
		tmp = y * (z / a);
	} else if (y <= -1.16e-147) {
		tmp = x;
	} else if (y <= -2.7e-305) {
		tmp = x * ((z - a) / t);
	} else if (y <= 10000000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.55e+250:
		tmp = y
	elif y <= -1.05e+96:
		tmp = y * (z / a)
	elif y <= -1.16e-147:
		tmp = x
	elif y <= -2.7e-305:
		tmp = x * ((z - a) / t)
	elif y <= 10000000.0:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.55e+250)
		tmp = y;
	elseif (y <= -1.05e+96)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= -1.16e-147)
		tmp = x;
	elseif (y <= -2.7e-305)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (y <= 10000000.0)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.55e+250)
		tmp = y;
	elseif (y <= -1.05e+96)
		tmp = y * (z / a);
	elseif (y <= -1.16e-147)
		tmp = x;
	elseif (y <= -2.7e-305)
		tmp = x * ((z - a) / t);
	elseif (y <= 10000000.0)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.55e+250], y, If[LessEqual[y, -1.05e+96], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.16e-147], x, If[LessEqual[y, -2.7e-305], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 10000000.0], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.55e250 or 1e7 < y

   1. Initial program 60.2%

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

   3. Taylor expanded in t around inf 45.3%

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

   if -2.55e250 < y < -1.0500000000000001e96

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 85.3%

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

      1. associate-+r+ 85.3%

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

      2. associate--l+ 85.3%

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

      3. fma-define 85.3%

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

      4. associate-/l* 90.1%

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

      5. *-commutative 90.1%

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

      6. div-sub 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in y around inf 81.4%

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

      1. div-sub 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in t around 0 40.4%

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

       1. associate-/l* 44.9%

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

   11. Simplified 44.9%

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

   if -1.0500000000000001e96 < y < -1.1599999999999999e-147 or -2.6999999999999999e-305 < y < 1e7

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 36.2%

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

   if -1.1599999999999999e-147 < y < -2.6999999999999999e-305

   1. Initial program 62.7%

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

   3. Taylor expanded in x around -inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. neg-mul-1 77.2%

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

      3. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around -inf 54.7%

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

      1. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+250}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 10000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+253}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.021:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+253)
   y
   (if (<= y -0.021)
     (* y (/ z (- a t)))
     (if (<= y -3.7e-145)
       x
       (if (<= y -8.6e-305) (* x (/ (- z a) t)) (if (<= y 8.6e+14) x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+253) {
		tmp = y;
	} else if (y <= -0.021) {
		tmp = y * (z / (a - t));
	} else if (y <= -3.7e-145) {
		tmp = x;
	} else if (y <= -8.6e-305) {
		tmp = x * ((z - a) / t);
	} else if (y <= 8.6e+14) {
		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 (y <= (-4.7d+253)) then
        tmp = y
    else if (y <= (-0.021d0)) then
        tmp = y * (z / (a - t))
    else if (y <= (-3.7d-145)) then
        tmp = x
    else if (y <= (-8.6d-305)) then
        tmp = x * ((z - a) / t)
    else if (y <= 8.6d+14) 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 (y <= -4.7e+253) {
		tmp = y;
	} else if (y <= -0.021) {
		tmp = y * (z / (a - t));
	} else if (y <= -3.7e-145) {
		tmp = x;
	} else if (y <= -8.6e-305) {
		tmp = x * ((z - a) / t);
	} else if (y <= 8.6e+14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+253:
		tmp = y
	elif y <= -0.021:
		tmp = y * (z / (a - t))
	elif y <= -3.7e-145:
		tmp = x
	elif y <= -8.6e-305:
		tmp = x * ((z - a) / t)
	elif y <= 8.6e+14:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+253)
		tmp = y;
	elseif (y <= -0.021)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (y <= -3.7e-145)
		tmp = x;
	elseif (y <= -8.6e-305)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (y <= 8.6e+14)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+253)
		tmp = y;
	elseif (y <= -0.021)
		tmp = y * (z / (a - t));
	elseif (y <= -3.7e-145)
		tmp = x;
	elseif (y <= -8.6e-305)
		tmp = x * ((z - a) / t);
	elseif (y <= 8.6e+14)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+253], y, If[LessEqual[y, -0.021], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-145], x, If[LessEqual[y, -8.6e-305], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+14], x, y]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.70000000000000022e253 or 8.6e14 < y

   1. Initial program 60.2%

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

   3. Taylor expanded in t around inf 45.3%

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

   if -4.70000000000000022e253 < y < -0.0210000000000000013

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. associate-+r+ 88.2%

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

      2. associate--l+ 88.2%

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

      3. fma-define 88.2%

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

      4. associate-/l* 92.6%

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

      5. *-commutative 92.6%

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

      6. div-sub 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in z around inf 39.8%

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

       1. associate-/l* 51.9%

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

   11. Simplified 51.9%

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

   if -0.0210000000000000013 < y < -3.70000000000000013e-145 or -8.6000000000000004e-305 < y < 8.6e14

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 37.9%

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

   if -3.70000000000000013e-145 < y < -8.6000000000000004e-305

   1. Initial program 62.7%

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

   3. Taylor expanded in x around -inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. neg-mul-1 77.2%

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

      3. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around -inf 54.7%

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

      1. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+253}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.021:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -8.6e+32)
     y
     (if (<= t 6e-200)
       t_1
       (if (<= t 9.5e-179) (* y (/ (- z t) a)) (if (<= t 5e+94) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.6e+32) {
		tmp = y;
	} else if (t <= 6e-200) {
		tmp = t_1;
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5e+94) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-8.6d+32)) then
        tmp = y
    else if (t <= 6d-200) then
        tmp = t_1
    else if (t <= 9.5d-179) then
        tmp = y * ((z - t) / a)
    else if (t <= 5d+94) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -8.6e+32) {
		tmp = y;
	} else if (t <= 6e-200) {
		tmp = t_1;
	} else if (t <= 9.5e-179) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5e+94) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -8.6e+32:
		tmp = y
	elif t <= 6e-200:
		tmp = t_1
	elif t <= 9.5e-179:
		tmp = y * ((z - t) / a)
	elif t <= 5e+94:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -8.6e+32)
		tmp = y;
	elseif (t <= 6e-200)
		tmp = t_1;
	elseif (t <= 9.5e-179)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 5e+94)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -8.6e+32)
		tmp = y;
	elseif (t <= 6e-200)
		tmp = t_1;
	elseif (t <= 9.5e-179)
		tmp = y * ((z - t) / a);
	elseif (t <= 5e+94)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+32], y, If[LessEqual[t, 6e-200], t$95$1, If[LessEqual[t, 9.5e-179], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+94], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5999999999999994e32 or 5.0000000000000001e94 < t

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 45.3%

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

   if -8.5999999999999994e32 < t < 5.99999999999999989e-200 or 9.50000000000000037e-179 < t < 5.0000000000000001e94

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. unsub-neg 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in t around 0 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

   if 5.99999999999999989e-200 < t < 9.50000000000000037e-179

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate--l+ 99.7%

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

      3. fma-define 99.7%

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

      4. associate-/l* 99.7%

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

      5. *-commutative 99.7%

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

      6. div-sub 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 99.7%

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

      1. div-sub 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in a around inf 80.9%

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

       1. associate-/l* 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.86 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.86e-78)
     t_1
     (if (<= x 4.6e-169)
       (* t (/ y (- t a)))
       (if (<= x 1.15e-8) (* y (/ z (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.86e-78) {
		tmp = t_1;
	} else if (x <= 4.6e-169) {
		tmp = t * (y / (t - a));
	} else if (x <= 1.15e-8) {
		tmp = y * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-1.86d-78)) then
        tmp = t_1
    else if (x <= 4.6d-169) then
        tmp = t * (y / (t - a))
    else if (x <= 1.15d-8) then
        tmp = y * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.86e-78) {
		tmp = t_1;
	} else if (x <= 4.6e-169) {
		tmp = t * (y / (t - a));
	} else if (x <= 1.15e-8) {
		tmp = y * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.86e-78:
		tmp = t_1
	elif x <= 4.6e-169:
		tmp = t * (y / (t - a))
	elif x <= 1.15e-8:
		tmp = y * (z / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.86e-78)
		tmp = t_1;
	elseif (x <= 4.6e-169)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	elseif (x <= 1.15e-8)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.86e-78)
		tmp = t_1;
	elseif (x <= 4.6e-169)
		tmp = t * (y / (t - a));
	elseif (x <= 1.15e-8)
		tmp = y * (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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.86e-78], t$95$1, If[LessEqual[x, 4.6e-169], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-8], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85999999999999996e-78 or 1.15e-8 < x

   1. Initial program 64.2%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in t around 0 55.4%

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

      1. *-commutative 55.4%

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

   8. Simplified 55.4%

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

   if -1.85999999999999996e-78 < x < 4.6000000000000002e-169

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

      3. associate-/l* 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in x around 0 40.6%

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

      1. mul-1-neg 40.6%

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

   8. Simplified 40.6%

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

      1. associate-*r/ 43.8%

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

      2. *-commutative 43.8%

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

   10. Applied egg-rr 43.8%

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

   if 4.6000000000000002e-169 < x < 1.15e-8

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 87.3%

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

      1. associate-+r+ 87.3%

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

      2. associate--l+ 87.3%

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

      3. fma-define 87.3%

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

      4. associate-/l* 87.3%

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

      5. *-commutative 87.3%

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

      6. div-sub 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around inf 70.5%

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

      1. div-sub 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in z around inf 45.5%

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

       1. associate-/l* 57.9%

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

   11. Simplified 57.9%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.86 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.05e-43)
     t_1
     (if (<= x 1.2e-167)
       (* y (/ (- t z) t))
       (if (<= x 3.3e-9) (* y (/ z (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.05e-43) {
		tmp = t_1;
	} else if (x <= 1.2e-167) {
		tmp = y * ((t - z) / t);
	} else if (x <= 3.3e-9) {
		tmp = y * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-1.05d-43)) then
        tmp = t_1
    else if (x <= 1.2d-167) then
        tmp = y * ((t - z) / t)
    else if (x <= 3.3d-9) then
        tmp = y * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.05e-43) {
		tmp = t_1;
	} else if (x <= 1.2e-167) {
		tmp = y * ((t - z) / t);
	} else if (x <= 3.3e-9) {
		tmp = y * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.05e-43:
		tmp = t_1
	elif x <= 1.2e-167:
		tmp = y * ((t - z) / t)
	elif x <= 3.3e-9:
		tmp = y * (z / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.05e-43)
		tmp = t_1;
	elseif (x <= 1.2e-167)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (x <= 3.3e-9)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.05e-43)
		tmp = t_1;
	elseif (x <= 1.2e-167)
		tmp = y * ((t - z) / t);
	elseif (x <= 3.3e-9)
		tmp = y * (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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-43], t$95$1, If[LessEqual[x, 1.2e-167], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-9], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e-43 or 3.30000000000000018e-9 < x

   1. Initial program 64.8%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 56.9%

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

      1. *-commutative 56.9%

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

   8. Simplified 56.9%

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

   if -1.05e-43 < x < 1.19999999999999997e-167

   1. Initial program 79.9%

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

   3. Taylor expanded in y around inf 94.4%

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

      1. associate-+r+ 94.4%

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

      2. associate--l+ 94.4%

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

      3. fma-define 94.4%

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

      4. associate-/l* 92.3%

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

      5. *-commutative 92.3%

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

      6. div-sub 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in y around inf 76.4%

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

      1. div-sub 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in a around 0 58.1%

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

       1. mul-1-neg 58.1%

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

   11. Simplified 58.1%

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

   if 1.19999999999999997e-167 < x < 3.30000000000000018e-9

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 86.7%

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

      1. associate-+r+ 86.7%

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

      2. associate--l+ 86.7%

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

      3. fma-define 86.7%

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

      4. associate-/l* 86.8%

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

      5. *-commutative 86.8%

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

      6. div-sub 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in z around inf 47.4%

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

       1. associate-/l* 60.3%

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

   11. Simplified 60.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-45} \lor \neg \left(x \leq 35000000\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.16e-45) (not (<= x 35000000.0)))
   (* x (+ 1.0 (/ (- z t) (- t a))))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.16e-45) || !(x <= 35000000.0)) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = 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 ((x <= (-1.16d-45)) .or. (.not. (x <= 35000000.0d0))) then
        tmp = x * (1.0d0 + ((z - t) / (t - a)))
    else
        tmp = 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 ((x <= -1.16e-45) || !(x <= 35000000.0)) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.16e-45) or not (x <= 35000000.0):
		tmp = x * (1.0 + ((z - t) / (t - a)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.16e-45) || !(x <= 35000000.0))
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.16e-45) || ~((x <= 35000000.0)))
		tmp = x * (1.0 + ((z - t) / (t - a)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.16e-45], N[Not[LessEqual[x, 35000000.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16000000000000002e-45 or 3.5e7 < x

   1. Initial program 65.1%

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

   3. Taylor expanded in x around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   5. Simplified 66.9%

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

   if -1.16000000000000002e-45 < x < 3.5e7

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 93.1%

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

      1. associate-+r+ 93.1%

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

      2. associate--l+ 93.1%

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

      3. fma-define 93.1%

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

      4. associate-/l* 91.5%

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

      5. *-commutative 91.5%

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

      6. div-sub 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

   8. Simplified 75.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-45} \lor \neg \left(x \leq 35000000\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{t - a}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-167} \lor \neg \left(y \leq 1.25 \cdot 10^{-164}\right):\\ \;\;\;\;x - y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- t a))))
   (if (or (<= y -5e-167) (not (<= y 1.25e-164)))
     (- x (* y t_1))
     (* x (+ 1.0 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (t - a);
	double tmp;
	if ((y <= -5e-167) || !(y <= 1.25e-164)) {
		tmp = x - (y * t_1);
	} else {
		tmp = x * (1.0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (t - a)
    if ((y <= (-5d-167)) .or. (.not. (y <= 1.25d-164))) then
        tmp = x - (y * t_1)
    else
        tmp = x * (1.0d0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (t - a);
	double tmp;
	if ((y <= -5e-167) || !(y <= 1.25e-164)) {
		tmp = x - (y * t_1);
	} else {
		tmp = x * (1.0 + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (t - a)
	tmp = 0
	if (y <= -5e-167) or not (y <= 1.25e-164):
		tmp = x - (y * t_1)
	else:
		tmp = x * (1.0 + t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(t - a))
	tmp = 0.0
	if ((y <= -5e-167) || !(y <= 1.25e-164))
		tmp = Float64(x - Float64(y * t_1));
	else
		tmp = Float64(x * Float64(1.0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (t - a);
	tmp = 0.0;
	if ((y <= -5e-167) || ~((y <= 1.25e-164)))
		tmp = x - (y * t_1);
	else
		tmp = x * (1.0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -5e-167], N[Not[LessEqual[y, 1.25e-164]], $MachinePrecision]], N[(x - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-167 or 1.2499999999999999e-164 < y

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -5.0000000000000002e-167 < y < 1.2499999999999999e-164

   1. Initial program 67.2%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-167} \lor \neg \left(y \leq 1.25 \cdot 10^{-164}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+89} \lor \neg \left(y \leq 4.5 \cdot 10^{-141}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.4e+89) (not (<= y 4.5e-141)))
   (- x (* y (/ (- z t) (- t a))))
   (- x (* z (/ (- y x) (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.4e+89) || !(y <= 4.5e-141)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = x - (z * ((y - x) / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.4d+89)) .or. (.not. (y <= 4.5d-141))) then
        tmp = x - (y * ((z - t) / (t - a)))
    else
        tmp = x - (z * ((y - x) / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.4e+89) || !(y <= 4.5e-141)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = x - (z * ((y - x) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.4e+89) or not (y <= 4.5e-141):
		tmp = x - (y * ((z - t) / (t - a)))
	else:
		tmp = x - (z * ((y - x) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.4e+89) || !(y <= 4.5e-141))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.4e+89) || ~((y <= 4.5e-141)))
		tmp = x - (y * ((z - t) / (t - a)));
	else
		tmp = x - (z * ((y - x) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.4e+89], N[Not[LessEqual[y, 4.5e-141]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4000000000000002e89 or 4.5e-141 < y

   1. Initial program 68.8%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   if -3.4000000000000002e89 < y < 4.5e-141

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+89} \lor \neg \left(y \leq 4.5 \cdot 10^{-141}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+43} \lor \neg \left(t \leq 2.05 \cdot 10^{+93}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+43) (not (<= t 2.05e+93)))
   (+ y (* (/ (- y x) t) (- a z)))
   (- x (* z (/ (- y x) (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+43) || !(t <= 2.05e+93)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x - (z * ((y - x) / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.3d+43)) .or. (.not. (t <= 2.05d+93))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x - (z * ((y - x) / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+43) || !(t <= 2.05e+93)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x - (z * ((y - x) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+43) or not (t <= 2.05e+93):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x - (z * ((y - x) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+43) || !(t <= 2.05e+93))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+43) || ~((t <= 2.05e+93)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x - (z * ((y - x) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+43], N[Not[LessEqual[t, 2.05e+93]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e43 or 2.0500000000000001e93 < t

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. distribute-lft-out-- 62.9%

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

      3. div-sub 62.9%

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

      4. mul-1-neg 62.9%

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

      5. unsub-neg 62.9%

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

      6. div-sub 62.9%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 84.2%

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

      9. distribute-rgt-out-- 84.2%

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

   5. Simplified 84.2%

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

   if -1.3000000000000001e43 < t < 2.0500000000000001e93

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf 76.1%

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

      1. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+43} \lor \neg \left(t \leq 2.05 \cdot 10^{+93}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+43} \lor \neg \left(x \leq 2.8 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.7e+43) (not (<= x 2.8e+20)))
   (* x (- 1.0 (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.7e+43) || !(x <= 2.8e+20)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = 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 ((x <= (-1.7d+43)) .or. (.not. (x <= 2.8d+20))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = 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 ((x <= -1.7e+43) || !(x <= 2.8e+20)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.7e+43) or not (x <= 2.8e+20):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.7e+43) || !(x <= 2.8e+20))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.7e+43) || ~((x <= 2.8e+20)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.7e+43], N[Not[LessEqual[x, 2.8e+20]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000006e43 or 2.8e20 < x

   1. Initial program 61.8%

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

   3. Taylor expanded in x around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0 60.5%

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

      1. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if -1.70000000000000006e43 < x < 2.8e20

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 92.1%

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

      1. associate-+r+ 92.1%

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

      2. associate--l+ 92.1%

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

      3. fma-define 92.1%

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

      4. associate-/l* 90.7%

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

      5. *-commutative 90.7%

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

      6. div-sub 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in y around inf 69.9%

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

      1. div-sub 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+43} \lor \neg \left(x \leq 2.8 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-43} \lor \neg \left(x \leq 600000000\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.8e-43) (not (<= x 600000000.0)))
   (+ x (* z (/ (- y x) a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e-43) || !(x <= 600000000.0)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = 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 ((x <= (-2.8d-43)) .or. (.not. (x <= 600000000.0d0))) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = 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 ((x <= -2.8e-43) || !(x <= 600000000.0)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.8e-43) or not (x <= 600000000.0):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.8e-43) || !(x <= 600000000.0))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.8e-43) || ~((x <= 600000000.0)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.8e-43], N[Not[LessEqual[x, 600000000.0]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999998e-43 or 6e8 < x

   1. Initial program 64.6%

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

   3. Taylor expanded in t around 0 53.0%

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

      1. associate-/l* 62.1%

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

   5. Simplified 62.1%

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

   if -2.7999999999999998e-43 < x < 6e8

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 92.4%

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

      1. associate-+r+ 92.4%

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

      2. associate--l+ 92.4%

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

      3. fma-define 92.4%

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

      4. associate-/l* 90.8%

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

      5. *-commutative 90.8%

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

      6. div-sub 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in y around inf 73.8%

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

      1. div-sub 73.8%

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

   8. Simplified 73.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-43} \lor \neg \left(x \leq 600000000\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.3e-27) x (if (<= a 3.5e+49) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.3e-27) {
		tmp = x;
	} else if (a <= 3.5e+49) {
		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 <= (-6.3d-27)) then
        tmp = x
    else if (a <= 3.5d+49) 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 <= -6.3e-27) {
		tmp = x;
	} else if (a <= 3.5e+49) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.3e-27:
		tmp = x
	elif a <= 3.5e+49:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.3e-27)
		tmp = x;
	elseif (a <= 3.5e+49)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.3e-27)
		tmp = x;
	elseif (a <= 3.5e+49)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.3e-27], x, If[LessEqual[a, 3.5e+49], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.3000000000000001e-27 or 3.49999999999999975e49 < a

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf 47.8%

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

   if -6.3000000000000001e-27 < a < 3.49999999999999975e49

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 31.8%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 25.2% 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 71.0%

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

3. Taylor expanded in a around inf 25.2%

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

4. Final simplification 25.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.8% 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 2024066 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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