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

Percentage Accurate: 67.4% → 89.8%

Time: 18.1s

Alternatives: 21

Speedup: 0.9×

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: 67.4% 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: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 -1e-262)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- z a) (- x y)) t))
       (fma (/ (- z t) (- a t)) (- y x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -1e-262) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-262)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-262], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000001e-262

   1. Initial program 76.4%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   if -1.00000000000000001e-262 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-sub 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-*r/ 94.9%

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

      3. *-commutative 94.9%

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

      4. fma-def 94.9%

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

   3. Simplified 94.9%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 81.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- z t) (- a t)))
     (if (<= t_1 -1e-262)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_1 4e+300) t_1 (- x (/ (- t z) (/ (- a t) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-262) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 4e+300) {
		tmp = t_1;
	} else {
		tmp = x - ((t - z) / ((a - t) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-262) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 4e+300) {
		tmp = t_1;
	} else {
		tmp = x - ((t - z) / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z - t) / (a - t))
	elif t_1 <= -1e-262:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_1 <= 4e+300:
		tmp = t_1
	else:
		tmp = x - ((t - z) / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t_1 <= -1e-262)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_1 <= 4e+300)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z - t) / (a - t));
	elseif (t_1 <= -1e-262)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_1 <= 4e+300)
		tmp = t_1;
	else
		tmp = x - ((t - z) / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-262], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+300], t$95$1, N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 37.9%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in x around 0 30.9%

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

      1. associate-*r/ 71.7%

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

   6. Simplified 71.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000001e-262 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.0000000000000002e300

   1. Initial program 97.3%

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

   if -1.00000000000000001e-262 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-sub 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

   if 4.0000000000000002e300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 34.7%

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

      1. *-commutative 34.7%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around inf 68.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 4 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 3: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-262} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-262) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ (* (- z a) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-262) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-1d-262)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (((z - a) * (x - y)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-262) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (((z - a) * (x - y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-262) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (((z - a) * (x - y)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-262) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-262) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (((z - a) * (x - y)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-262], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000001e-262 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 75.2%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   if -1.00000000000000001e-262 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. div-sub 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-262} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 4: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+51} \lor \neg \left(a \leq 10^{+81}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (* x (* (- z a) (/ 1.0 t)))))
   (if (<= a -1.4e-55)
     t_1
     (if (<= a 1.3e-130)
       (- y (* z (/ y t)))
       (if (<= a 1.35e-102)
         t_2
         (if (<= a 3.9e-89)
           (+ x (/ (* y z) a))
           (if (<= a 5.5e-67)
             (* x (- 1.0 (/ z a)))
             (if (or (<= a 5e+51) (not (<= a 1e+81))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = x * ((z - a) * (1.0 / t));
	double tmp;
	if (a <= -1.4e-55) {
		tmp = t_1;
	} else if (a <= 1.3e-130) {
		tmp = y - (z * (y / t));
	} else if (a <= 1.35e-102) {
		tmp = t_2;
	} else if (a <= 3.9e-89) {
		tmp = x + ((y * z) / a);
	} else if (a <= 5.5e-67) {
		tmp = x * (1.0 - (z / a));
	} else if ((a <= 5e+51) || !(a <= 1e+81)) {
		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 + (y / (a / z))
    t_2 = x * ((z - a) * (1.0d0 / t))
    if (a <= (-1.4d-55)) then
        tmp = t_1
    else if (a <= 1.3d-130) then
        tmp = y - (z * (y / t))
    else if (a <= 1.35d-102) then
        tmp = t_2
    else if (a <= 3.9d-89) then
        tmp = x + ((y * z) / a)
    else if (a <= 5.5d-67) then
        tmp = x * (1.0d0 - (z / a))
    else if ((a <= 5d+51) .or. (.not. (a <= 1d+81))) 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 + (y / (a / z));
	double t_2 = x * ((z - a) * (1.0 / t));
	double tmp;
	if (a <= -1.4e-55) {
		tmp = t_1;
	} else if (a <= 1.3e-130) {
		tmp = y - (z * (y / t));
	} else if (a <= 1.35e-102) {
		tmp = t_2;
	} else if (a <= 3.9e-89) {
		tmp = x + ((y * z) / a);
	} else if (a <= 5.5e-67) {
		tmp = x * (1.0 - (z / a));
	} else if ((a <= 5e+51) || !(a <= 1e+81)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = x * ((z - a) * (1.0 / t))
	tmp = 0
	if a <= -1.4e-55:
		tmp = t_1
	elif a <= 1.3e-130:
		tmp = y - (z * (y / t))
	elif a <= 1.35e-102:
		tmp = t_2
	elif a <= 3.9e-89:
		tmp = x + ((y * z) / a)
	elif a <= 5.5e-67:
		tmp = x * (1.0 - (z / a))
	elif (a <= 5e+51) or not (a <= 1e+81):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(x * Float64(Float64(z - a) * Float64(1.0 / t)))
	tmp = 0.0
	if (a <= -1.4e-55)
		tmp = t_1;
	elseif (a <= 1.3e-130)
		tmp = Float64(y - Float64(z * Float64(y / t)));
	elseif (a <= 1.35e-102)
		tmp = t_2;
	elseif (a <= 3.9e-89)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 5.5e-67)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((a <= 5e+51) || !(a <= 1e+81))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = x * ((z - a) * (1.0 / t));
	tmp = 0.0;
	if (a <= -1.4e-55)
		tmp = t_1;
	elseif (a <= 1.3e-130)
		tmp = y - (z * (y / t));
	elseif (a <= 1.35e-102)
		tmp = t_2;
	elseif (a <= 3.9e-89)
		tmp = x + ((y * z) / a);
	elseif (a <= 5.5e-67)
		tmp = x * (1.0 - (z / a));
	elseif ((a <= 5e+51) || ~((a <= 1e+81)))
		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[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - a), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e-55], t$95$1, If[LessEqual[a, 1.3e-130], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-102], t$95$2, If[LessEqual[a, 3.9e-89], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-67], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5e+51], N[Not[LessEqual[a, 1e+81]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999992e-55 or 5.5000000000000003e-67 < a < 5e51 or 9.99999999999999921e80 < a

   1. Initial program 74.1%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around inf 78.2%

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

   5. Taylor expanded in x around 0 65.2%

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

   6. Taylor expanded in t around 0 59.0%

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

      1. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

   if -1.39999999999999992e-55 < a < 1.3e-130

   1. Initial program 66.4%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

      1. associate-/l* 66.4%

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

      2. div-inv 66.3%

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

      3. *-commutative 66.3%

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

      4. associate-*r* 81.5%

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

      5. div-inv 81.6%

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

      6. clear-num 81.5%

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

      7. div-inv 81.7%

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

      8. associate-/r/ 83.1%

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

      9. div-inv 82.9%

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

      10. associate-*l* 81.5%

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

   5. Applied egg-rr 81.5%

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

   6. Taylor expanded in x around 0 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in a around 0 63.9%

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

       1. mul-1-neg 63.9%

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

       2. distribute-neg-frac 63.9%

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

   11. Simplified 63.9%

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

   12. Taylor expanded in z around 0 62.8%

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

       1. +-commutative 62.8%

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

       2. mul-1-neg 62.8%

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

       3. *-commutative 62.8%

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

       4. associate-*r/ 66.1%

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

       5. unsub-neg 66.1%

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

   14. Simplified 66.1%

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

   if 1.3e-130 < a < 1.35e-102 or 5e51 < a < 9.99999999999999921e80

   1. Initial program 36.0%

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

      1. associate-/l* 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in x around -inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. distribute-rgt-neg-in 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in t around -inf 61.6%

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

      1. div-inv 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-*l* 79.1%

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

   9. Applied egg-rr 79.1%

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

   if 1.35e-102 < a < 3.89999999999999978e-89

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if 3.89999999999999978e-89 < a < 5.5000000000000003e-67

   1. Initial program 89.0%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around 0 74.9%

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

   5. Taylor expanded in x around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   7. Simplified 75.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+51} \lor \neg \left(a \leq 10^{+81}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \end{array} \]

Alternative 5: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -0.26:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ y a)))))
   (if (<= a -2.8e+54)
     t_2
     (if (<= a -9.2e+39)
       t_1
       (if (<= a -0.26)
         t_2
         (if (<= a -1e-104)
           (* z (/ (- y x) (- a t)))
           (if (<= a 1.3e-130)
             t_1
             (if (<= a 2.5e-72)
               (* x (* (- z a) (/ 1.0 t)))
               (if (<= a 5.1e+75) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -2.8e+54) {
		tmp = t_2;
	} else if (a <= -9.2e+39) {
		tmp = t_1;
	} else if (a <= -0.26) {
		tmp = t_2;
	} else if (a <= -1e-104) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.3e-130) {
		tmp = t_1;
	} else if (a <= 2.5e-72) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (a <= 5.1e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * (y / a))
    if (a <= (-2.8d+54)) then
        tmp = t_2
    else if (a <= (-9.2d+39)) then
        tmp = t_1
    else if (a <= (-0.26d0)) then
        tmp = t_2
    else if (a <= (-1d-104)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.3d-130) then
        tmp = t_1
    else if (a <= 2.5d-72) then
        tmp = x * ((z - a) * (1.0d0 / t))
    else if (a <= 5.1d+75) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (a <= -2.8e+54) {
		tmp = t_2;
	} else if (a <= -9.2e+39) {
		tmp = t_1;
	} else if (a <= -0.26) {
		tmp = t_2;
	} else if (a <= -1e-104) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.3e-130) {
		tmp = t_1;
	} else if (a <= 2.5e-72) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (a <= 5.1e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * (y / a))
	tmp = 0
	if a <= -2.8e+54:
		tmp = t_2
	elif a <= -9.2e+39:
		tmp = t_1
	elif a <= -0.26:
		tmp = t_2
	elif a <= -1e-104:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.3e-130:
		tmp = t_1
	elif a <= 2.5e-72:
		tmp = x * ((z - a) * (1.0 / t))
	elif a <= 5.1e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.8e+54)
		tmp = t_2;
	elseif (a <= -9.2e+39)
		tmp = t_1;
	elseif (a <= -0.26)
		tmp = t_2;
	elseif (a <= -1e-104)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.3e-130)
		tmp = t_1;
	elseif (a <= 2.5e-72)
		tmp = Float64(x * Float64(Float64(z - a) * Float64(1.0 / t)));
	elseif (a <= 5.1e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * (y / a));
	tmp = 0.0;
	if (a <= -2.8e+54)
		tmp = t_2;
	elseif (a <= -9.2e+39)
		tmp = t_1;
	elseif (a <= -0.26)
		tmp = t_2;
	elseif (a <= -1e-104)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.3e-130)
		tmp = t_1;
	elseif (a <= 2.5e-72)
		tmp = x * ((z - a) * (1.0 / t));
	elseif (a <= 5.1e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+54], t$95$2, If[LessEqual[a, -9.2e+39], t$95$1, If[LessEqual[a, -0.26], t$95$2, If[LessEqual[a, -1e-104], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-130], t$95$1, If[LessEqual[a, 2.5e-72], N[(x * N[(N[(z - a), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e+75], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.80000000000000015e54 or -9.20000000000000047e39 < a < -0.26000000000000001 or 5.10000000000000037e75 < a

   1. Initial program 72.7%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 85.2%

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

   5. Taylor expanded in y around inf 71.1%

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

      1. associate-/l* 80.7%

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

      2. associate-/r/ 77.9%

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

   7. Simplified 77.9%

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

   if -2.80000000000000015e54 < a < -9.20000000000000047e39 or -9.99999999999999927e-105 < a < 1.3e-130 or 2.4999999999999998e-72 < a < 5.10000000000000037e75

   1. Initial program 64.4%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around 0 55.1%

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

      1. associate-*r/ 76.3%

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

   6. Simplified 76.3%

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

   if -0.26000000000000001 < a < -9.99999999999999927e-105

   1. Initial program 76.7%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. div-sub 56.9%

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

   6. Simplified 56.9%

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

   if 1.3e-130 < a < 2.4999999999999998e-72

   1. Initial program 74.4%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in x around -inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in t around -inf 52.9%

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

      1. div-inv 52.4%

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

      2. *-commutative 52.4%

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

      3. associate-*l* 59.7%

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

   9. Applied egg-rr 59.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -0.26:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 38.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ z (- a t)))))
   (if (<= y -2.4e+230)
     y
     (if (<= y -1.25e+163)
       t_2
       (if (<= y -6e+64)
         y
         (if (<= y 1.8e-235)
           t_1
           (if (<= y 1.7e-163)
             (* x (/ z t))
             (if (<= y 7e-24) t_1 (if (<= y 9e+220) t_2 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (y <= -2.4e+230) {
		tmp = y;
	} else if (y <= -1.25e+163) {
		tmp = t_2;
	} else if (y <= -6e+64) {
		tmp = y;
	} else if (y <= 1.8e-235) {
		tmp = t_1;
	} else if (y <= 1.7e-163) {
		tmp = x * (z / t);
	} else if (y <= 7e-24) {
		tmp = t_1;
	} else if (y <= 9e+220) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * (z / (a - t))
    if (y <= (-2.4d+230)) then
        tmp = y
    else if (y <= (-1.25d+163)) then
        tmp = t_2
    else if (y <= (-6d+64)) then
        tmp = y
    else if (y <= 1.8d-235) then
        tmp = t_1
    else if (y <= 1.7d-163) then
        tmp = x * (z / t)
    else if (y <= 7d-24) then
        tmp = t_1
    else if (y <= 9d+220) then
        tmp = t_2
    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 t_2 = y * (z / (a - t));
	double tmp;
	if (y <= -2.4e+230) {
		tmp = y;
	} else if (y <= -1.25e+163) {
		tmp = t_2;
	} else if (y <= -6e+64) {
		tmp = y;
	} else if (y <= 1.8e-235) {
		tmp = t_1;
	} else if (y <= 1.7e-163) {
		tmp = x * (z / t);
	} else if (y <= 7e-24) {
		tmp = t_1;
	} else if (y <= 9e+220) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (z / (a - t))
	tmp = 0
	if y <= -2.4e+230:
		tmp = y
	elif y <= -1.25e+163:
		tmp = t_2
	elif y <= -6e+64:
		tmp = y
	elif y <= 1.8e-235:
		tmp = t_1
	elif y <= 1.7e-163:
		tmp = x * (z / t)
	elif y <= 7e-24:
		tmp = t_1
	elif y <= 9e+220:
		tmp = t_2
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (y <= -2.4e+230)
		tmp = y;
	elseif (y <= -1.25e+163)
		tmp = t_2;
	elseif (y <= -6e+64)
		tmp = y;
	elseif (y <= 1.8e-235)
		tmp = t_1;
	elseif (y <= 1.7e-163)
		tmp = Float64(x * Float64(z / t));
	elseif (y <= 7e-24)
		tmp = t_1;
	elseif (y <= 9e+220)
		tmp = t_2;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (z / (a - t));
	tmp = 0.0;
	if (y <= -2.4e+230)
		tmp = y;
	elseif (y <= -1.25e+163)
		tmp = t_2;
	elseif (y <= -6e+64)
		tmp = y;
	elseif (y <= 1.8e-235)
		tmp = t_1;
	elseif (y <= 1.7e-163)
		tmp = x * (z / t);
	elseif (y <= 7e-24)
		tmp = t_1;
	elseif (y <= 9e+220)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+230], y, If[LessEqual[y, -1.25e+163], t$95$2, If[LessEqual[y, -6e+64], y, If[LessEqual[y, 1.8e-235], t$95$1, If[LessEqual[y, 1.7e-163], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-24], t$95$1, If[LessEqual[y, 9e+220], t$95$2, y]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.39999999999999998e230 or -1.25e163 < y < -6.0000000000000004e64 or 9.00000000000000022e220 < y

   1. Initial program 53.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 54.4%

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

   if -2.39999999999999998e230 < y < -1.25e163 or 6.9999999999999993e-24 < y < 9.00000000000000022e220

   1. Initial program 79.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around 0 58.1%

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

      1. associate-*r/ 73.9%

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

   6. Simplified 73.9%

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

   7. Taylor expanded in z around inf 55.2%

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

   if -6.0000000000000004e64 < y < 1.79999999999999999e-235 or 1.70000000000000007e-163 < y < 6.9999999999999993e-24

   1. Initial program 75.9%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 63.4%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   7. Simplified 59.4%

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

   if 1.79999999999999999e-235 < y < 1.70000000000000007e-163

   1. Initial program 53.9%

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

      1. associate-/l* 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in x around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-rgt-neg-in 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in a around 0 43.2%

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

      1. associate-/l* 43.3%

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

      2. associate-/r/ 49.0%

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

   9. Applied egg-rr 49.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+230}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-41} \lor \neg \left(y \leq 3.1 \cdot 10^{-22}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -1.8e+64)
     t_1
     (if (<= y -1.4e+33)
       (* x (- 1.0 (/ z a)))
       (if (or (<= y -5.2e-41) (not (<= y 3.1e-22)))
         t_1
         (* x (+ (/ (- t z) (- a t)) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.8e+64) {
		tmp = t_1;
	} else if (y <= -1.4e+33) {
		tmp = x * (1.0 - (z / a));
	} else if ((y <= -5.2e-41) || !(y <= 3.1e-22)) {
		tmp = t_1;
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-1.8d+64)) then
        tmp = t_1
    else if (y <= (-1.4d+33)) then
        tmp = x * (1.0d0 - (z / a))
    else if ((y <= (-5.2d-41)) .or. (.not. (y <= 3.1d-22))) then
        tmp = t_1
    else
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.8e+64) {
		tmp = t_1;
	} else if (y <= -1.4e+33) {
		tmp = x * (1.0 - (z / a));
	} else if ((y <= -5.2e-41) || !(y <= 3.1e-22)) {
		tmp = t_1;
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -1.8e+64:
		tmp = t_1
	elif y <= -1.4e+33:
		tmp = x * (1.0 - (z / a))
	elif (y <= -5.2e-41) or not (y <= 3.1e-22):
		tmp = t_1
	else:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -1.8e+64)
		tmp = t_1;
	elseif (y <= -1.4e+33)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((y <= -5.2e-41) || !(y <= 3.1e-22))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -1.8e+64)
		tmp = t_1;
	elseif (y <= -1.4e+33)
		tmp = x * (1.0 - (z / a));
	elseif ((y <= -5.2e-41) || ~((y <= 3.1e-22)))
		tmp = t_1;
	else
		tmp = x * (((t - z) / (a - t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+64], t$95$1, If[LessEqual[y, -1.4e+33], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.2e-41], N[Not[LessEqual[y, 3.1e-22]], $MachinePrecision]], t$95$1, N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000007e64 or -1.4e33 < y < -5.1999999999999999e-41 or 3.10000000000000013e-22 < y

   1. Initial program 67.5%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 80.9%

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

   6. Simplified 80.9%

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

   if -1.80000000000000007e64 < y < -1.4e33

   1. Initial program 75.3%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around 0 76.3%

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

   5. Taylor expanded in x around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. unsub-neg 77.0%

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

   7. Simplified 77.0%

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

   if -5.1999999999999999e-41 < y < 3.10000000000000013e-22

   1. Initial program 72.1%

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

      1. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   6. Simplified 62.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-41} \lor \neg \left(y \leq 3.1 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \]

Alternative 8: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-73}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-101}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.4e-73)
   (- x (/ (- t z) (/ (- a t) y)))
   (if (<= a 2e-101)
     (+ y (/ (* (- z a) (- x y)) t))
     (if (<= a 1.22e+55)
       (+ x (/ (- y x) (/ a z)))
       (if (<= a 7.1e+80)
         (* x (* (- z a) (/ 1.0 t)))
         (+ x (/ (- y x) (/ a (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.4e-73) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if (a <= 2e-101) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (a <= 1.22e+55) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 7.1e+80) {
		tmp = x * ((z - a) * (1.0 / t));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.4d-73)) then
        tmp = x - ((t - z) / ((a - t) / y))
    else if (a <= 2d-101) then
        tmp = y + (((z - a) * (x - y)) / t)
    else if (a <= 1.22d+55) then
        tmp = x + ((y - x) / (a / z))
    else if (a <= 7.1d+80) then
        tmp = x * ((z - a) * (1.0d0 / t))
    else
        tmp = x + ((y - x) / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.4e-73) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if (a <= 2e-101) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (a <= 1.22e+55) {
		tmp = x + ((y - x) / (a / z));
	} else if (a <= 7.1e+80) {
		tmp = x * ((z - a) * (1.0 / t));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.4e-73:
		tmp = x - ((t - z) / ((a - t) / y))
	elif a <= 2e-101:
		tmp = y + (((z - a) * (x - y)) / t)
	elif a <= 1.22e+55:
		tmp = x + ((y - x) / (a / z))
	elif a <= 7.1e+80:
		tmp = x * ((z - a) * (1.0 / t))
	else:
		tmp = x + ((y - x) / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.4e-73)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	elseif (a <= 2e-101)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (a <= 1.22e+55)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (a <= 7.1e+80)
		tmp = Float64(x * Float64(Float64(z - a) * Float64(1.0 / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.4e-73)
		tmp = x - ((t - z) / ((a - t) / y));
	elseif (a <= 2e-101)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (a <= 1.22e+55)
		tmp = x + ((y - x) / (a / z));
	elseif (a <= 7.1e+80)
		tmp = x * ((z - a) * (1.0 / t));
	else
		tmp = x + ((y - x) / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.4e-73], N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-101], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e+55], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.1e+80], N[(x * N[(N[(z - a), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.3999999999999994e-73

   1. Initial program 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around inf 74.7%

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

   if -8.3999999999999994e-73 < a < 2.0000000000000001e-101

   1. Initial program 65.7%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around -inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

      3. div-sub 82.8%

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

      4. *-commutative 82.8%

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

      5. div-sub 82.9%

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

      6. distribute-rgt-out-- 82.9%

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

   6. Simplified 82.9%

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

   if 2.0000000000000001e-101 < a < 1.22e55

   1. Initial program 80.9%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 68.1%

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

   if 1.22e55 < a < 7.09999999999999988e80

   1. Initial program 4.2%

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

      1. associate-/l* 15.9%

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

   3. Simplified 15.9%

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

   4. Taylor expanded in x around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-in 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in t around -inf 52.6%

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

      1. div-inv 52.3%

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

      2. *-commutative 52.3%

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

      3. associate-*l* 81.0%

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

   9. Applied egg-rr 81.0%

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

   if 7.09999999999999988e80 < a

   1. Initial program 78.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around inf 93.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-73}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-101}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 9: 41.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-33} \lor \neg \left(a \leq 2.7 \cdot 10^{+32}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -1.35e-104)
     t_1
     (if (<= a 3.6e-142)
       y
       (if (<= a 5.8e-104)
         (* x (/ z t))
         (if (or (<= a 4.8e-33) (not (<= a 2.7e+32))) t_1 (* y (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.35e-104) {
		tmp = t_1;
	} else if (a <= 3.6e-142) {
		tmp = y;
	} else if (a <= 5.8e-104) {
		tmp = x * (z / t);
	} else if ((a <= 4.8e-33) || !(a <= 2.7e+32)) {
		tmp = t_1;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-1.35d-104)) then
        tmp = t_1
    else if (a <= 3.6d-142) then
        tmp = y
    else if (a <= 5.8d-104) then
        tmp = x * (z / t)
    else if ((a <= 4.8d-33) .or. (.not. (a <= 2.7d+32))) then
        tmp = t_1
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.35e-104) {
		tmp = t_1;
	} else if (a <= 3.6e-142) {
		tmp = y;
	} else if (a <= 5.8e-104) {
		tmp = x * (z / t);
	} else if ((a <= 4.8e-33) || !(a <= 2.7e+32)) {
		tmp = t_1;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -1.35e-104:
		tmp = t_1
	elif a <= 3.6e-142:
		tmp = y
	elif a <= 5.8e-104:
		tmp = x * (z / t)
	elif (a <= 4.8e-33) or not (a <= 2.7e+32):
		tmp = t_1
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -1.35e-104)
		tmp = t_1;
	elseif (a <= 3.6e-142)
		tmp = y;
	elseif (a <= 5.8e-104)
		tmp = Float64(x * Float64(z / t));
	elseif ((a <= 4.8e-33) || !(a <= 2.7e+32))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z / a));
	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 (a <= -1.35e-104)
		tmp = t_1;
	elseif (a <= 3.6e-142)
		tmp = y;
	elseif (a <= 5.8e-104)
		tmp = x * (z / t);
	elseif ((a <= 4.8e-33) || ~((a <= 2.7e+32)))
		tmp = t_1;
	else
		tmp = y * (z / a);
	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[a, -1.35e-104], t$95$1, If[LessEqual[a, 3.6e-142], y, If[LessEqual[a, 5.8e-104], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 4.8e-33], N[Not[LessEqual[a, 2.7e+32]], $MachinePrecision]], t$95$1, N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3499999999999999e-104 or 5.8000000000000002e-104 < a < 4.8e-33 or 2.70000000000000013e32 < a

   1. Initial program 71.9%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around 0 65.8%

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

   5. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

   7. Simplified 51.7%

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

   if -1.3499999999999999e-104 < a < 3.6e-142

   1. Initial program 64.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around inf 53.6%

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

   if 3.6e-142 < a < 5.8000000000000002e-104

   1. Initial program 67.9%

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

      1. associate-/l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around -inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-in 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in a around 0 57.0%

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

      1. associate-/l* 46.2%

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

      2. associate-/r/ 67.6%

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

   9. Applied egg-rr 67.6%

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

   if 4.8e-33 < a < 2.70000000000000013e32

   1. Initial program 74.4%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in t around 0 64.9%

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

   5. Taylor expanded in y around inf 64.5%

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

   6. Taylor expanded in x around 0 57.0%

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

      1. associate-*r/ 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-33} \lor \neg \left(a \leq 2.7 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+125}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+38} \lor \neg \left(x \leq -1.1 \cdot 10^{-105}\right) \land x \leq 3 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+125)
   (- x (/ z (/ a x)))
   (if (or (<= x -5e+38) (and (not (<= x -1.1e-105)) (<= x 3e-44)))
     (* y (/ (- z t) (- a t)))
     (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+125) {
		tmp = x - (z / (a / x));
	} else if ((x <= -5e+38) || (!(x <= -1.1e-105) && (x <= 3e-44))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d+125)) then
        tmp = x - (z / (a / x))
    else if ((x <= (-5d+38)) .or. (.not. (x <= (-1.1d-105))) .and. (x <= 3d-44)) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+125) {
		tmp = x - (z / (a / x));
	} else if ((x <= -5e+38) || (!(x <= -1.1e-105) && (x <= 3e-44))) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+125:
		tmp = x - (z / (a / x))
	elif (x <= -5e+38) or (not (x <= -1.1e-105) and (x <= 3e-44)):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+125)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif ((x <= -5e+38) || (!(x <= -1.1e-105) && (x <= 3e-44)))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+125)
		tmp = x - (z / (a / x));
	elseif ((x <= -5e+38) || (~((x <= -1.1e-105)) && (x <= 3e-44)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+125], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e+38], And[N[Not[LessEqual[x, -1.1e-105]], $MachinePrecision], LessEqual[x, 3e-44]]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999998e125

   1. Initial program 63.5%

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

      1. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in t around 0 74.4%

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

   5. Taylor expanded in y around 0 57.3%

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

      1. +-commutative 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

      4. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   if -6.7999999999999998e125 < x < -4.9999999999999997e38 or -1.10000000000000002e-105 < x < 3.0000000000000002e-44

   1. Initial program 71.0%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 55.7%

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

      1. associate-*r/ 75.6%

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

   6. Simplified 75.6%

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

   if -4.9999999999999997e38 < x < -1.10000000000000002e-105 or 3.0000000000000002e-44 < x

   1. Initial program 70.7%

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

      1. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in t around 0 54.6%

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

   5. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

   7. Simplified 51.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+125}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+38} \lor \neg \left(x \leq -1.1 \cdot 10^{-105}\right) \land x \leq 3 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 11: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;y \leq 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -1.95e+64)
     t_2
     (if (<= y 2.65e-235)
       t_1
       (if (<= y 1.8e-163)
         (* x (* (- z a) (/ 1.0 t)))
         (if (<= y 1e-26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.95e+64) {
		tmp = t_2;
	} else if (y <= 2.65e-235) {
		tmp = t_1;
	} else if (y <= 1.8e-163) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (y <= 1e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-1.95d+64)) then
        tmp = t_2
    else if (y <= 2.65d-235) then
        tmp = t_1
    else if (y <= 1.8d-163) then
        tmp = x * ((z - a) * (1.0d0 / t))
    else if (y <= 1d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.95e+64) {
		tmp = t_2;
	} else if (y <= 2.65e-235) {
		tmp = t_1;
	} else if (y <= 1.8e-163) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (y <= 1e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -1.95e+64:
		tmp = t_2
	elif y <= 2.65e-235:
		tmp = t_1
	elif y <= 1.8e-163:
		tmp = x * ((z - a) * (1.0 / t))
	elif y <= 1e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -1.95e+64)
		tmp = t_2;
	elseif (y <= 2.65e-235)
		tmp = t_1;
	elseif (y <= 1.8e-163)
		tmp = Float64(x * Float64(Float64(z - a) * Float64(1.0 / t)));
	elseif (y <= 1e-26)
		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 / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -1.95e+64)
		tmp = t_2;
	elseif (y <= 2.65e-235)
		tmp = t_1;
	elseif (y <= 1.8e-163)
		tmp = x * ((z - a) * (1.0 / t));
	elseif (y <= 1e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+64], t$95$2, If[LessEqual[y, 2.65e-235], t$95$1, If[LessEqual[y, 1.8e-163], N[(x * N[(N[(z - a), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9499999999999999e64 or 1e-26 < y

   1. Initial program 66.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-*r/ 80.5%

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

   6. Simplified 80.5%

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

   if -1.9499999999999999e64 < y < 2.6500000000000001e-235 or 1.7999999999999999e-163 < y < 1e-26

   1. Initial program 75.9%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 59.5%

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

      1. +-commutative 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 62.6%

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

   6. Simplified 62.6%

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

   if 2.6500000000000001e-235 < y < 1.7999999999999999e-163

   1. Initial program 53.9%

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

      1. associate-/l* 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in x around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-rgt-neg-in 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in t around -inf 49.7%

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

      1. div-inv 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*l* 61.2%

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

   9. Applied egg-rr 61.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-235}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;y \leq 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 12: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-236}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -3.8e+64)
     t_1
     (if (<= y 1e-236)
       (+ x (/ (- y x) (/ a z)))
       (if (<= y 1.9e-163)
         (* x (* (- z a) (/ 1.0 t)))
         (if (<= y 9e-23) (+ x (/ z (/ a (- y x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.8e+64) {
		tmp = t_1;
	} else if (y <= 1e-236) {
		tmp = x + ((y - x) / (a / z));
	} else if (y <= 1.9e-163) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (y <= 9e-23) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-3.8d+64)) then
        tmp = t_1
    else if (y <= 1d-236) then
        tmp = x + ((y - x) / (a / z))
    else if (y <= 1.9d-163) then
        tmp = x * ((z - a) * (1.0d0 / t))
    else if (y <= 9d-23) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -3.8e+64) {
		tmp = t_1;
	} else if (y <= 1e-236) {
		tmp = x + ((y - x) / (a / z));
	} else if (y <= 1.9e-163) {
		tmp = x * ((z - a) * (1.0 / t));
	} else if (y <= 9e-23) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -3.8e+64:
		tmp = t_1
	elif y <= 1e-236:
		tmp = x + ((y - x) / (a / z))
	elif y <= 1.9e-163:
		tmp = x * ((z - a) * (1.0 / t))
	elif y <= 9e-23:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -3.8e+64)
		tmp = t_1;
	elseif (y <= 1e-236)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (y <= 1.9e-163)
		tmp = Float64(x * Float64(Float64(z - a) * Float64(1.0 / t)));
	elseif (y <= 9e-23)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -3.8e+64)
		tmp = t_1;
	elseif (y <= 1e-236)
		tmp = x + ((y - x) / (a / z));
	elseif (y <= 1.9e-163)
		tmp = x * ((z - a) * (1.0 / t));
	elseif (y <= 9e-23)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+64], t$95$1, If[LessEqual[y, 1e-236], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-163], N[(x * N[(N[(z - a), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-23], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000001e64 or 8.9999999999999995e-23 < y

   1. Initial program 66.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 51.7%

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

      1. associate-*r/ 80.5%

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

   6. Simplified 80.5%

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

   if -3.8000000000000001e64 < y < 1e-236

   1. Initial program 73.0%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around 0 61.5%

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

   if 1e-236 < y < 1.9e-163

   1. Initial program 53.9%

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

      1. associate-/l* 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in x around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-rgt-neg-in 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in t around -inf 49.7%

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

      1. div-inv 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*l* 61.2%

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

   9. Applied egg-rr 61.2%

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

   if 1.9e-163 < y < 8.9999999999999995e-23

   1. Initial program 84.1%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 10^{-236}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(\left(z - a\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+51} \lor \neg \left(a \leq 7.1 \cdot 10^{+80}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -1.4e-55)
     t_1
     (if (<= a 3.9e-142)
       (- y (* z (/ y t)))
       (if (or (<= a 5e+51) (not (<= a 7.1e+80))) t_1 (/ (- z a) (/ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -1.4e-55) {
		tmp = t_1;
	} else if (a <= 3.9e-142) {
		tmp = y - (z * (y / t));
	} else if ((a <= 5e+51) || !(a <= 7.1e+80)) {
		tmp = t_1;
	} else {
		tmp = (z - a) / (t / 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 + (y / (a / z))
    if (a <= (-1.4d-55)) then
        tmp = t_1
    else if (a <= 3.9d-142) then
        tmp = y - (z * (y / t))
    else if ((a <= 5d+51) .or. (.not. (a <= 7.1d+80))) then
        tmp = t_1
    else
        tmp = (z - a) / (t / 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 + (y / (a / z));
	double tmp;
	if (a <= -1.4e-55) {
		tmp = t_1;
	} else if (a <= 3.9e-142) {
		tmp = y - (z * (y / t));
	} else if ((a <= 5e+51) || !(a <= 7.1e+80)) {
		tmp = t_1;
	} else {
		tmp = (z - a) / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -1.4e-55:
		tmp = t_1
	elif a <= 3.9e-142:
		tmp = y - (z * (y / t))
	elif (a <= 5e+51) or not (a <= 7.1e+80):
		tmp = t_1
	else:
		tmp = (z - a) / (t / x)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.4e-55)
		tmp = t_1;
	elseif (a <= 3.9e-142)
		tmp = Float64(y - Float64(z * Float64(y / t)));
	elseif ((a <= 5e+51) || !(a <= 7.1e+80))
		tmp = t_1;
	else
		tmp = Float64(Float64(z - a) / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -1.4e-55)
		tmp = t_1;
	elseif (a <= 3.9e-142)
		tmp = y - (z * (y / t));
	elseif ((a <= 5e+51) || ~((a <= 7.1e+80)))
		tmp = t_1;
	else
		tmp = (z - a) / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e-55], t$95$1, If[LessEqual[a, 3.9e-142], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5e+51], N[Not[LessEqual[a, 7.1e+80]], $MachinePrecision]], t$95$1, N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999992e-55 or 3.9000000000000003e-142 < a < 5e51 or 7.09999999999999988e80 < a

   1. Initial program 74.6%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 76.2%

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

   5. Taylor expanded in x around 0 62.7%

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

   6. Taylor expanded in t around 0 57.2%

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

      1. associate-/l* 61.4%

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

   8. Simplified 61.4%

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

   if -1.39999999999999992e-55 < a < 3.9000000000000003e-142

   1. Initial program 65.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

      1. associate-/l* 65.6%

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

      2. div-inv 65.5%

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

      3. *-commutative 65.5%

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

      4. associate-*r* 81.1%

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

      5. div-inv 81.2%

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

      6. clear-num 81.1%

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

      7. div-inv 81.2%

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

      8. associate-/r/ 82.7%

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

      9. div-inv 82.5%

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

      10. associate-*l* 81.1%

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

   5. Applied egg-rr 81.1%

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

   6. Taylor expanded in x around 0 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in a around 0 64.1%

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

       1. mul-1-neg 64.1%

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

       2. distribute-neg-frac 64.1%

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

   11. Simplified 64.1%

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

   12. Taylor expanded in z around 0 63.1%

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

       1. +-commutative 63.1%

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

       2. mul-1-neg 63.1%

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

       3. *-commutative 63.1%

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

       4. associate-*r/ 66.5%

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

       5. unsub-neg 66.5%

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

   14. Simplified 66.5%

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

   if 5e51 < a < 7.09999999999999988e80

   1. Initial program 16.2%

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

      1. associate-/l* 36.7%

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

   3. Simplified 36.7%

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

   4. Taylor expanded in x around -inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-rgt-neg-in 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in t around -inf 52.1%

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

      1. associate-/l* 62.2%

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

   9. Simplified 62.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+51} \lor \neg \left(a \leq 7.1 \cdot 10^{+80}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \end{array} \]

Alternative 14: 45.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= a -4.6e-57)
     t_1
     (if (<= a 3.1e-142)
       y
       (if (<= a 1.1e-103)
         (* x (/ z t))
         (if (<= a 6.5e-36) (* x (- 1.0 (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -4.6e-57) {
		tmp = t_1;
	} else if (a <= 3.1e-142) {
		tmp = y;
	} else if (a <= 1.1e-103) {
		tmp = x * (z / t);
	} else if (a <= 6.5e-36) {
		tmp = x * (1.0 - (z / 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 + (z * (y / a))
    if (a <= (-4.6d-57)) then
        tmp = t_1
    else if (a <= 3.1d-142) then
        tmp = y
    else if (a <= 1.1d-103) then
        tmp = x * (z / t)
    else if (a <= 6.5d-36) then
        tmp = x * (1.0d0 - (z / 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 + (z * (y / a));
	double tmp;
	if (a <= -4.6e-57) {
		tmp = t_1;
	} else if (a <= 3.1e-142) {
		tmp = y;
	} else if (a <= 1.1e-103) {
		tmp = x * (z / t);
	} else if (a <= 6.5e-36) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if a <= -4.6e-57:
		tmp = t_1
	elif a <= 3.1e-142:
		tmp = y
	elif a <= 1.1e-103:
		tmp = x * (z / t)
	elif a <= 6.5e-36:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -4.6e-57)
		tmp = t_1;
	elseif (a <= 3.1e-142)
		tmp = y;
	elseif (a <= 1.1e-103)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 6.5e-36)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (a <= -4.6e-57)
		tmp = t_1;
	elseif (a <= 3.1e-142)
		tmp = y;
	elseif (a <= 1.1e-103)
		tmp = x * (z / t);
	elseif (a <= 6.5e-36)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e-57], t$95$1, If[LessEqual[a, 3.1e-142], y, If[LessEqual[a, 1.1e-103], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-36], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6e-57 or 6.50000000000000012e-36 < a

   1. Initial program 70.7%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around 0 66.4%

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

   5. Taylor expanded in y around inf 56.5%

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

      1. associate-/l* 60.4%

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

      2. associate-/r/ 59.3%

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

   7. Simplified 59.3%

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

   if -4.6e-57 < a < 3.1e-142

   1. Initial program 65.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around inf 49.0%

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

   if 3.1e-142 < a < 1.1e-103

   1. Initial program 67.9%

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

      1. associate-/l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around -inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-in 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in a around 0 57.0%

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

      1. associate-/l* 46.2%

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

      2. associate-/r/ 67.6%

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

   9. Applied egg-rr 67.6%

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

   if 1.1e-103 < a < 6.50000000000000012e-36

   1. Initial program 95.6%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in x around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

   7. Simplified 56.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 15: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+34} \lor \neg \left(t \leq 3 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e+34) (not (<= t 3e-70)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e+34) || !(t <= 3e-70)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.2d+34)) .or. (.not. (t <= 3d-70))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e+34) || !(t <= 3e-70)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e+34) or not (t <= 3e-70):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e+34) || !(t <= 3e-70))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e+34) || ~((t <= 3e-70)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e+34], N[Not[LessEqual[t, 3e-70]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000002e34 or 3.0000000000000001e-70 < t

   1. Initial program 49.1%

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

      1. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 35.5%

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

      1. associate-*r/ 60.3%

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

   6. Simplified 60.3%

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

   if -2.2000000000000002e34 < t < 3.0000000000000001e-70

   1. Initial program 90.7%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around inf 81.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+34} \lor \neg \left(t \leq 3 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 16: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-44} \lor \neg \left(y \leq 3.7 \cdot 10^{-118}\right):\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.7e-44) (not (<= y 3.7e-118)))
   (- x (/ (- t z) (/ (- a t) y)))
   (* x (+ (/ (- t z) (- a t)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e-44) || !(y <= 3.7e-118)) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.7d-44)) .or. (.not. (y <= 3.7d-118))) then
        tmp = x - ((t - z) / ((a - t) / y))
    else
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e-44) || !(y <= 3.7e-118)) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.7e-44) or not (y <= 3.7e-118):
		tmp = x - ((t - z) / ((a - t) / y))
	else:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.7e-44) || !(y <= 3.7e-118))
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.7e-44) || ~((y <= 3.7e-118)))
		tmp = x - ((t - z) / ((a - t) / y));
	else
		tmp = x * (((t - z) / (a - t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.7e-44], N[Not[LessEqual[y, 3.7e-118]], $MachinePrecision]], N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e-44 or 3.70000000000000014e-118 < y

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 84.7%

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

   if -3.7e-44 < y < 3.70000000000000014e-118

   1. Initial program 70.6%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-44} \lor \neg \left(y \leq 3.7 \cdot 10^{-118}\right):\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \]

Alternative 17: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-56)
   x
   (if (<= a 3.9e-142) y (if (<= a 1.06e+30) (* y (/ z a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-56) {
		tmp = x;
	} else if (a <= 3.9e-142) {
		tmp = y;
	} else if (a <= 1.06e+30) {
		tmp = y * (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) :: tmp
    if (a <= (-1.45d-56)) then
        tmp = x
    else if (a <= 3.9d-142) then
        tmp = y
    else if (a <= 1.06d+30) then
        tmp = y * (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 tmp;
	if (a <= -1.45e-56) {
		tmp = x;
	} else if (a <= 3.9e-142) {
		tmp = y;
	} else if (a <= 1.06e+30) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e-56:
		tmp = x
	elif a <= 3.9e-142:
		tmp = y
	elif a <= 1.06e+30:
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e-56)
		tmp = x;
	elseif (a <= 3.9e-142)
		tmp = y;
	elseif (a <= 1.06e+30)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e-56)
		tmp = x;
	elseif (a <= 3.9e-142)
		tmp = y;
	elseif (a <= 1.06e+30)
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e-56], x, If[LessEqual[a, 3.9e-142], y, If[LessEqual[a, 1.06e+30], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.44999999999999996e-56 or 1.06e30 < a

   1. Initial program 70.4%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -1.44999999999999996e-56 < a < 3.9000000000000003e-142

   1. Initial program 65.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around inf 49.0%

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

   if 3.9000000000000003e-142 < a < 1.06e30

   1. Initial program 79.5%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around 0 58.2%

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

   5. Taylor expanded in y around inf 48.8%

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

   6. Taylor expanded in x around 0 33.1%

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

      1. associate-*r/ 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 45.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-57} \lor \neg \left(a \leq 3.6 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-57) (not (<= a 3.6e-142))) (+ x (/ y (/ a z))) y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-57) || !(a <= 3.6e-142)) {
		tmp = x + (y / (a / z));
	} 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 ((a <= (-2.2d-57)) .or. (.not. (a <= 3.6d-142))) then
        tmp = x + (y / (a / z))
    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 ((a <= -2.2e-57) || !(a <= 3.6e-142)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-57) or not (a <= 3.6e-142):
		tmp = x + (y / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-57) || !(a <= 3.6e-142))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-57) || ~((a <= 3.6e-142)))
		tmp = x + (y / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e-57], N[Not[LessEqual[a, 3.6e-142]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if a < -2.19999999999999999e-57 or 3.6e-142 < a

   1. Initial program 71.9%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 73.4%

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

   5. Taylor expanded in x around 0 60.0%

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

   6. Taylor expanded in t around 0 54.7%

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

      1. associate-/l* 58.7%

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

   8. Simplified 58.7%

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

   if -2.19999999999999999e-57 < a < 3.6e-142

   1. Initial program 65.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around inf 49.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-57} \lor \neg \left(a \leq 3.6 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-57} \lor \neg \left(a \leq 3.9 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e-57) (not (<= a 3.9e-142)))
   (+ x (/ y (/ a z)))
   (- y (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-57) || !(a <= 3.9e-142)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.6d-57)) .or. (.not. (a <= 3.9d-142))) then
        tmp = x + (y / (a / z))
    else
        tmp = y - (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-57) || !(a <= 3.9e-142)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y - (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e-57) or not (a <= 3.9e-142):
		tmp = x + (y / (a / z))
	else:
		tmp = y - (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e-57) || !(a <= 3.9e-142))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y - Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e-57) || ~((a <= 3.9e-142)))
		tmp = x + (y / (a / z));
	else
		tmp = y - (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e-57], N[Not[LessEqual[a, 3.9e-142]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-57 or 3.9000000000000003e-142 < a

   1. Initial program 71.9%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 73.4%

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

   5. Taylor expanded in x around 0 60.0%

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

   6. Taylor expanded in t around 0 54.7%

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

      1. associate-/l* 58.7%

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

   8. Simplified 58.7%

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

   if -1.6e-57 < a < 3.9000000000000003e-142

   1. Initial program 65.6%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

      1. associate-/l* 65.6%

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

      2. div-inv 65.5%

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

      3. *-commutative 65.5%

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

      4. associate-*r* 81.1%

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

      5. div-inv 81.2%

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

      6. clear-num 81.1%

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

      7. div-inv 81.2%

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

      8. associate-/r/ 82.7%

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

      9. div-inv 82.5%

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

      10. associate-*l* 81.1%

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

   5. Applied egg-rr 81.1%

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

   6. Taylor expanded in x around 0 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in a around 0 64.1%

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

       1. mul-1-neg 64.1%

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

       2. distribute-neg-frac 64.1%

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

   11. Simplified 64.1%

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

   12. Taylor expanded in z around 0 63.1%

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

       1. +-commutative 63.1%

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

       2. mul-1-neg 63.1%

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

       3. *-commutative 63.1%

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

       4. associate-*r/ 66.5%

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

       5. unsub-neg 66.5%

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

   14. Simplified 66.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-57} \lor \neg \left(a \leq 3.9 \cdot 10^{-142}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 20: 37.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1300000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e-55) x (if (<= a 1300000000.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-55) {
		tmp = x;
	} else if (a <= 1300000000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.4d-55)) then
        tmp = x
    else if (a <= 1300000000.0d0) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-55) {
		tmp = x;
	} else if (a <= 1300000000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e-55:
		tmp = x
	elif a <= 1300000000.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e-55)
		tmp = x;
	elseif (a <= 1300000000.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e-55)
		tmp = x;
	elseif (a <= 1300000000.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e-55], x, If[LessEqual[a, 1300000000.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.39999999999999992e-55 or 1.3e9 < a

   1. Initial program 71.0%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 45.6%

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

   if -1.39999999999999992e-55 < a < 1.3e9

   1. Initial program 68.5%

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

      1. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in t around inf 41.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1300000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 24.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 69.9%

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

   1. associate-/l* 87.0%

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

3. Simplified 87.0%

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

4. Taylor expanded in a around inf 29.1%

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

5. Final simplification 29.1%

   \[\leadsto x \]

Developer target: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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