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

Percentage Accurate: 68.2% → 90.9%

Time: 28.5s

Alternatives: 23

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ (- x y) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-290)
       t_2
       (if (<= t_2 0.0)
         (+ y (* x (/ (- z a) t)))
         (if (<= t_2 5e+290) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-290) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (x * ((z - a) / t));
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-290) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (x * ((z - a) / t));
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * ((x - y) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-290:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (x * ((z - a) / t))
	elif t_2 <= 5e+290:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-290)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - t) * ((x - y) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-290)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (x * ((z - a) / t));
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-290], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+290], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 4.9999999999999998e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 42.1%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999998e290

   1. Initial program 96.8%

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

   if -2.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.7%

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

      1. associate-*l/ 3.6%

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

   3. Simplified 3.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r/ 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y - x, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -2e-290)
     (fma t_1 (- y x) x)
     (if (<= t_2 0.0) (- y (* x (/ (- a z) t))) (+ x (* (- y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-290) {
		tmp = fma(t_1, (y - x), x);
	} else if (t_2 <= 0.0) {
		tmp = y - (x * ((a - z) / t));
	} else {
		tmp = x + ((y - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-290)
		tmp = fma(t_1, Float64(y - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(x * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-290], N[(t$95$1 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-290

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 81.1%

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

      4. associate-/r/ 89.1%

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

      5. fma-def 89.1%

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

   3. Simplified 89.1%

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

   if -2.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.7%

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

      1. associate-*l/ 3.6%

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

   3. Simplified 3.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r/ 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

   10. Simplified 99.9%

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

   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-*l/ 88.3%

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

      3. fma-def 88.3%

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

   3. Simplified 88.3%

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

      1. fma-udef 88.3%

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

      2. associate-/r/ 93.0%

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

      3. div-inv 93.0%

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

      4. clear-num 93.0%

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

   6. Applied egg-rr 93.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ t_3 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-169}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.56 \cdot 10^{-253}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (* z (/ (- y x) (- a t))))
        (t_3 (+ x (/ y (/ a z)))))
   (if (<= z -8e+36)
     t_2
     (if (<= z -3.5e-44)
       t_1
       (if (<= z -3.6e-169)
         t_3
         (if (<= z 3.95e-296)
           t_1
           (if (<= z 2.56e-253)
             t_3
             (if (<= z 1.9e-209)
               (* y (/ t (- t a)))
               (if (<= z 1.7e-81)
                 (+ x (/ z (/ a y)))
                 (if (<= z 4.1e+68) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = x + (y / (a / z));
	double tmp;
	if (z <= -8e+36) {
		tmp = t_2;
	} else if (z <= -3.5e-44) {
		tmp = t_1;
	} else if (z <= -3.6e-169) {
		tmp = t_3;
	} else if (z <= 3.95e-296) {
		tmp = t_1;
	} else if (z <= 2.56e-253) {
		tmp = t_3;
	} else if (z <= 1.9e-209) {
		tmp = y * (t / (t - a));
	} else if (z <= 1.7e-81) {
		tmp = x + (z / (a / y));
	} else if (z <= 4.1e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    t_3 = x + (y / (a / z))
    if (z <= (-8d+36)) then
        tmp = t_2
    else if (z <= (-3.5d-44)) then
        tmp = t_1
    else if (z <= (-3.6d-169)) then
        tmp = t_3
    else if (z <= 3.95d-296) then
        tmp = t_1
    else if (z <= 2.56d-253) then
        tmp = t_3
    else if (z <= 1.9d-209) then
        tmp = y * (t / (t - a))
    else if (z <= 1.7d-81) then
        tmp = x + (z / (a / y))
    else if (z <= 4.1d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = x + (y / (a / z));
	double tmp;
	if (z <= -8e+36) {
		tmp = t_2;
	} else if (z <= -3.5e-44) {
		tmp = t_1;
	} else if (z <= -3.6e-169) {
		tmp = t_3;
	} else if (z <= 3.95e-296) {
		tmp = t_1;
	} else if (z <= 2.56e-253) {
		tmp = t_3;
	} else if (z <= 1.9e-209) {
		tmp = y * (t / (t - a));
	} else if (z <= 1.7e-81) {
		tmp = x + (z / (a / y));
	} else if (z <= 4.1e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	t_3 = x + (y / (a / z))
	tmp = 0
	if z <= -8e+36:
		tmp = t_2
	elif z <= -3.5e-44:
		tmp = t_1
	elif z <= -3.6e-169:
		tmp = t_3
	elif z <= 3.95e-296:
		tmp = t_1
	elif z <= 2.56e-253:
		tmp = t_3
	elif z <= 1.9e-209:
		tmp = y * (t / (t - a))
	elif z <= 1.7e-81:
		tmp = x + (z / (a / y))
	elif z <= 4.1e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_3 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -8e+36)
		tmp = t_2;
	elseif (z <= -3.5e-44)
		tmp = t_1;
	elseif (z <= -3.6e-169)
		tmp = t_3;
	elseif (z <= 3.95e-296)
		tmp = t_1;
	elseif (z <= 2.56e-253)
		tmp = t_3;
	elseif (z <= 1.9e-209)
		tmp = Float64(y * Float64(t / Float64(t - a)));
	elseif (z <= 1.7e-81)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 4.1e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	t_3 = x + (y / (a / z));
	tmp = 0.0;
	if (z <= -8e+36)
		tmp = t_2;
	elseif (z <= -3.5e-44)
		tmp = t_1;
	elseif (z <= -3.6e-169)
		tmp = t_3;
	elseif (z <= 3.95e-296)
		tmp = t_1;
	elseif (z <= 2.56e-253)
		tmp = t_3;
	elseif (z <= 1.9e-209)
		tmp = y * (t / (t - a));
	elseif (z <= 1.7e-81)
		tmp = x + (z / (a / y));
	elseif (z <= 4.1e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+36], t$95$2, If[LessEqual[z, -3.5e-44], t$95$1, If[LessEqual[z, -3.6e-169], t$95$3, If[LessEqual[z, 3.95e-296], t$95$1, If[LessEqual[z, 2.56e-253], t$95$3, If[LessEqual[z, 1.9e-209], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-81], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+68], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.00000000000000034e36 or 4.0999999999999999e68 < z

   1. Initial program 72.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. div-sub 83.1%

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

   7. Simplified 83.1%

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

   if -8.00000000000000034e36 < z < -3.4999999999999998e-44 or -3.60000000000000001e-169 < z < 3.94999999999999979e-296 or 1.6999999999999999e-81 < z < 4.0999999999999999e68

   1. Initial program 59.8%

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

      1. +-commutative 59.8%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.0%

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

   3. Simplified 72.0%

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

      1. fma-udef 72.1%

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

      2. associate-/r/ 77.4%

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

      3. div-inv 77.4%

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

      4. clear-num 77.5%

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

   6. Applied egg-rr 77.5%

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

   7. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if -3.4999999999999998e-44 < z < -3.60000000000000001e-169 or 3.94999999999999979e-296 < z < 2.56e-253

   1. Initial program 83.9%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 65.4%

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

   10. Simplified 65.4%

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

   if 2.56e-253 < z < 1.8999999999999999e-209

   1. Initial program 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-*l/ 56.8%

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

      3. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 56.8%

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

      2. associate-/r/ 67.3%

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

      3. div-inv 67.5%

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

      4. clear-num 67.5%

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

   6. Applied egg-rr 67.5%

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

   7. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in z around 0 67.7%

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

       1. neg-mul-1 67.7%

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

       2. distribute-neg-frac 67.7%

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

   12. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.3%

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

       3. remove-double-neg 67.3%

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

       4. sub-neg 67.3%

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

       5. distribute-neg-in 67.3%

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

       6. remove-double-neg 67.3%

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

   14. Applied egg-rr 67.3%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   16. Simplified 67.7%

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

   if 1.8999999999999999e-209 < z < 1.6999999999999999e-81

   1. Initial program 69.6%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around 0 56.4%

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

      1. associate-/l* 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in y around inf 56.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 2.56 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= z -2.7e+28)
     (* z (/ (- y x) (- a t)))
     (if (<= z -7.2e-44)
       t_1
       (if (<= z -3.7e-169)
         t_2
         (if (<= z 7.3e-298)
           t_1
           (if (<= z 7.5e-254)
             t_2
             (if (<= z 2.4e-207)
               (* y (/ t (- t a)))
               (if (<= z 3.6e-83)
                 (+ x (/ z (/ a y)))
                 (if (<= z 3.2e+67) t_1 (* (- y x) (/ z (- a t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (z <= -2.7e+28) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -7.2e-44) {
		tmp = t_1;
	} else if (z <= -3.7e-169) {
		tmp = t_2;
	} else if (z <= 7.3e-298) {
		tmp = t_1;
	} else if (z <= 7.5e-254) {
		tmp = t_2;
	} else if (z <= 2.4e-207) {
		tmp = y * (t / (t - a));
	} else if (z <= 3.6e-83) {
		tmp = x + (z / (a / y));
	} else if (z <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (z <= (-2.7d+28)) then
        tmp = z * ((y - x) / (a - t))
    else if (z <= (-7.2d-44)) then
        tmp = t_1
    else if (z <= (-3.7d-169)) then
        tmp = t_2
    else if (z <= 7.3d-298) then
        tmp = t_1
    else if (z <= 7.5d-254) then
        tmp = t_2
    else if (z <= 2.4d-207) then
        tmp = y * (t / (t - a))
    else if (z <= 3.6d-83) then
        tmp = x + (z / (a / y))
    else if (z <= 3.2d+67) then
        tmp = t_1
    else
        tmp = (y - x) * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (z <= -2.7e+28) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -7.2e-44) {
		tmp = t_1;
	} else if (z <= -3.7e-169) {
		tmp = t_2;
	} else if (z <= 7.3e-298) {
		tmp = t_1;
	} else if (z <= 7.5e-254) {
		tmp = t_2;
	} else if (z <= 2.4e-207) {
		tmp = y * (t / (t - a));
	} else if (z <= 3.6e-83) {
		tmp = x + (z / (a / y));
	} else if (z <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if z <= -2.7e+28:
		tmp = z * ((y - x) / (a - t))
	elif z <= -7.2e-44:
		tmp = t_1
	elif z <= -3.7e-169:
		tmp = t_2
	elif z <= 7.3e-298:
		tmp = t_1
	elif z <= 7.5e-254:
		tmp = t_2
	elif z <= 2.4e-207:
		tmp = y * (t / (t - a))
	elif z <= 3.6e-83:
		tmp = x + (z / (a / y))
	elif z <= 3.2e+67:
		tmp = t_1
	else:
		tmp = (y - x) * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -2.7e+28)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (z <= -7.2e-44)
		tmp = t_1;
	elseif (z <= -3.7e-169)
		tmp = t_2;
	elseif (z <= 7.3e-298)
		tmp = t_1;
	elseif (z <= 7.5e-254)
		tmp = t_2;
	elseif (z <= 2.4e-207)
		tmp = Float64(y * Float64(t / Float64(t - a)));
	elseif (z <= 3.6e-83)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 3.2e+67)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (z <= -2.7e+28)
		tmp = z * ((y - x) / (a - t));
	elseif (z <= -7.2e-44)
		tmp = t_1;
	elseif (z <= -3.7e-169)
		tmp = t_2;
	elseif (z <= 7.3e-298)
		tmp = t_1;
	elseif (z <= 7.5e-254)
		tmp = t_2;
	elseif (z <= 2.4e-207)
		tmp = y * (t / (t - a));
	elseif (z <= 3.6e-83)
		tmp = x + (z / (a / y));
	elseif (z <= 3.2e+67)
		tmp = t_1;
	else
		tmp = (y - x) * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+28], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-44], t$95$1, If[LessEqual[z, -3.7e-169], t$95$2, If[LessEqual[z, 7.3e-298], t$95$1, If[LessEqual[z, 7.5e-254], t$95$2, If[LessEqual[z, 2.4e-207], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-83], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+67], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.7000000000000002e28

   1. Initial program 68.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. div-sub 84.6%

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

   7. Simplified 84.6%

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

   if -2.7000000000000002e28 < z < -7.1999999999999998e-44 or -3.6999999999999997e-169 < z < 7.3000000000000003e-298 or 3.60000000000000012e-83 < z < 3.19999999999999983e67

   1. Initial program 59.8%

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

      1. +-commutative 59.8%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.0%

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

   3. Simplified 72.0%

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

      1. fma-udef 72.1%

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

      2. associate-/r/ 77.4%

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

      3. div-inv 77.4%

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

      4. clear-num 77.5%

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

   6. Applied egg-rr 77.5%

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

   7. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if -7.1999999999999998e-44 < z < -3.6999999999999997e-169 or 7.3000000000000003e-298 < z < 7.5000000000000005e-254

   1. Initial program 83.9%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 65.4%

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

   10. Simplified 65.4%

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

   if 7.5000000000000005e-254 < z < 2.39999999999999989e-207

   1. Initial program 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-*l/ 56.8%

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

      3. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 56.8%

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

      2. associate-/r/ 67.3%

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

      3. div-inv 67.5%

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

      4. clear-num 67.5%

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

   6. Applied egg-rr 67.5%

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

   7. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in z around 0 67.7%

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

       1. neg-mul-1 67.7%

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

       2. distribute-neg-frac 67.7%

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

   12. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.3%

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

       3. remove-double-neg 67.3%

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

       4. sub-neg 67.3%

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

       5. distribute-neg-in 67.3%

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

       6. remove-double-neg 67.3%

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

   14. Applied egg-rr 67.3%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   16. Simplified 67.7%

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

   if 2.39999999999999989e-207 < z < 3.60000000000000012e-83

   1. Initial program 69.6%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around 0 56.4%

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

      1. associate-/l* 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in y around inf 56.4%

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

   if 3.19999999999999983e67 < z

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*l/ 89.2%

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

      3. fma-def 89.4%

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

   3. Simplified 89.4%

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

      1. fma-udef 89.2%

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

      2. associate-/r/ 91.9%

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

      3. div-inv 92.0%

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

      4. clear-num 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in z around inf 81.6%

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

      1. div-sub 81.6%

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

      2. associate-*r/ 64.7%

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

      3. associate-/l* 80.0%

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

   9. Simplified 80.0%

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

       1. associate-/r/ 82.3%

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

   11. Applied egg-rr 82.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot \left(t - z\right)}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;z \leq 10^{-294}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y (- t z)) a))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= z -7.5e+26)
     (* z (/ (- y x) (- a t)))
     (if (<= z -1.25e-32)
       t_2
       (if (<= z -1.7e-169)
         (+ x (/ (* (- y x) z) a))
         (if (<= z 1e-294)
           t_2
           (if (<= z 1.06e-253)
             t_1
             (if (<= z 1.45e-209)
               (* y (/ t (- t a)))
               (if (<= z 9.2e-80)
                 t_1
                 (if (<= z 1.95e+67) t_2 (* (- y x) (/ z (- a t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (t - z)) / a);
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (z <= -7.5e+26) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -1.25e-32) {
		tmp = t_2;
	} else if (z <= -1.7e-169) {
		tmp = x + (((y - x) * z) / a);
	} else if (z <= 1e-294) {
		tmp = t_2;
	} else if (z <= 1.06e-253) {
		tmp = t_1;
	} else if (z <= 1.45e-209) {
		tmp = y * (t / (t - a));
	} else if (z <= 9.2e-80) {
		tmp = t_1;
	} else if (z <= 1.95e+67) {
		tmp = t_2;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y * (t - z)) / a)
    t_2 = y * ((z - t) / (a - t))
    if (z <= (-7.5d+26)) then
        tmp = z * ((y - x) / (a - t))
    else if (z <= (-1.25d-32)) then
        tmp = t_2
    else if (z <= (-1.7d-169)) then
        tmp = x + (((y - x) * z) / a)
    else if (z <= 1d-294) then
        tmp = t_2
    else if (z <= 1.06d-253) then
        tmp = t_1
    else if (z <= 1.45d-209) then
        tmp = y * (t / (t - a))
    else if (z <= 9.2d-80) then
        tmp = t_1
    else if (z <= 1.95d+67) then
        tmp = t_2
    else
        tmp = (y - x) * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (t - z)) / a);
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (z <= -7.5e+26) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -1.25e-32) {
		tmp = t_2;
	} else if (z <= -1.7e-169) {
		tmp = x + (((y - x) * z) / a);
	} else if (z <= 1e-294) {
		tmp = t_2;
	} else if (z <= 1.06e-253) {
		tmp = t_1;
	} else if (z <= 1.45e-209) {
		tmp = y * (t / (t - a));
	} else if (z <= 9.2e-80) {
		tmp = t_1;
	} else if (z <= 1.95e+67) {
		tmp = t_2;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * (t - z)) / a)
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if z <= -7.5e+26:
		tmp = z * ((y - x) / (a - t))
	elif z <= -1.25e-32:
		tmp = t_2
	elif z <= -1.7e-169:
		tmp = x + (((y - x) * z) / a)
	elif z <= 1e-294:
		tmp = t_2
	elif z <= 1.06e-253:
		tmp = t_1
	elif z <= 1.45e-209:
		tmp = y * (t / (t - a))
	elif z <= 9.2e-80:
		tmp = t_1
	elif z <= 1.95e+67:
		tmp = t_2
	else:
		tmp = (y - x) * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * Float64(t - z)) / a))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (z <= -7.5e+26)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (z <= -1.25e-32)
		tmp = t_2;
	elseif (z <= -1.7e-169)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (z <= 1e-294)
		tmp = t_2;
	elseif (z <= 1.06e-253)
		tmp = t_1;
	elseif (z <= 1.45e-209)
		tmp = Float64(y * Float64(t / Float64(t - a)));
	elseif (z <= 9.2e-80)
		tmp = t_1;
	elseif (z <= 1.95e+67)
		tmp = t_2;
	else
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * (t - z)) / a);
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (z <= -7.5e+26)
		tmp = z * ((y - x) / (a - t));
	elseif (z <= -1.25e-32)
		tmp = t_2;
	elseif (z <= -1.7e-169)
		tmp = x + (((y - x) * z) / a);
	elseif (z <= 1e-294)
		tmp = t_2;
	elseif (z <= 1.06e-253)
		tmp = t_1;
	elseif (z <= 1.45e-209)
		tmp = y * (t / (t - a));
	elseif (z <= 9.2e-80)
		tmp = t_1;
	elseif (z <= 1.95e+67)
		tmp = t_2;
	else
		tmp = (y - x) * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+26], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-32], t$95$2, If[LessEqual[z, -1.7e-169], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-294], t$95$2, If[LessEqual[z, 1.06e-253], t$95$1, If[LessEqual[z, 1.45e-209], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-80], t$95$1, If[LessEqual[z, 1.95e+67], t$95$2, N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -7.49999999999999941e26

   1. Initial program 68.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. div-sub 84.6%

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

   7. Simplified 84.6%

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

   if -7.49999999999999941e26 < z < -1.25e-32 or -1.7e-169 < z < 1.00000000000000002e-294 or 9.1999999999999993e-80 < z < 1.95000000000000003e67

   1. Initial program 59.5%

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

      1. +-commutative 59.5%

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

      2. associate-*l/ 72.3%

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

      3. fma-def 72.2%

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

   3. Simplified 72.2%

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

      1. fma-udef 72.3%

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

      2. associate-/r/ 77.8%

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

      3. div-inv 77.8%

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

      4. clear-num 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if -1.25e-32 < z < -1.7e-169

   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/ 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in t around 0 68.6%

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

   if 1.00000000000000002e-294 < z < 1.06000000000000007e-253 or 1.45000000000000013e-209 < z < 9.1999999999999993e-80

   1. Initial program 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-*l/ 79.6%

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

      3. fma-def 79.8%

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

   3. Simplified 79.8%

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

      1. fma-udef 79.6%

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

      2. associate-/r/ 84.6%

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

      3. div-inv 84.6%

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

      4. clear-num 84.6%

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

   6. Applied egg-rr 84.6%

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

   7. Taylor expanded in a around inf 63.8%

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

      1. associate-/l* 76.5%

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

   9. Simplified 76.5%

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

   10. Taylor expanded in y around inf 73.3%

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

   if 1.06000000000000007e-253 < z < 1.45000000000000013e-209

   1. Initial program 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-*l/ 56.8%

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

      3. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 56.8%

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

      2. associate-/r/ 67.3%

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

      3. div-inv 67.5%

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

      4. clear-num 67.5%

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

   6. Applied egg-rr 67.5%

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

   7. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in z around 0 67.7%

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

       1. neg-mul-1 67.7%

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

       2. distribute-neg-frac 67.7%

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

   12. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.3%

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

       3. remove-double-neg 67.3%

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

       4. sub-neg 67.3%

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

       5. distribute-neg-in 67.3%

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

       6. remove-double-neg 67.3%

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

   14. Applied egg-rr 67.3%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   16. Simplified 67.7%

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

   if 1.95000000000000003e67 < z

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*l/ 89.2%

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

      3. fma-def 89.4%

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

   3. Simplified 89.4%

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

      1. fma-udef 89.2%

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

      2. associate-/r/ 91.9%

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

      3. div-inv 92.0%

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

      4. clear-num 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in z around inf 81.6%

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

      1. div-sub 81.6%

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

      2. associate-*r/ 64.7%

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

      3. associate-/l* 80.0%

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

   9. Simplified 80.0%

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

       1. associate-/r/ 82.3%

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

   11. Applied egg-rr 82.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;z \leq 10^{-294}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-253}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-80}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-290) (not (<= t_1 0.0)))
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (- y (* x (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (x * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-2d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y - (x * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (x * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-290) or not (t_1 <= 0.0):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y - (x * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-290) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(x * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-290) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y - (x * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-*l/ 85.2%

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

      3. fma-def 85.3%

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

   3. Simplified 85.3%

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

      1. fma-udef 85.2%

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

      2. associate-/r/ 91.0%

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

      3. div-inv 91.0%

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

      4. clear-num 91.0%

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

   6. Applied egg-rr 91.0%

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

   if -2.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.7%

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

      1. associate-*l/ 3.6%

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

   3. Simplified 3.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

      10. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r/ 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-290} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z - t}}\\ t_2 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -4100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a (- z t))))) (t_2 (+ y (/ (- x y) (/ t z)))))
   (if (<= a -4100000000.0)
     t_1
     (if (<= a -8.5e-20)
       (+ y (* x (/ (- z a) t)))
       (if (<= a -3.15e-72)
         t_1
         (if (<= a 4.5e-86)
           t_2
           (if (<= a 2.45e-68)
             (- x (/ (* y (- t z)) a))
             (if (<= a 4.7e-5) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double t_2 = y + ((x - y) / (t / z));
	double tmp;
	if (a <= -4100000000.0) {
		tmp = t_1;
	} else if (a <= -8.5e-20) {
		tmp = y + (x * ((z - a) / t));
	} else if (a <= -3.15e-72) {
		tmp = t_1;
	} else if (a <= 4.5e-86) {
		tmp = t_2;
	} else if (a <= 2.45e-68) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 4.7e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) / (a / (z - t)))
    t_2 = y + ((x - y) / (t / z))
    if (a <= (-4100000000.0d0)) then
        tmp = t_1
    else if (a <= (-8.5d-20)) then
        tmp = y + (x * ((z - a) / t))
    else if (a <= (-3.15d-72)) then
        tmp = t_1
    else if (a <= 4.5d-86) then
        tmp = t_2
    else if (a <= 2.45d-68) then
        tmp = x - ((y * (t - z)) / a)
    else if (a <= 4.7d-5) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / (z - t)));
	double t_2 = y + ((x - y) / (t / z));
	double tmp;
	if (a <= -4100000000.0) {
		tmp = t_1;
	} else if (a <= -8.5e-20) {
		tmp = y + (x * ((z - a) / t));
	} else if (a <= -3.15e-72) {
		tmp = t_1;
	} else if (a <= 4.5e-86) {
		tmp = t_2;
	} else if (a <= 2.45e-68) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 4.7e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / (z - t)))
	t_2 = y + ((x - y) / (t / z))
	tmp = 0
	if a <= -4100000000.0:
		tmp = t_1
	elif a <= -8.5e-20:
		tmp = y + (x * ((z - a) / t))
	elif a <= -3.15e-72:
		tmp = t_1
	elif a <= 4.5e-86:
		tmp = t_2
	elif a <= 2.45e-68:
		tmp = x - ((y * (t - z)) / a)
	elif a <= 4.7e-5:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (a <= -4100000000.0)
		tmp = t_1;
	elseif (a <= -8.5e-20)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	elseif (a <= -3.15e-72)
		tmp = t_1;
	elseif (a <= 4.5e-86)
		tmp = t_2;
	elseif (a <= 2.45e-68)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	elseif (a <= 4.7e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / (z - t)));
	t_2 = y + ((x - y) / (t / z));
	tmp = 0.0;
	if (a <= -4100000000.0)
		tmp = t_1;
	elseif (a <= -8.5e-20)
		tmp = y + (x * ((z - a) / t));
	elseif (a <= -3.15e-72)
		tmp = t_1;
	elseif (a <= 4.5e-86)
		tmp = t_2;
	elseif (a <= 2.45e-68)
		tmp = x - ((y * (t - z)) / a);
	elseif (a <= 4.7e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4100000000.0], t$95$1, If[LessEqual[a, -8.5e-20], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.15e-72], t$95$1, If[LessEqual[a, 4.5e-86], t$95$2, If[LessEqual[a, 2.45e-68], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-5], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.1e9 or -8.5000000000000005e-20 < a < -3.1500000000000002e-72 or 4.69999999999999972e-5 < a

   1. Initial program 72.6%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in a around inf 66.2%

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

      1. associate-/l* 83.3%

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

   7. Simplified 83.3%

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

   if -4.1e9 < a < -8.5000000000000005e-20

   1. Initial program 51.6%

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

      1. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-*r/ 67.6%

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

      7. mul-1-neg 67.6%

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

      8. unsub-neg 67.6%

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

      9. distribute-rgt-out-- 67.6%

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

      10. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-*r/ 75.4%

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

      3. distribute-lft-neg-in 75.4%

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

   10. Simplified 75.4%

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

   if -3.1500000000000002e-72 < a < 4.4999999999999998e-86 or 2.44999999999999988e-68 < a < 4.69999999999999972e-5

   1. Initial program 65.4%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. associate-*r/ 78.0%

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

      3. associate-*r/ 78.0%

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

      4. div-sub 79.0%

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

      5. distribute-lft-out-- 79.0%

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

      6. associate-*r/ 79.0%

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

      7. mul-1-neg 79.0%

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

      8. unsub-neg 79.0%

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

      9. distribute-rgt-out-- 79.0%

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

      10. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around inf 81.6%

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

   if 4.4999999999999998e-86 < a < 2.44999999999999988e-68

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 70.0%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

      1. fma-udef 70.0%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around inf 86.6%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

   10. Taylor expanded in y around inf 86.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4100000000:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -6.6e+22)
     t_2
     (if (<= t -6.6e-72)
       t_1
       (if (<= t -1.25e-98)
         t_2
         (if (<= t -3.5e-151)
           (* x (- 1.0 (/ z a)))
           (if (<= t 2.9e-79)
             t_1
             (if (<= t 1.2e+145) (* z (/ (- y x) (- a t))) 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 (t <= -6.6e+22) {
		tmp = t_2;
	} else if (t <= -6.6e-72) {
		tmp = t_1;
	} else if (t <= -1.25e-98) {
		tmp = t_2;
	} else if (t <= -3.5e-151) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.9e-79) {
		tmp = t_1;
	} else if (t <= 1.2e+145) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-6.6d+22)) then
        tmp = t_2
    else if (t <= (-6.6d-72)) then
        tmp = t_1
    else if (t <= (-1.25d-98)) then
        tmp = t_2
    else if (t <= (-3.5d-151)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 2.9d-79) then
        tmp = t_1
    else if (t <= 1.2d+145) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -6.6e+22) {
		tmp = t_2;
	} else if (t <= -6.6e-72) {
		tmp = t_1;
	} else if (t <= -1.25e-98) {
		tmp = t_2;
	} else if (t <= -3.5e-151) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 2.9e-79) {
		tmp = t_1;
	} else if (t <= 1.2e+145) {
		tmp = z * ((y - x) / (a - t));
	} 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 t <= -6.6e+22:
		tmp = t_2
	elif t <= -6.6e-72:
		tmp = t_1
	elif t <= -1.25e-98:
		tmp = t_2
	elif t <= -3.5e-151:
		tmp = x * (1.0 - (z / a))
	elif t <= 2.9e-79:
		tmp = t_1
	elif t <= 1.2e+145:
		tmp = z * ((y - x) / (a - t))
	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 (t <= -6.6e+22)
		tmp = t_2;
	elseif (t <= -6.6e-72)
		tmp = t_1;
	elseif (t <= -1.25e-98)
		tmp = t_2;
	elseif (t <= -3.5e-151)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 2.9e-79)
		tmp = t_1;
	elseif (t <= 1.2e+145)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -6.6e+22)
		tmp = t_2;
	elseif (t <= -6.6e-72)
		tmp = t_1;
	elseif (t <= -1.25e-98)
		tmp = t_2;
	elseif (t <= -3.5e-151)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 2.9e-79)
		tmp = t_1;
	elseif (t <= 1.2e+145)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(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[t, -6.6e+22], t$95$2, If[LessEqual[t, -6.6e-72], t$95$1, If[LessEqual[t, -1.25e-98], t$95$2, If[LessEqual[t, -3.5e-151], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-79], t$95$1, If[LessEqual[t, 1.2e+145], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.5999999999999996e22 or -6.6e-72 < t < -1.25000000000000005e-98 or 1.19999999999999996e145 < t

   1. Initial program 44.2%

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

      1. +-commutative 44.2%

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

      2. associate-*l/ 69.9%

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

      3. fma-def 70.5%

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

   3. Simplified 70.5%

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

      1. fma-udef 69.9%

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

      2. associate-/r/ 74.7%

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

      3. div-inv 74.8%

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

      4. clear-num 74.8%

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

   6. Applied egg-rr 74.8%

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

   7. Taylor expanded in y around inf 66.1%

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

      1. div-sub 66.1%

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

   9. Simplified 66.1%

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

   if -6.5999999999999996e22 < t < -6.6e-72 or -3.49999999999999995e-151 < t < 2.9000000000000001e-79

   1. Initial program 89.4%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around 0 70.3%

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

      1. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

   if -1.25000000000000005e-98 < t < -3.49999999999999995e-151

   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/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around 0 70.9%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in x around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

   10. Simplified 70.9%

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

   if 2.9000000000000001e-79 < t < 1.19999999999999996e145

   1. Initial program 71.1%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in z around inf 61.6%

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

      1. div-sub 61.6%

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

   7. Simplified 61.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ (* (- y x) z) a))))
   (if (<= z -7.4e+27)
     (* z (/ (- y x) (- a t)))
     (if (<= z -1.76e-32)
       t_1
       (if (<= z -8e-170)
         t_2
         (if (<= z 5.2e-295)
           t_1
           (if (<= z 4.9e-89)
             t_2
             (if (<= z 1.4e+68) t_1 (* (- y x) (/ z (- a t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (((y - x) * z) / a);
	double tmp;
	if (z <= -7.4e+27) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -1.76e-32) {
		tmp = t_1;
	} else if (z <= -8e-170) {
		tmp = t_2;
	} else if (z <= 5.2e-295) {
		tmp = t_1;
	} else if (z <= 4.9e-89) {
		tmp = t_2;
	} else if (z <= 1.4e+68) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (((y - x) * z) / a)
    if (z <= (-7.4d+27)) then
        tmp = z * ((y - x) / (a - t))
    else if (z <= (-1.76d-32)) then
        tmp = t_1
    else if (z <= (-8d-170)) then
        tmp = t_2
    else if (z <= 5.2d-295) then
        tmp = t_1
    else if (z <= 4.9d-89) then
        tmp = t_2
    else if (z <= 1.4d+68) then
        tmp = t_1
    else
        tmp = (y - x) * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (((y - x) * z) / a);
	double tmp;
	if (z <= -7.4e+27) {
		tmp = z * ((y - x) / (a - t));
	} else if (z <= -1.76e-32) {
		tmp = t_1;
	} else if (z <= -8e-170) {
		tmp = t_2;
	} else if (z <= 5.2e-295) {
		tmp = t_1;
	} else if (z <= 4.9e-89) {
		tmp = t_2;
	} else if (z <= 1.4e+68) {
		tmp = t_1;
	} else {
		tmp = (y - x) * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (((y - x) * z) / a)
	tmp = 0
	if z <= -7.4e+27:
		tmp = z * ((y - x) / (a - t))
	elif z <= -1.76e-32:
		tmp = t_1
	elif z <= -8e-170:
		tmp = t_2
	elif z <= 5.2e-295:
		tmp = t_1
	elif z <= 4.9e-89:
		tmp = t_2
	elif z <= 1.4e+68:
		tmp = t_1
	else:
		tmp = (y - x) * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * z) / a))
	tmp = 0.0
	if (z <= -7.4e+27)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (z <= -1.76e-32)
		tmp = t_1;
	elseif (z <= -8e-170)
		tmp = t_2;
	elseif (z <= 5.2e-295)
		tmp = t_1;
	elseif (z <= 4.9e-89)
		tmp = t_2;
	elseif (z <= 1.4e+68)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (((y - x) * z) / a);
	tmp = 0.0;
	if (z <= -7.4e+27)
		tmp = z * ((y - x) / (a - t));
	elseif (z <= -1.76e-32)
		tmp = t_1;
	elseif (z <= -8e-170)
		tmp = t_2;
	elseif (z <= 5.2e-295)
		tmp = t_1;
	elseif (z <= 4.9e-89)
		tmp = t_2;
	elseif (z <= 1.4e+68)
		tmp = t_1;
	else
		tmp = (y - x) * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e+27], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e-32], t$95$1, If[LessEqual[z, -8e-170], t$95$2, If[LessEqual[z, 5.2e-295], t$95$1, If[LessEqual[z, 4.9e-89], t$95$2, If[LessEqual[z, 1.4e+68], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.40000000000000004e27

   1. Initial program 68.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. div-sub 84.6%

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

   7. Simplified 84.6%

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

   if -7.40000000000000004e27 < z < -1.76000000000000004e-32 or -7.99999999999999987e-170 < z < 5.1999999999999997e-295 or 4.9e-89 < z < 1.4e68

   1. Initial program 58.7%

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

      1. +-commutative 58.7%

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

      2. associate-*l/ 71.4%

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

      3. fma-def 71.3%

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

   3. Simplified 71.3%

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

      1. fma-udef 71.4%

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

      2. associate-/r/ 76.8%

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

      3. div-inv 76.8%

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

      4. clear-num 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   9. Simplified 67.6%

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

   if -1.76000000000000004e-32 < z < -7.99999999999999987e-170 or 5.1999999999999997e-295 < z < 4.9e-89

   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/ 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around 0 60.7%

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

   if 1.4e68 < z

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*l/ 89.2%

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

      3. fma-def 89.4%

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

   3. Simplified 89.4%

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

      1. fma-udef 89.2%

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

      2. associate-/r/ 91.9%

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

      3. div-inv 92.0%

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

      4. clear-num 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in z around inf 81.6%

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

      1. div-sub 81.6%

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

      2. associate-*r/ 64.7%

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

      3. associate-/l* 80.0%

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

   9. Simplified 80.0%

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

       1. associate-/r/ 82.3%

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

   11. Applied egg-rr 82.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-170}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -46000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 0.0086:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (+ x (/ z (/ a (- y x))))))
   (if (<= a -46000000000.0)
     t_2
     (if (<= a -8.5e-20)
       (+ y (* x (/ (- z a) t)))
       (if (<= a -6e-43)
         (+ x (/ (* (- y x) z) a))
         (if (<= a 4.5e-86)
           t_1
           (if (<= a 4.2e-74)
             (- x (/ (* y (- t z)) a))
             (if (<= a 0.0086) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -46000000000.0) {
		tmp = t_2;
	} else if (a <= -8.5e-20) {
		tmp = y + (x * ((z - a) / t));
	} else if (a <= -6e-43) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 4.5e-86) {
		tmp = t_1;
	} else if (a <= 4.2e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 0.0086) {
		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 + ((x - y) / (t / z))
    t_2 = x + (z / (a / (y - x)))
    if (a <= (-46000000000.0d0)) then
        tmp = t_2
    else if (a <= (-8.5d-20)) then
        tmp = y + (x * ((z - a) / t))
    else if (a <= (-6d-43)) then
        tmp = x + (((y - x) * z) / a)
    else if (a <= 4.5d-86) then
        tmp = t_1
    else if (a <= 4.2d-74) then
        tmp = x - ((y * (t - z)) / a)
    else if (a <= 0.0086d0) 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 + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -46000000000.0) {
		tmp = t_2;
	} else if (a <= -8.5e-20) {
		tmp = y + (x * ((z - a) / t));
	} else if (a <= -6e-43) {
		tmp = x + (((y - x) * z) / a);
	} else if (a <= 4.5e-86) {
		tmp = t_1;
	} else if (a <= 4.2e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 0.0086) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = x + (z / (a / (y - x)))
	tmp = 0
	if a <= -46000000000.0:
		tmp = t_2
	elif a <= -8.5e-20:
		tmp = y + (x * ((z - a) / t))
	elif a <= -6e-43:
		tmp = x + (((y - x) * z) / a)
	elif a <= 4.5e-86:
		tmp = t_1
	elif a <= 4.2e-74:
		tmp = x - ((y * (t - z)) / a)
	elif a <= 0.0086:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -46000000000.0)
		tmp = t_2;
	elseif (a <= -8.5e-20)
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	elseif (a <= -6e-43)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (a <= 4.5e-86)
		tmp = t_1;
	elseif (a <= 4.2e-74)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	elseif (a <= 0.0086)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (a <= -46000000000.0)
		tmp = t_2;
	elseif (a <= -8.5e-20)
		tmp = y + (x * ((z - a) / t));
	elseif (a <= -6e-43)
		tmp = x + (((y - x) * z) / a);
	elseif (a <= 4.5e-86)
		tmp = t_1;
	elseif (a <= 4.2e-74)
		tmp = x - ((y * (t - z)) / a);
	elseif (a <= 0.0086)
		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[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -46000000000.0], t$95$2, If[LessEqual[a, -8.5e-20], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-43], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-86], t$95$1, If[LessEqual[a, 4.2e-74], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0086], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.6e10 or 0.0086 < a

   1. Initial program 71.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around 0 64.6%

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

      1. associate-/l* 71.2%

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

   7. Simplified 71.2%

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

   if -4.6e10 < a < -8.5000000000000005e-20

   1. Initial program 51.6%

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

      1. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-*r/ 67.6%

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

      7. mul-1-neg 67.6%

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

      8. unsub-neg 67.6%

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

      9. distribute-rgt-out-- 67.6%

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

      10. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-*r/ 75.4%

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

      3. distribute-lft-neg-in 75.4%

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

   10. Simplified 75.4%

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

   if -8.5000000000000005e-20 < a < -6.00000000000000007e-43

   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%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   if -6.00000000000000007e-43 < a < 4.4999999999999998e-86 or 4.2e-74 < a < 0.0086

   1. Initial program 65.9%

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

      1. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in t around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. div-sub 76.7%

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

      5. distribute-lft-out-- 76.7%

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

      6. associate-*r/ 76.7%

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

      7. mul-1-neg 76.7%

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

      8. unsub-neg 76.7%

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

      9. distribute-rgt-out-- 76.7%

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

      10. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in z around inf 80.1%

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

   if 4.4999999999999998e-86 < a < 4.2e-74

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 70.0%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

      1. fma-udef 70.0%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around inf 86.6%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

   10. Taylor expanded in y around inf 86.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -46000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 0.0086:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ t_2 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 0.00112:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a)))))
        (t_2 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -2.1e+20)
     t_2
     (if (<= a 2.5e-103)
       t_1
       (if (<= a 1.7e-74)
         (- x (/ (* y (- t z)) a))
         (if (<= a 0.00112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double t_2 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -2.1e+20) {
		tmp = t_2;
	} else if (a <= 2.5e-103) {
		tmp = t_1;
	} else if (a <= 1.7e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 0.00112) {
		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 + ((x - y) / (t / (z - a)))
    t_2 = x + ((y - x) / (a / (z - t)))
    if (a <= (-2.1d+20)) then
        tmp = t_2
    else if (a <= 2.5d-103) then
        tmp = t_1
    else if (a <= 1.7d-74) then
        tmp = x - ((y * (t - z)) / a)
    else if (a <= 0.00112d0) 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 + ((x - y) / (t / (z - a)));
	double t_2 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -2.1e+20) {
		tmp = t_2;
	} else if (a <= 2.5e-103) {
		tmp = t_1;
	} else if (a <= 1.7e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 0.00112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	t_2 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -2.1e+20:
		tmp = t_2
	elif a <= 2.5e-103:
		tmp = t_1
	elif a <= 1.7e-74:
		tmp = x - ((y * (t - z)) / a)
	elif a <= 0.00112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -2.1e+20)
		tmp = t_2;
	elseif (a <= 2.5e-103)
		tmp = t_1;
	elseif (a <= 1.7e-74)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	elseif (a <= 0.00112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	t_2 = x + ((y - x) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -2.1e+20)
		tmp = t_2;
	elseif (a <= 2.5e-103)
		tmp = t_1;
	elseif (a <= 1.7e-74)
		tmp = x - ((y * (t - z)) / a);
	elseif (a <= 0.00112)
		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[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+20], t$95$2, If[LessEqual[a, 2.5e-103], t$95$1, If[LessEqual[a, 1.7e-74], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e20 or 0.0011199999999999999 < a

   1. Initial program 71.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in a around inf 65.7%

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

      1. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if -2.1e20 < a < 2.49999999999999983e-103 or 1.7e-74 < a < 0.0011199999999999999

   1. Initial program 65.4%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. associate-*r/ 72.9%

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

      3. associate-*r/ 72.9%

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

      4. div-sub 74.6%

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

      5. distribute-lft-out-- 74.6%

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

      6. associate-*r/ 74.6%

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

      7. mul-1-neg 74.6%

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

      8. unsub-neg 74.6%

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

      9. distribute-rgt-out-- 74.6%

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

      10. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

   if 2.49999999999999983e-103 < a < 1.7e-74

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 69.2%

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

      3. fma-def 69.2%

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

   3. Simplified 69.2%

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

      1. fma-udef 69.2%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around inf 71.3%

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

      1. associate-/l* 71.3%

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

   9. Simplified 71.3%

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

   10. Taylor expanded in y around inf 71.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-103}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 0.00112:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+50)
   y
   (if (<= t -1.5e-184)
     x
     (if (<= t 2.9e-222)
       (* y (/ z a))
       (if (<= t 3.5e-89) x (if (<= t 1.35e+145) (/ x (/ t z)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+50) {
		tmp = y;
	} else if (t <= -1.5e-184) {
		tmp = x;
	} else if (t <= 2.9e-222) {
		tmp = y * (z / a);
	} else if (t <= 3.5e-89) {
		tmp = x;
	} else if (t <= 1.35e+145) {
		tmp = x / (t / 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 (t <= (-1.7d+50)) then
        tmp = y
    else if (t <= (-1.5d-184)) then
        tmp = x
    else if (t <= 2.9d-222) then
        tmp = y * (z / a)
    else if (t <= 3.5d-89) then
        tmp = x
    else if (t <= 1.35d+145) then
        tmp = x / (t / 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 (t <= -1.7e+50) {
		tmp = y;
	} else if (t <= -1.5e-184) {
		tmp = x;
	} else if (t <= 2.9e-222) {
		tmp = y * (z / a);
	} else if (t <= 3.5e-89) {
		tmp = x;
	} else if (t <= 1.35e+145) {
		tmp = x / (t / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+50:
		tmp = y
	elif t <= -1.5e-184:
		tmp = x
	elif t <= 2.9e-222:
		tmp = y * (z / a)
	elif t <= 3.5e-89:
		tmp = x
	elif t <= 1.35e+145:
		tmp = x / (t / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+50)
		tmp = y;
	elseif (t <= -1.5e-184)
		tmp = x;
	elseif (t <= 2.9e-222)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.5e-89)
		tmp = x;
	elseif (t <= 1.35e+145)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+50)
		tmp = y;
	elseif (t <= -1.5e-184)
		tmp = x;
	elseif (t <= 2.9e-222)
		tmp = y * (z / a);
	elseif (t <= 3.5e-89)
		tmp = x;
	elseif (t <= 1.35e+145)
		tmp = x / (t / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+50], y, If[LessEqual[t, -1.5e-184], x, If[LessEqual[t, 2.9e-222], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-89], x, If[LessEqual[t, 1.35e+145], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6999999999999999e50 or 1.35000000000000011e145 < t

   1. Initial program 37.3%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in t around inf 51.3%

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

   if -1.6999999999999999e50 < t < -1.49999999999999996e-184 or 2.9000000000000002e-222 < t < 3.4999999999999997e-89

   1. Initial program 86.8%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in a around inf 36.3%

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

   if -1.49999999999999996e-184 < t < 2.9000000000000002e-222

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-*l/ 87.8%

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

      3. fma-def 87.8%

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

   3. Simplified 87.8%

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

      1. fma-udef 87.8%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.6%

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

      4. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 50.9%

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

      1. div-sub 50.9%

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

   9. Simplified 50.9%

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

   10. Taylor expanded in t around 0 43.1%

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

   if 3.4999999999999997e-89 < t < 1.35000000000000011e145

   1. Initial program 69.0%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in z around -inf 52.7%

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

   6. Taylor expanded in a around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-*r/ 46.5%

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

      3. distribute-rgt-neg-in 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in y around 0 29.3%

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

       1. associate-/l* 36.7%

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

   11. Simplified 36.7%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+50}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-221}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.52e+50)
   y
   (if (<= t -1.3e-184)
     x
     (if (<= t 2e-221)
       (/ y (/ a z))
       (if (<= t 5.2e-89) x (if (<= t 1.2e+145) (/ x (/ t z)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.52e+50) {
		tmp = y;
	} else if (t <= -1.3e-184) {
		tmp = x;
	} else if (t <= 2e-221) {
		tmp = y / (a / z);
	} else if (t <= 5.2e-89) {
		tmp = x;
	} else if (t <= 1.2e+145) {
		tmp = x / (t / 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 (t <= (-1.52d+50)) then
        tmp = y
    else if (t <= (-1.3d-184)) then
        tmp = x
    else if (t <= 2d-221) then
        tmp = y / (a / z)
    else if (t <= 5.2d-89) then
        tmp = x
    else if (t <= 1.2d+145) then
        tmp = x / (t / 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 (t <= -1.52e+50) {
		tmp = y;
	} else if (t <= -1.3e-184) {
		tmp = x;
	} else if (t <= 2e-221) {
		tmp = y / (a / z);
	} else if (t <= 5.2e-89) {
		tmp = x;
	} else if (t <= 1.2e+145) {
		tmp = x / (t / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.52e+50:
		tmp = y
	elif t <= -1.3e-184:
		tmp = x
	elif t <= 2e-221:
		tmp = y / (a / z)
	elif t <= 5.2e-89:
		tmp = x
	elif t <= 1.2e+145:
		tmp = x / (t / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.52e+50)
		tmp = y;
	elseif (t <= -1.3e-184)
		tmp = x;
	elseif (t <= 2e-221)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.2e-89)
		tmp = x;
	elseif (t <= 1.2e+145)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.52e+50)
		tmp = y;
	elseif (t <= -1.3e-184)
		tmp = x;
	elseif (t <= 2e-221)
		tmp = y / (a / z);
	elseif (t <= 5.2e-89)
		tmp = x;
	elseif (t <= 1.2e+145)
		tmp = x / (t / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.52e+50], y, If[LessEqual[t, -1.3e-184], x, If[LessEqual[t, 2e-221], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-89], x, If[LessEqual[t, 1.2e+145], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5199999999999999e50 or 1.19999999999999996e145 < t

   1. Initial program 37.3%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in t around inf 51.3%

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

   if -1.5199999999999999e50 < t < -1.29999999999999989e-184 or 2.00000000000000003e-221 < t < 5.1999999999999997e-89

   1. Initial program 86.8%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in a around inf 36.3%

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

   if -1.29999999999999989e-184 < t < 2.00000000000000003e-221

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-*l/ 87.8%

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

      3. fma-def 87.8%

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

   3. Simplified 87.8%

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

      1. fma-udef 87.8%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.6%

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

      4. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 50.9%

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

      1. div-sub 50.9%

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

   9. Simplified 50.9%

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

   10. Taylor expanded in t around 0 39.3%

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

       1. associate-/l* 43.2%

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

   12. Simplified 43.2%

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

   if 5.1999999999999997e-89 < t < 1.19999999999999996e145

   1. Initial program 69.0%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in z around -inf 52.7%

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

   6. Taylor expanded in a around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-*r/ 46.5%

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

      3. distribute-rgt-neg-in 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in y around 0 29.3%

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

       1. associate-/l* 36.7%

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

   11. Simplified 36.7%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+50}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-221}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -3.75 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -3.75e+239)
     t_1
     (if (<= x -8.5e+198)
       (/ (- x) (/ (- a t) z))
       (if (<= x -1.2e+119)
         t_1
         (if (<= x 1.5e+54) (* y (/ (- z t) (- a t))) (- x (* x (/ 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 (x <= -3.75e+239) {
		tmp = t_1;
	} else if (x <= -8.5e+198) {
		tmp = -x / ((a - t) / z);
	} else if (x <= -1.2e+119) {
		tmp = t_1;
	} else if (x <= 1.5e+54) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (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 (x <= (-3.75d+239)) then
        tmp = t_1
    else if (x <= (-8.5d+198)) then
        tmp = -x / ((a - t) / z)
    else if (x <= (-1.2d+119)) then
        tmp = t_1
    else if (x <= 1.5d+54) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (x * (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 (x <= -3.75e+239) {
		tmp = t_1;
	} else if (x <= -8.5e+198) {
		tmp = -x / ((a - t) / z);
	} else if (x <= -1.2e+119) {
		tmp = t_1;
	} else if (x <= 1.5e+54) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -3.75e+239:
		tmp = t_1
	elif x <= -8.5e+198:
		tmp = -x / ((a - t) / z)
	elif x <= -1.2e+119:
		tmp = t_1
	elif x <= 1.5e+54:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (x * (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 (x <= -3.75e+239)
		tmp = t_1;
	elseif (x <= -8.5e+198)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (x <= -1.2e+119)
		tmp = t_1;
	elseif (x <= 1.5e+54)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(x * 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 (x <= -3.75e+239)
		tmp = t_1;
	elseif (x <= -8.5e+198)
		tmp = -x / ((a - t) / z);
	elseif (x <= -1.2e+119)
		tmp = t_1;
	elseif (x <= 1.5e+54)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (x * (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[x, -3.75e+239], t$95$1, If[LessEqual[x, -8.5e+198], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e+119], t$95$1, If[LessEqual[x, 1.5e+54], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.7499999999999998e239 or -8.5000000000000001e198 < x < -1.2e119

   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/ 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around 0 63.6%

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

      1. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   10. Simplified 71.0%

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

   if -3.7499999999999998e239 < x < -8.5000000000000001e198

   1. Initial program 41.4%

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

      1. associate-*l/ 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in z around -inf 42.9%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. associate-/l* 61.6%

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

      3. distribute-neg-frac 61.6%

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

   8. Simplified 61.6%

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

   if -1.2e119 < x < 1.4999999999999999e54

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-*l/ 87.0%

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

      3. fma-def 87.0%

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

   3. Simplified 87.0%

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

      1. fma-udef 87.0%

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

      2. associate-/r/ 92.5%

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

      3. div-inv 92.5%

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

      4. clear-num 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around inf 69.5%

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

      1. div-sub 69.5%

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

   9. Simplified 69.5%

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

   if 1.4999999999999999e54 < x

   1. Initial program 58.1%

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

      1. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in t around 0 50.1%

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

      1. associate-/l* 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in y around 0 50.1%

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

      1. associate-*r/ 50.1%

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

      2. mul-1-neg 50.1%

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

      3. distribute-lft-neg-out 50.1%

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

      4. associate-*r/ 53.8%

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

      5. *-commutative 53.8%

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

   10. Simplified 53.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{+239}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -2100000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (+ x (/ z (/ a (- y x))))))
   (if (<= a -2100000000.0)
     t_2
     (if (<= a 4.5e-86)
       t_1
       (if (<= a 1.7e-74)
         (- x (/ (* y (- t z)) a))
         (if (<= a 4.5e-5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -2100000000.0) {
		tmp = t_2;
	} else if (a <= 4.5e-86) {
		tmp = t_1;
	} else if (a <= 1.7e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 4.5e-5) {
		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 + ((x - y) / (t / z))
    t_2 = x + (z / (a / (y - x)))
    if (a <= (-2100000000.0d0)) then
        tmp = t_2
    else if (a <= 4.5d-86) then
        tmp = t_1
    else if (a <= 1.7d-74) then
        tmp = x - ((y * (t - z)) / a)
    else if (a <= 4.5d-5) 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 + ((x - y) / (t / z));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -2100000000.0) {
		tmp = t_2;
	} else if (a <= 4.5e-86) {
		tmp = t_1;
	} else if (a <= 1.7e-74) {
		tmp = x - ((y * (t - z)) / a);
	} else if (a <= 4.5e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = x + (z / (a / (y - x)))
	tmp = 0
	if a <= -2100000000.0:
		tmp = t_2
	elif a <= 4.5e-86:
		tmp = t_1
	elif a <= 1.7e-74:
		tmp = x - ((y * (t - z)) / a)
	elif a <= 4.5e-5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -2100000000.0)
		tmp = t_2;
	elseif (a <= 4.5e-86)
		tmp = t_1;
	elseif (a <= 1.7e-74)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	elseif (a <= 4.5e-5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (a <= -2100000000.0)
		tmp = t_2;
	elseif (a <= 4.5e-86)
		tmp = t_1;
	elseif (a <= 1.7e-74)
		tmp = x - ((y * (t - z)) / a);
	elseif (a <= 4.5e-5)
		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[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2100000000.0], t$95$2, If[LessEqual[a, 4.5e-86], t$95$1, If[LessEqual[a, 1.7e-74], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-5], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e9 or 4.50000000000000028e-5 < a

   1. Initial program 71.2%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around 0 64.1%

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

      1. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   if -2.1e9 < a < 4.4999999999999998e-86 or 1.7e-74 < a < 4.50000000000000028e-5

   1. Initial program 66.1%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-*r/ 72.4%

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

      3. associate-*r/ 72.4%

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

      4. div-sub 74.0%

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

      5. distribute-lft-out-- 74.0%

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

      6. associate-*r/ 74.0%

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

      7. mul-1-neg 74.0%

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

      8. unsub-neg 74.0%

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

      9. distribute-rgt-out-- 74.0%

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

      10. associate-/l* 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in z around inf 77.0%

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

   if 4.4999999999999998e-86 < a < 1.7e-74

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l/ 70.0%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

      1. fma-udef 70.0%

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

      2. associate-/r/ 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around inf 86.6%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

   10. Taylor expanded in y around inf 86.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2100000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+21)
   (* y (/ t (- t a)))
   (if (<= t 1.4e-89)
     (+ x (/ y (/ a z)))
     (if (<= t 2.6e+145) (/ z (/ t (- x y))) (/ (- y) (/ t (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+21) {
		tmp = y * (t / (t - a));
	} else if (t <= 1.4e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.6e+145) {
		tmp = z / (t / (x - y));
	} else {
		tmp = -y / (t / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.1d+21)) then
        tmp = y * (t / (t - a))
    else if (t <= 1.4d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 2.6d+145) then
        tmp = z / (t / (x - y))
    else
        tmp = -y / (t / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+21) {
		tmp = y * (t / (t - a));
	} else if (t <= 1.4e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.6e+145) {
		tmp = z / (t / (x - y));
	} else {
		tmp = -y / (t / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+21:
		tmp = y * (t / (t - a))
	elif t <= 1.4e-89:
		tmp = x + (y / (a / z))
	elif t <= 2.6e+145:
		tmp = z / (t / (x - y))
	else:
		tmp = -y / (t / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+21)
		tmp = Float64(y * Float64(t / Float64(t - a)));
	elseif (t <= 1.4e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.6e+145)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	else
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e+21)
		tmp = y * (t / (t - a));
	elseif (t <= 1.4e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 2.6e+145)
		tmp = z / (t / (x - y));
	else
		tmp = -y / (t / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+21], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+145], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.1e21

   1. Initial program 42.6%

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

      1. +-commutative 42.6%

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

      2. associate-*l/ 67.0%

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

      3. fma-def 68.0%

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

   3. Simplified 68.0%

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

      1. fma-udef 67.0%

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

      2. associate-/r/ 68.9%

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

      3. div-inv 69.0%

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

      4. clear-num 68.9%

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

   6. Applied egg-rr 68.9%

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

   7. Taylor expanded in y around inf 58.1%

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

      1. div-sub 58.1%

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

   9. Simplified 58.1%

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

   10. Taylor expanded in z around 0 50.4%

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

       1. neg-mul-1 50.4%

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

       2. distribute-neg-frac 50.4%

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

   12. Simplified 50.4%

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

       1. frac-2neg 50.4%

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

       2. div-inv 50.3%

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

       3. remove-double-neg 50.3%

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

       4. sub-neg 50.3%

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

       5. distribute-neg-in 50.3%

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

       6. remove-double-neg 50.3%

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

   14. Applied egg-rr 50.3%

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

       1. associate-*r/ 50.4%

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

       2. *-rgt-identity 50.4%

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

       3. +-commutative 50.4%

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

       4. unsub-neg 50.4%

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

   16. Simplified 50.4%

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

   if -3.1e21 < t < 1.3999999999999999e-89

   1. Initial program 89.8%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t around 0 69.8%

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

      1. associate-/l* 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in y around inf 55.0%

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

      1. associate-/l* 59.6%

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

   10. Simplified 59.6%

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

   if 1.3999999999999999e-89 < t < 2.60000000000000003e145

   1. Initial program 69.6%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in z around -inf 53.6%

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

   6. Taylor expanded in a around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. associate-*r/ 47.5%

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

      3. distribute-rgt-neg-in 47.5%

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

   8. Simplified 47.5%

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

   9. Taylor expanded in t around 0 42.3%

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

       1. associate-/l* 47.6%

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

   11. Simplified 47.6%

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

   if 2.60000000000000003e145 < t

   1. Initial program 32.5%

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

      1. +-commutative 32.5%

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

      2. associate-*l/ 71.6%

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

      3. fma-def 71.6%

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

   3. Simplified 71.6%

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

      1. fma-udef 71.6%

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

      2. associate-/r/ 77.9%

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

      3. div-inv 77.9%

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

      4. clear-num 78.0%

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

   6. Applied egg-rr 78.0%

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

   7. Taylor expanded in y around inf 74.9%

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

      1. div-sub 74.9%

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

   9. Simplified 74.9%

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

   10. Taylor expanded in a around 0 25.4%

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

       1. mul-1-neg 25.4%

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

       2. associate-/l* 66.0%

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

       3. distribute-neg-frac 66.0%

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

   12. Simplified 66.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-76} \lor \neg \left(a \leq 4.7 \cdot 10^{-115}\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-76) (not (<= a 4.7e-115)))
   (- x (* (- z t) (/ (- x y) (- a t))))
   (+ y (/ (- x y) (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-76) || !(a <= 4.7e-115)) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (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 ((a <= (-8.5d-76)) .or. (.not. (a <= 4.7d-115))) then
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    else
        tmp = y + ((x - y) / (t / (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 ((a <= -8.5e-76) || !(a <= 4.7e-115)) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-76) or not (a <= 4.7e-115):
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-76) || !(a <= 4.7e-115))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-76) || ~((a <= 4.7e-115)))
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-76], N[Not[LessEqual[a, 4.7e-115]], $MachinePrecision]], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000038e-76 or 4.7000000000000001e-115 < a

   1. Initial program 72.2%

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

      1. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   if -8.50000000000000038e-76 < a < 4.7000000000000001e-115

   1. Initial program 63.8%

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

      1. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. associate-*r/ 78.5%

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

      4. div-sub 78.5%

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

      5. distribute-lft-out-- 78.5%

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

      6. associate-*r/ 78.5%

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

      7. mul-1-neg 78.5%

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

      8. unsub-neg 78.5%

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

      9. distribute-rgt-out-- 78.5%

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

      10. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-76} \lor \neg \left(a \leq 4.7 \cdot 10^{-115}\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- t a)))))
   (if (<= t -2.5e+22)
     t_1
     (if (<= t 3.5e-25)
       (+ x (/ y (/ a z)))
       (if (<= t 1.3e+146) (/ x (/ t z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (t - a));
	double tmp;
	if (t <= -2.5e+22) {
		tmp = t_1;
	} else if (t <= 3.5e-25) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.3e+146) {
		tmp = x / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (t - a))
    if (t <= (-2.5d+22)) then
        tmp = t_1
    else if (t <= 3.5d-25) then
        tmp = x + (y / (a / z))
    else if (t <= 1.3d+146) then
        tmp = x / (t / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (t - a));
	double tmp;
	if (t <= -2.5e+22) {
		tmp = t_1;
	} else if (t <= 3.5e-25) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.3e+146) {
		tmp = x / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (t - a))
	tmp = 0
	if t <= -2.5e+22:
		tmp = t_1
	elif t <= 3.5e-25:
		tmp = x + (y / (a / z))
	elif t <= 1.3e+146:
		tmp = x / (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(t - a)))
	tmp = 0.0
	if (t <= -2.5e+22)
		tmp = t_1;
	elseif (t <= 3.5e-25)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.3e+146)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (t - a));
	tmp = 0.0;
	if (t <= -2.5e+22)
		tmp = t_1;
	elseif (t <= 3.5e-25)
		tmp = x + (y / (a / z));
	elseif (t <= 1.3e+146)
		tmp = x / (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+22], t$95$1, If[LessEqual[t, 3.5e-25], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+146], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999998e22 or 1.30000000000000007e146 < t

   1. Initial program 38.8%

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

      1. +-commutative 38.8%

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

      2. associate-*l/ 68.7%

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

      3. fma-def 69.3%

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

   3. Simplified 69.3%

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

      1. fma-udef 68.7%

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

      2. associate-/r/ 72.3%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 72.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 72.3%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 72.3%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 64.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 64.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 64.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in z around 0 56.1%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a - t}\right)} \]
   11. Step-by-step derivation

       1. neg-mul-1 56.1%

          \[\leadsto y \cdot \color{blue}{\left(-\frac{t}{a - t}\right)} \]

       2. distribute-neg-frac 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]

   12. Simplified 56.1%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]
   13. Step-by-step derivation

       1. frac-2neg 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{-\left(-t\right)}{-\left(a - t\right)}} \]

       2. div-inv 55.9%

          \[\leadsto y \cdot \color{blue}{\left(\left(-\left(-t\right)\right) \cdot \frac{1}{-\left(a - t\right)}\right)} \]

       3. remove-double-neg 55.9%

          \[\leadsto y \cdot \left(\color{blue}{t} \cdot \frac{1}{-\left(a - t\right)}\right) \]

       4. sub-neg 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{-\color{blue}{\left(a + \left(-t\right)\right)}}\right) \]

       5. distribute-neg-in 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\color{blue}{\left(-a\right) + \left(-\left(-t\right)\right)}}\right) \]

       6. remove-double-neg 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\left(-a\right) + \color{blue}{t}}\right) \]

   14. Applied egg-rr 55.9%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \frac{1}{\left(-a\right) + t}\right)} \]
   15. Step-by-step derivation

       1. associate-*r/ 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{t \cdot 1}{\left(-a\right) + t}} \]

       2. *-rgt-identity 56.1%

          \[\leadsto y \cdot \frac{\color{blue}{t}}{\left(-a\right) + t} \]

       3. +-commutative 56.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t + \left(-a\right)}} \]

       4. unsub-neg 56.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t - a}} \]

   16. Simplified 56.1%

       \[\leadsto y \cdot \color{blue}{\frac{t}{t - a}} \]

   if -2.4999999999999998e22 < t < 3.5000000000000002e-25

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.4%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 70.3%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 70.3%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in y around inf 53.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 57.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   10. Simplified 57.4%

       \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 3.5000000000000002e-25 < t < 1.30000000000000007e146

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 53.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Taylor expanded in a around 0 41.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

      2. associate-*r/ 49.1%

         \[\leadsto -\color{blue}{z \cdot \frac{y - x}{t}} \]

      3. distribute-rgt-neg-in 49.1%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   8. Simplified 49.1%

      \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   9. Taylor expanded in y around 0 32.1%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   10. Step-by-step derivation

       1. associate-/l* 40.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   11. Simplified 40.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- t a)))))
   (if (<= t -2.7e+22)
     t_1
     (if (<= t 1.5e-90)
       (+ x (/ y (/ a z)))
       (if (<= t 2.6e+145) (/ z (/ t (- x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (t - a));
	double tmp;
	if (t <= -2.7e+22) {
		tmp = t_1;
	} else if (t <= 1.5e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.6e+145) {
		tmp = z / (t / (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (t - a))
    if (t <= (-2.7d+22)) then
        tmp = t_1
    else if (t <= 1.5d-90) then
        tmp = x + (y / (a / z))
    else if (t <= 2.6d+145) then
        tmp = z / (t / (x - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (t - a));
	double tmp;
	if (t <= -2.7e+22) {
		tmp = t_1;
	} else if (t <= 1.5e-90) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.6e+145) {
		tmp = z / (t / (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (t - a))
	tmp = 0
	if t <= -2.7e+22:
		tmp = t_1
	elif t <= 1.5e-90:
		tmp = x + (y / (a / z))
	elif t <= 2.6e+145:
		tmp = z / (t / (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(t - a)))
	tmp = 0.0
	if (t <= -2.7e+22)
		tmp = t_1;
	elseif (t <= 1.5e-90)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.6e+145)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (t - a));
	tmp = 0.0;
	if (t <= -2.7e+22)
		tmp = t_1;
	elseif (t <= 1.5e-90)
		tmp = x + (y / (a / z));
	elseif (t <= 2.6e+145)
		tmp = z / (t / (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+22], t$95$1, If[LessEqual[t, 1.5e-90], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+145], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000002e22 or 2.60000000000000003e145 < t

   1. Initial program 38.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 38.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 68.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 69.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 68.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 72.3%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 72.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 72.3%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 72.3%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 64.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 64.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 64.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in z around 0 56.1%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a - t}\right)} \]
   11. Step-by-step derivation

       1. neg-mul-1 56.1%

          \[\leadsto y \cdot \color{blue}{\left(-\frac{t}{a - t}\right)} \]

       2. distribute-neg-frac 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]

   12. Simplified 56.1%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]
   13. Step-by-step derivation

       1. frac-2neg 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{-\left(-t\right)}{-\left(a - t\right)}} \]

       2. div-inv 55.9%

          \[\leadsto y \cdot \color{blue}{\left(\left(-\left(-t\right)\right) \cdot \frac{1}{-\left(a - t\right)}\right)} \]

       3. remove-double-neg 55.9%

          \[\leadsto y \cdot \left(\color{blue}{t} \cdot \frac{1}{-\left(a - t\right)}\right) \]

       4. sub-neg 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{-\color{blue}{\left(a + \left(-t\right)\right)}}\right) \]

       5. distribute-neg-in 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\color{blue}{\left(-a\right) + \left(-\left(-t\right)\right)}}\right) \]

       6. remove-double-neg 55.9%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\left(-a\right) + \color{blue}{t}}\right) \]

   14. Applied egg-rr 55.9%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \frac{1}{\left(-a\right) + t}\right)} \]
   15. Step-by-step derivation

       1. associate-*r/ 56.1%

          \[\leadsto y \cdot \color{blue}{\frac{t \cdot 1}{\left(-a\right) + t}} \]

       2. *-rgt-identity 56.1%

          \[\leadsto y \cdot \frac{\color{blue}{t}}{\left(-a\right) + t} \]

       3. +-commutative 56.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t + \left(-a\right)}} \]

       4. unsub-neg 56.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t - a}} \]

   16. Simplified 56.1%

       \[\leadsto y \cdot \color{blue}{\frac{t}{t - a}} \]

   if -2.7000000000000002e22 < t < 1.5000000000000001e-90

   1. Initial program 89.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.8%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.6%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in y around inf 55.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 59.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   10. Simplified 59.6%

       \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 1.5000000000000001e-90 < t < 2.60000000000000003e145

   1. Initial program 69.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 53.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Taylor expanded in a around 0 42.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

      2. associate-*r/ 47.5%

         \[\leadsto -\color{blue}{z \cdot \frac{y - x}{t}} \]

      3. distribute-rgt-neg-in 47.5%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   8. Simplified 47.5%

      \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   9. Taylor expanded in t around 0 42.3%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   10. Step-by-step derivation

       1. associate-/l* 47.6%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   11. Simplified 47.6%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1800000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+47)
   y
   (if (<= t 1800000000.0)
     (* x (- 1.0 (/ z a)))
     (if (<= t 1.5e+145) (/ x (/ t z)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+47) {
		tmp = y;
	} else if (t <= 1800000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.5e+145) {
		tmp = x / (t / 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 (t <= (-2.6d+47)) then
        tmp = y
    else if (t <= 1800000000.0d0) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.5d+145) then
        tmp = x / (t / 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 (t <= -2.6e+47) {
		tmp = y;
	} else if (t <= 1800000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.5e+145) {
		tmp = x / (t / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+47:
		tmp = y
	elif t <= 1800000000.0:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.5e+145:
		tmp = x / (t / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+47)
		tmp = y;
	elseif (t <= 1800000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.5e+145)
		tmp = Float64(x / Float64(t / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+47)
		tmp = y;
	elseif (t <= 1800000000.0)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.5e+145)
		tmp = x / (t / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+47], y, If[LessEqual[t, 1800000000.0], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+145], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.60000000000000003e47 or 1.5000000000000001e145 < t

   1. Initial program 38.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 50.7%

      \[\leadsto \color{blue}{y} \]

   if -2.60000000000000003e47 < t < 1.8e9

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.9%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.5%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 52.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 52.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 52.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 52.1%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if 1.8e9 < t < 1.5000000000000001e145

   1. Initial program 63.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 48.3%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   6. Taylor expanded in a around 0 41.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

      2. associate-*r/ 50.6%

         \[\leadsto -\color{blue}{z \cdot \frac{y - x}{t}} \]

      3. distribute-rgt-neg-in 50.6%

         \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   8. Simplified 50.6%

      \[\leadsto \color{blue}{z \cdot \left(-\frac{y - x}{t}\right)} \]

   9. Taylor expanded in y around 0 33.5%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   10. Step-by-step derivation

       1. associate-/l* 43.0%

          \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   11. Simplified 43.0%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1800000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+33} \lor \neg \left(t \leq 5.8 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+33) (not (<= t 5.8e+31)))
   (* y (/ t (- t a)))
   (* x (- 1.0 (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+33) || !(t <= 5.8e+31)) {
		tmp = y * (t / (t - a));
	} 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 ((t <= (-6.6d+33)) .or. (.not. (t <= 5.8d+31))) then
        tmp = y * (t / (t - a))
    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 ((t <= -6.6e+33) || !(t <= 5.8e+31)) {
		tmp = y * (t / (t - a));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+33) or not (t <= 5.8e+31):
		tmp = y * (t / (t - a))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+33) || !(t <= 5.8e+31))
		tmp = Float64(y * Float64(t / Float64(t - a)));
	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 ((t <= -6.6e+33) || ~((t <= 5.8e+31)))
		tmp = y * (t / (t - a));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+33], N[Not[LessEqual[t, 5.8e+31]], $MachinePrecision]], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999953e33 or 5.8000000000000001e31 < t

   1. Initial program 43.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 43.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 69.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 69.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 72.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 72.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 72.5%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 60.3%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 60.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in z around 0 50.1%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a - t}\right)} \]
   11. Step-by-step derivation

       1. neg-mul-1 50.1%

          \[\leadsto y \cdot \color{blue}{\left(-\frac{t}{a - t}\right)} \]

       2. distribute-neg-frac 50.1%

          \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]

   12. Simplified 50.1%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{a - t}} \]
   13. Step-by-step derivation

       1. frac-2neg 50.1%

          \[\leadsto y \cdot \color{blue}{\frac{-\left(-t\right)}{-\left(a - t\right)}} \]

       2. div-inv 50.0%

          \[\leadsto y \cdot \color{blue}{\left(\left(-\left(-t\right)\right) \cdot \frac{1}{-\left(a - t\right)}\right)} \]

       3. remove-double-neg 50.0%

          \[\leadsto y \cdot \left(\color{blue}{t} \cdot \frac{1}{-\left(a - t\right)}\right) \]

       4. sub-neg 50.0%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{-\color{blue}{\left(a + \left(-t\right)\right)}}\right) \]

       5. distribute-neg-in 50.0%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\color{blue}{\left(-a\right) + \left(-\left(-t\right)\right)}}\right) \]

       6. remove-double-neg 50.0%

          \[\leadsto y \cdot \left(t \cdot \frac{1}{\left(-a\right) + \color{blue}{t}}\right) \]

   14. Applied egg-rr 50.0%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \frac{1}{\left(-a\right) + t}\right)} \]
   15. Step-by-step derivation

       1. associate-*r/ 50.1%

          \[\leadsto y \cdot \color{blue}{\frac{t \cdot 1}{\left(-a\right) + t}} \]

       2. *-rgt-identity 50.1%

          \[\leadsto y \cdot \frac{\color{blue}{t}}{\left(-a\right) + t} \]

       3. +-commutative 50.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t + \left(-a\right)}} \]

       4. unsub-neg 50.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{t - a}} \]

   16. Simplified 50.1%

       \[\leadsto y \cdot \color{blue}{\frac{t}{t - a}} \]

   if -6.59999999999999953e33 < t < 5.8000000000000001e31

   1. Initial program 87.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 64.4%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.8%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 52.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 52.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 52.7%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+33} \lor \neg \left(t \leq 5.8 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1350000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1350000000000.0) x (if (<= a 4.3e+80) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1350000000000.0) {
		tmp = x;
	} else if (a <= 4.3e+80) {
		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 <= (-1350000000000.0d0)) then
        tmp = x
    else if (a <= 4.3d+80) 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 <= -1350000000000.0) {
		tmp = x;
	} else if (a <= 4.3e+80) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1350000000000.0:
		tmp = x
	elif a <= 4.3e+80:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1350000000000.0)
		tmp = x;
	elseif (a <= 4.3e+80)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1350000000000.0)
		tmp = x;
	elseif (a <= 4.3e+80)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1350000000000.0], x, If[LessEqual[a, 4.3e+80], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e12 or 4.30000000000000004e80 < a

   1. Initial program 70.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.8%

      \[\leadsto \color{blue}{x} \]

   if -1.35e12 < a < 4.30000000000000004e80

   1. Initial program 68.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 29.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1350000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.4% 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 69.4%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 79.8%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 79.8%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 25.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 25.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024036 
(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))))