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

Percentage Accurate: 68.1% → 90.3%

Time: 22.1s

Alternatives: 25

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-225}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -1e-225)
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (- y (/ (* (- x y) (- a z)) t))
       (fma (/ (- z t) (- a t)) (- y x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-225) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-225)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-225], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999996e-226

   1. Initial program 74.5%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   if -9.9999999999999996e-226 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 19.9%

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

      1. associate-/l* 20.2%

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

   3. Simplified 20.2%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

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

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. associate-*r/ 94.4%

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

      3. *-commutative 94.4%

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

      4. fma-def 94.5%

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

   3. Simplified 94.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-225}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 81.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+279}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ 1.0 (/ (/ (- a t) z) (- y x)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-225)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (if (<= t_2 2e+279) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-225) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 2e+279) {
		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 + (1.0 / (((a - t) / z) / (y - x)));
	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 <= -1e-225) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 2e+279) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-225:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	elif t_2 <= 2e+279:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / z) / Float64(y - x))))
	t_2 = Float64(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 <= -1e-225)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	elseif (t_2 <= 2e+279)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-225)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	elseif (t_2 <= 2e+279)
		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[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(y - x), $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, -1e-225], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+279], 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 2.00000000000000012e279 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.7%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

      1. associate-/l* 41.7%

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

      2. clear-num 41.7%

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

      3. inv-pow 41.7%

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

   5. Applied egg-rr 41.7%

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

      1. unpow-1 41.7%

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

      2. associate-/r* 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in z around inf 44.5%

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

      1. associate-/r* 67.9%

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

   10. Simplified 67.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999996e-226 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000012e279

   1. Initial program 96.6%

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

   if -9.9999999999999996e-226 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 19.9%

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

      1. associate-/l* 20.2%

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

   3. Simplified 20.2%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+279}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \end{array} \]

Alternative 3: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-225} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-225) (not (<= t_1 0.0)))
     (- x (/ (- x y) (/ (- a t) (- z t))))
     (- y (/ (* (- x y) (- 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 <= -1e-225) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((x - y) * (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 <= (-1d-225)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    else
        tmp = y - (((x - y) * (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 <= -1e-225) || !(t_1 <= 0.0)) {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	} else {
		tmp = y - (((x - y) * (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 <= -1e-225) or not (t_1 <= 0.0):
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	else:
		tmp = y - (((x - y) * (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 <= -1e-225) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * 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 <= -1e-225) || ~((t_1 <= 0.0)))
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	else
		tmp = y - (((x - y) * (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, -1e-225], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999996e-226 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 77.1%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   if -9.9999999999999996e-226 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 19.9%

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

      1. associate-/l* 20.2%

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

   3. Simplified 20.2%

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

   4. Taylor expanded in t around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-sub 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-225} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 4: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-116}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ 1.0 (/ (/ (- a t) z) (- y x))))))
   (if (<= z -5.8e-31)
     t_1
     (if (<= z 1.7e-202)
       (+ x (/ (- y x) (/ (- t a) t)))
       (if (<= z 3e-116)
         (- y (/ (* (- x y) (- a z)) t))
         (if (<= z 1.05e+69) (+ x (/ 1.0 (/ (- a t) (* y (- z t))))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	double tmp;
	if (z <= -5.8e-31) {
		tmp = t_1;
	} else if (z <= 1.7e-202) {
		tmp = x + ((y - x) / ((t - a) / t));
	} else if (z <= 3e-116) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (z <= 1.05e+69) {
		tmp = x + (1.0 / ((a - t) / (y * (z - t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (1.0d0 / (((a - t) / z) / (y - x)))
    if (z <= (-5.8d-31)) then
        tmp = t_1
    else if (z <= 1.7d-202) then
        tmp = x + ((y - x) / ((t - a) / t))
    else if (z <= 3d-116) then
        tmp = y - (((x - y) * (a - z)) / t)
    else if (z <= 1.05d+69) then
        tmp = x + (1.0d0 / ((a - t) / (y * (z - t))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	double tmp;
	if (z <= -5.8e-31) {
		tmp = t_1;
	} else if (z <= 1.7e-202) {
		tmp = x + ((y - x) / ((t - a) / t));
	} else if (z <= 3e-116) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (z <= 1.05e+69) {
		tmp = x + (1.0 / ((a - t) / (y * (z - t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)))
	tmp = 0
	if z <= -5.8e-31:
		tmp = t_1
	elif z <= 1.7e-202:
		tmp = x + ((y - x) / ((t - a) / t))
	elif z <= 3e-116:
		tmp = y - (((x - y) * (a - z)) / t)
	elif z <= 1.05e+69:
		tmp = x + (1.0 / ((a - t) / (y * (z - t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / z) / Float64(y - x))))
	tmp = 0.0
	if (z <= -5.8e-31)
		tmp = t_1;
	elseif (z <= 1.7e-202)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(t - a) / t)));
	elseif (z <= 3e-116)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	elseif (z <= 1.05e+69)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a - t) / Float64(y * Float64(z - t)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (1.0 / (((a - t) / z) / (y - x)));
	tmp = 0.0;
	if (z <= -5.8e-31)
		tmp = t_1;
	elseif (z <= 1.7e-202)
		tmp = x + ((y - x) / ((t - a) / t));
	elseif (z <= 3e-116)
		tmp = y - (((x - y) * (a - z)) / t);
	elseif (z <= 1.05e+69)
		tmp = x + (1.0 / ((a - t) / (y * (z - t))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-31], t$95$1, If[LessEqual[z, 1.7e-202], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-116], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+69], N[(x + N[(1.0 / N[(N[(a - t), $MachinePrecision] / N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8000000000000001e-31 or 1.05000000000000008e69 < z

   1. Initial program 71.4%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. associate-/l* 71.4%

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

      2. clear-num 71.3%

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

      3. inv-pow 71.3%

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

   5. Applied egg-rr 71.3%

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

      1. unpow-1 71.3%

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

      2. associate-/r* 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in z around inf 67.3%

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

      1. associate-/r* 82.9%

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

   10. Simplified 82.9%

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

   if -5.8000000000000001e-31 < z < 1.70000000000000006e-202

   1. Initial program 77.4%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   6. Simplified 78.5%

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

   if 1.70000000000000006e-202 < z < 3.00000000000000026e-116

   1. Initial program 39.4%

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

      1. associate-/l* 39.9%

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

   3. Simplified 39.9%

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

   4. Taylor expanded in t around -inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. div-sub 74.8%

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

      4. *-commutative 74.8%

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

      5. div-sub 75.5%

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

      6. distribute-rgt-out-- 75.5%

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

   6. Simplified 75.5%

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

   if 3.00000000000000026e-116 < z < 1.05000000000000008e69

   1. Initial program 82.1%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

      1. associate-/l* 82.1%

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

      2. clear-num 82.0%

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

      3. inv-pow 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. unpow-1 82.0%

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

      2. associate-/r* 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in y around inf 75.8%

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

      1. *-commutative 75.8%

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

   10. Simplified 75.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-116}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z}}{y - x}}\\ \end{array} \]

Alternative 5: 46.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+130}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -6e+130)
     y
     (if (<= t -5e-218)
       t_1
       (if (<= t -7.8e-247)
         (* y (/ z a))
         (if (<= t 6.5e-254)
           t_1
           (if (<= t 6.5e-197) (/ y (/ a z)) (if (<= t 5.3e+136) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6e+130) {
		tmp = y;
	} else if (t <= -5e-218) {
		tmp = t_1;
	} else if (t <= -7.8e-247) {
		tmp = y * (z / a);
	} else if (t <= 6.5e-254) {
		tmp = t_1;
	} else if (t <= 6.5e-197) {
		tmp = y / (a / z);
	} else if (t <= 5.3e+136) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-6d+130)) then
        tmp = y
    else if (t <= (-5d-218)) then
        tmp = t_1
    else if (t <= (-7.8d-247)) then
        tmp = y * (z / a)
    else if (t <= 6.5d-254) then
        tmp = t_1
    else if (t <= 6.5d-197) then
        tmp = y / (a / z)
    else if (t <= 5.3d+136) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -6e+130) {
		tmp = y;
	} else if (t <= -5e-218) {
		tmp = t_1;
	} else if (t <= -7.8e-247) {
		tmp = y * (z / a);
	} else if (t <= 6.5e-254) {
		tmp = t_1;
	} else if (t <= 6.5e-197) {
		tmp = y / (a / z);
	} else if (t <= 5.3e+136) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -6e+130:
		tmp = y
	elif t <= -5e-218:
		tmp = t_1
	elif t <= -7.8e-247:
		tmp = y * (z / a)
	elif t <= 6.5e-254:
		tmp = t_1
	elif t <= 6.5e-197:
		tmp = y / (a / z)
	elif t <= 5.3e+136:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -6e+130)
		tmp = y;
	elseif (t <= -5e-218)
		tmp = t_1;
	elseif (t <= -7.8e-247)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 6.5e-254)
		tmp = t_1;
	elseif (t <= 6.5e-197)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.3e+136)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -6e+130)
		tmp = y;
	elseif (t <= -5e-218)
		tmp = t_1;
	elseif (t <= -7.8e-247)
		tmp = y * (z / a);
	elseif (t <= 6.5e-254)
		tmp = t_1;
	elseif (t <= 6.5e-197)
		tmp = y / (a / z);
	elseif (t <= 5.3e+136)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+130], y, If[LessEqual[t, -5e-218], t$95$1, If[LessEqual[t, -7.8e-247], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-254], t$95$1, If[LessEqual[t, 6.5e-197], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+136], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.9999999999999999e130 or 5.3000000000000003e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -5.9999999999999999e130 < t < -5.00000000000000041e-218 or -7.8000000000000006e-247 < t < 6.5e-254 or 6.4999999999999995e-197 < t < 5.3000000000000003e136

   1. Initial program 86.0%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 64.5%

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

   5. Taylor expanded in x around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

   7. Simplified 51.0%

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

   if -5.00000000000000041e-218 < t < -7.8000000000000006e-247

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 85.5%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

      2. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 99.8%

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

   if 6.5e-254 < t < 6.4999999999999995e-197

   1. Initial program 83.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 99.9%

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

   5. Taylor expanded in y around inf 82.3%

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

      1. div-sub 82.3%

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

      2. *-commutative 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in z around inf 56.8%

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

      1. associate-/l* 73.6%

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

   10. Simplified 73.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+130}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.22e+131)
     y
     (if (<= t -2.6e-222)
       t_1
       (if (<= t -7.8e-247)
         (* y (/ z a))
         (if (<= t 8.5e-255)
           t_1
           (if (<= t 2.15e-197)
             (* y (/ (- z t) a))
             (if (<= t 5.2e+136) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.22e+131) {
		tmp = y;
	} else if (t <= -2.6e-222) {
		tmp = t_1;
	} else if (t <= -7.8e-247) {
		tmp = y * (z / a);
	} else if (t <= 8.5e-255) {
		tmp = t_1;
	} else if (t <= 2.15e-197) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5.2e+136) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.22d+131)) then
        tmp = y
    else if (t <= (-2.6d-222)) then
        tmp = t_1
    else if (t <= (-7.8d-247)) then
        tmp = y * (z / a)
    else if (t <= 8.5d-255) then
        tmp = t_1
    else if (t <= 2.15d-197) then
        tmp = y * ((z - t) / a)
    else if (t <= 5.2d+136) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.22e+131) {
		tmp = y;
	} else if (t <= -2.6e-222) {
		tmp = t_1;
	} else if (t <= -7.8e-247) {
		tmp = y * (z / a);
	} else if (t <= 8.5e-255) {
		tmp = t_1;
	} else if (t <= 2.15e-197) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5.2e+136) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.22e+131:
		tmp = y
	elif t <= -2.6e-222:
		tmp = t_1
	elif t <= -7.8e-247:
		tmp = y * (z / a)
	elif t <= 8.5e-255:
		tmp = t_1
	elif t <= 2.15e-197:
		tmp = y * ((z - t) / a)
	elif t <= 5.2e+136:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.22e+131)
		tmp = y;
	elseif (t <= -2.6e-222)
		tmp = t_1;
	elseif (t <= -7.8e-247)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 8.5e-255)
		tmp = t_1;
	elseif (t <= 2.15e-197)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 5.2e+136)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.22e+131)
		tmp = y;
	elseif (t <= -2.6e-222)
		tmp = t_1;
	elseif (t <= -7.8e-247)
		tmp = y * (z / a);
	elseif (t <= 8.5e-255)
		tmp = t_1;
	elseif (t <= 2.15e-197)
		tmp = y * ((z - t) / a);
	elseif (t <= 5.2e+136)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+131], y, If[LessEqual[t, -2.6e-222], t$95$1, If[LessEqual[t, -7.8e-247], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-255], t$95$1, If[LessEqual[t, 2.15e-197], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+136], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.22e131 or 5.2000000000000003e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -1.22e131 < t < -2.5999999999999998e-222 or -7.8000000000000006e-247 < t < 8.49999999999999982e-255 or 2.15e-197 < t < 5.2000000000000003e136

   1. Initial program 86.0%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 64.5%

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

   5. Taylor expanded in x around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

   7. Simplified 51.0%

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

   if -2.5999999999999998e-222 < t < -7.8000000000000006e-247

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around inf 85.5%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

      2. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 99.8%

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

   if 8.49999999999999982e-255 < t < 2.15e-197

   1. Initial program 83.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 99.9%

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

   5. Taylor expanded in y around inf 82.3%

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

      1. div-sub 82.3%

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

      2. *-commutative 82.3%

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

   7. Simplified 82.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -2.75 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-190}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ (- y x) (/ a (- z t))))))
   (if (<= a -2.75e+25)
     t_2
     (if (<= a -2.1e-200)
       t_1
       (if (<= a 3.1e-190)
         (* (- y x) (/ z (- a t)))
         (if (<= a 4.2) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -2.75e+25) {
		tmp = t_2;
	} else if (a <= -2.1e-200) {
		tmp = t_1;
	} else if (a <= 3.1e-190) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((y - x) / (a / (z - t)))
    if (a <= (-2.75d+25)) then
        tmp = t_2
    else if (a <= (-2.1d-200)) then
        tmp = t_1
    else if (a <= 3.1d-190) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 4.2d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((y - x) / (a / (z - t)));
	double tmp;
	if (a <= -2.75e+25) {
		tmp = t_2;
	} else if (a <= -2.1e-200) {
		tmp = t_1;
	} else if (a <= 3.1e-190) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((y - x) / (a / (z - t)))
	tmp = 0
	if a <= -2.75e+25:
		tmp = t_2
	elif a <= -2.1e-200:
		tmp = t_1
	elif a <= 3.1e-190:
		tmp = (y - x) * (z / (a - t))
	elif a <= 4.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -2.75e+25)
		tmp = t_2;
	elseif (a <= -2.1e-200)
		tmp = t_1;
	elseif (a <= 3.1e-190)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 4.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((y - x) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -2.75e+25)
		tmp = t_2;
	elseif (a <= -2.1e-200)
		tmp = t_1;
	elseif (a <= 3.1e-190)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 4.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.75e+25], t$95$2, If[LessEqual[a, -2.1e-200], t$95$1, If[LessEqual[a, 3.1e-190], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.75000000000000009e25 or 4.20000000000000018 < a

   1. Initial program 73.4%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 80.5%

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

   if -2.75000000000000009e25 < a < -2.0999999999999999e-200 or 3.09999999999999993e-190 < a < 4.20000000000000018

   1. Initial program 74.9%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. associate-*r/ 72.0%

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

   6. Simplified 72.0%

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

   if -2.0999999999999999e-200 < a < 3.09999999999999993e-190

   1. Initial program 74.1%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. associate-/l* 74.1%

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

      2. clear-num 74.0%

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

      3. inv-pow 74.0%

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

   5. Applied egg-rr 74.0%

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

      1. unpow-1 74.0%

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

      2. associate-/r* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in z around -inf 67.2%

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

      1. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 75.0%

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

   12. Applied egg-rr 75.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-190}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4.2:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 8: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+128}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e+128)
   y
   (if (<= t -1.5e-116)
     (* x (- 1.0 (/ z a)))
     (if (<= t -1.46e-207)
       (/ z (/ a (- y x)))
       (if (<= t 1.15e-59)
         (+ x (/ y (/ a z)))
         (if (<= t 6.3e+136) (- x (/ (* y t) a)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+128) {
		tmp = y;
	} else if (t <= -1.5e-116) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= -1.46e-207) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.15e-59) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.3e+136) {
		tmp = x - ((y * t) / a);
	} 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 <= (-7.5d+128)) then
        tmp = y
    else if (t <= (-1.5d-116)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= (-1.46d-207)) then
        tmp = z / (a / (y - x))
    else if (t <= 1.15d-59) then
        tmp = x + (y / (a / z))
    else if (t <= 6.3d+136) then
        tmp = x - ((y * t) / a)
    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 <= -7.5e+128) {
		tmp = y;
	} else if (t <= -1.5e-116) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= -1.46e-207) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.15e-59) {
		tmp = x + (y / (a / z));
	} else if (t <= 6.3e+136) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e+128:
		tmp = y
	elif t <= -1.5e-116:
		tmp = x * (1.0 - (z / a))
	elif t <= -1.46e-207:
		tmp = z / (a / (y - x))
	elif t <= 1.15e-59:
		tmp = x + (y / (a / z))
	elif t <= 6.3e+136:
		tmp = x - ((y * t) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e+128)
		tmp = y;
	elseif (t <= -1.5e-116)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= -1.46e-207)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 1.15e-59)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 6.3e+136)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.5e+128)
		tmp = y;
	elseif (t <= -1.5e-116)
		tmp = x * (1.0 - (z / a));
	elseif (t <= -1.46e-207)
		tmp = z / (a / (y - x));
	elseif (t <= 1.15e-59)
		tmp = x + (y / (a / z));
	elseif (t <= 6.3e+136)
		tmp = x - ((y * t) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e+128], y, If[LessEqual[t, -1.5e-116], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.46e-207], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-59], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.3e+136], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.50000000000000076e128 or 6.2999999999999997e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -7.50000000000000076e128 < t < -1.50000000000000013e-116

   1. Initial program 78.2%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around 0 47.9%

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

   5. Taylor expanded in x around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

   7. Simplified 45.4%

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

   if -1.50000000000000013e-116 < t < -1.46e-207

   1. Initial program 88.5%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. associate-/l* 88.5%

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

      2. clear-num 88.5%

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

      3. inv-pow 88.5%

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

   5. Applied egg-rr 88.5%

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

      1. unpow-1 88.5%

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

      2. associate-/r* 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in z around -inf 67.6%

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

      1. associate-/l* 67.7%

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

   10. Simplified 67.7%

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

   11. Taylor expanded in a around inf 67.7%

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

   if -1.46e-207 < t < 1.1499999999999999e-59

   1. Initial program 92.7%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around 0 83.0%

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

   5. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 70.5%

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

   7. Simplified 70.5%

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

   if 1.1499999999999999e-59 < t < 6.2999999999999997e136

   1. Initial program 80.6%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 60.1%

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

      1. fma-def 60.1%

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

      2. associate-*r/ 60.3%

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

      3. fma-def 60.3%

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

      4. neg-mul-1 60.3%

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

      5. +-commutative 60.3%

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

      6. unsub-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y around inf 59.6%

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

   8. Taylor expanded in t around 0 52.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+128}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-43} \lor \neg \left(t \leq 1.82 \cdot 10^{-31}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7e+128)
     t_1
     (if (<= t -2.1e+79)
       (* (- y x) (/ z (- a t)))
       (if (or (<= t -7.1e-43) (not (<= t 1.82e-31)))
         t_1
         (- x (/ (- x y) (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e+128) {
		tmp = t_1;
	} else if (t <= -2.1e+79) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -7.1e-43) || !(t <= 1.82e-31)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-7d+128)) then
        tmp = t_1
    else if (t <= (-2.1d+79)) then
        tmp = (y - x) * (z / (a - t))
    else if ((t <= (-7.1d-43)) .or. (.not. (t <= 1.82d-31))) then
        tmp = t_1
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e+128) {
		tmp = t_1;
	} else if (t <= -2.1e+79) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -7.1e-43) || !(t <= 1.82e-31)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7e+128:
		tmp = t_1
	elif t <= -2.1e+79:
		tmp = (y - x) * (z / (a - t))
	elif (t <= -7.1e-43) or not (t <= 1.82e-31):
		tmp = t_1
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -7e+128)
		tmp = t_1;
	elseif (t <= -2.1e+79)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif ((t <= -7.1e-43) || !(t <= 1.82e-31))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -7e+128)
		tmp = t_1;
	elseif (t <= -2.1e+79)
		tmp = (y - x) * (z / (a - t));
	elseif ((t <= -7.1e-43) || ~((t <= 1.82e-31)))
		tmp = t_1;
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+128], t$95$1, If[LessEqual[t, -2.1e+79], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -7.1e-43], N[Not[LessEqual[t, 1.82e-31]], $MachinePrecision]], t$95$1, N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999937e128 or -2.10000000000000008e79 < t < -7.10000000000000025e-43 or 1.8199999999999999e-31 < t

   1. Initial program 57.0%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. associate-*r/ 62.5%

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

   6. Simplified 62.5%

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

   if -6.99999999999999937e128 < t < -2.10000000000000008e79

   1. Initial program 52.8%

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

      1. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

      1. associate-/l* 52.8%

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

      2. clear-num 52.7%

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

      3. inv-pow 52.7%

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

   5. Applied egg-rr 52.7%

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

      1. unpow-1 52.7%

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

      2. associate-/r* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around -inf 41.6%

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

      1. associate-/l* 56.7%

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

   10. Simplified 56.7%

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

       1. associate-/r/ 64.6%

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

   12. Applied egg-rr 64.6%

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

   if -7.10000000000000025e-43 < t < 1.8199999999999999e-31

   1. Initial program 91.6%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 83.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-43} \lor \neg \left(t \leq 1.82 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43} \lor \neg \left(t \leq 4 \cdot 10^{-31}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -5e+129)
     t_1
     (if (<= t -1.55e+110)
       (* x (+ (/ (- t z) (- a t)) 1.0))
       (if (or (<= t -8.8e-43) (not (<= t 4e-31)))
         t_1
         (- x (/ (- x y) (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5e+129) {
		tmp = t_1;
	} else if (t <= -1.55e+110) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if ((t <= -8.8e-43) || !(t <= 4e-31)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-5d+129)) then
        tmp = t_1
    else if (t <= (-1.55d+110)) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if ((t <= (-8.8d-43)) .or. (.not. (t <= 4d-31))) then
        tmp = t_1
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5e+129) {
		tmp = t_1;
	} else if (t <= -1.55e+110) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if ((t <= -8.8e-43) || !(t <= 4e-31)) {
		tmp = t_1;
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -5e+129:
		tmp = t_1
	elif t <= -1.55e+110:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif (t <= -8.8e-43) or not (t <= 4e-31):
		tmp = t_1
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -5e+129)
		tmp = t_1;
	elseif (t <= -1.55e+110)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif ((t <= -8.8e-43) || !(t <= 4e-31))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -5e+129)
		tmp = t_1;
	elseif (t <= -1.55e+110)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif ((t <= -8.8e-43) || ~((t <= 4e-31)))
		tmp = t_1;
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+129], t$95$1, If[LessEqual[t, -1.55e+110], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -8.8e-43], N[Not[LessEqual[t, 4e-31]], $MachinePrecision]], t$95$1, N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000003e129 or -1.55000000000000009e110 < t < -8.79999999999999989e-43 or 4e-31 < t

   1. Initial program 56.4%

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

      1. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in x around 0 43.3%

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

      1. associate-*r/ 61.5%

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

   6. Simplified 61.5%

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

   if -5.0000000000000003e129 < t < -1.55000000000000009e110

   1. Initial program 62.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

   6. Simplified 99.4%

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

   if -8.79999999999999989e-43 < t < 4e-31

   1. Initial program 91.6%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 83.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43} \lor \neg \left(t \leq 4 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -7.9 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-192}:\\ \;\;\;\;\frac{z}{\frac{t - a}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -7.9e+24)
     t_2
     (if (<= a 8.8e-287)
       t_1
       (if (<= a 7.8e-192) (/ z (/ (- t a) x)) (if (<= a 9.5e+96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -7.9e+24) {
		tmp = t_2;
	} else if (a <= 8.8e-287) {
		tmp = t_1;
	} else if (a <= 7.8e-192) {
		tmp = z / ((t - a) / x);
	} else if (a <= 9.5e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-7.9d+24)) then
        tmp = t_2
    else if (a <= 8.8d-287) then
        tmp = t_1
    else if (a <= 7.8d-192) then
        tmp = z / ((t - a) / x)
    else if (a <= 9.5d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -7.9e+24) {
		tmp = t_2;
	} else if (a <= 8.8e-287) {
		tmp = t_1;
	} else if (a <= 7.8e-192) {
		tmp = z / ((t - a) / x);
	} else if (a <= 9.5e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -7.9e+24:
		tmp = t_2
	elif a <= 8.8e-287:
		tmp = t_1
	elif a <= 7.8e-192:
		tmp = z / ((t - a) / x)
	elif a <= 9.5e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -7.9e+24)
		tmp = t_2;
	elseif (a <= 8.8e-287)
		tmp = t_1;
	elseif (a <= 7.8e-192)
		tmp = Float64(z / Float64(Float64(t - a) / x));
	elseif (a <= 9.5e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -7.9e+24)
		tmp = t_2;
	elseif (a <= 8.8e-287)
		tmp = t_1;
	elseif (a <= 7.8e-192)
		tmp = z / ((t - a) / x);
	elseif (a <= 9.5e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.9e+24], t$95$2, If[LessEqual[a, 8.8e-287], t$95$1, If[LessEqual[a, 7.8e-192], N[(z / N[(N[(t - a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.8999999999999997e24 or 9.50000000000000089e96 < a

   1. Initial program 76.4%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 74.6%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   if -7.8999999999999997e24 < a < 8.8000000000000001e-287 or 7.8000000000000005e-192 < a < 9.50000000000000089e96

   1. Initial program 73.1%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 55.0%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   if 8.8000000000000001e-287 < a < 7.8000000000000005e-192

   1. Initial program 62.1%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

      1. associate-/l* 62.1%

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

      2. clear-num 62.0%

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

      3. inv-pow 62.0%

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

   5. Applied egg-rr 62.0%

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

      1. unpow-1 62.0%

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

      2. associate-/r* 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in z around -inf 61.6%

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

      1. associate-/l* 67.6%

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

   10. Simplified 67.6%

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

   11. Taylor expanded in y around 0 60.9%

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

       1. associate-*r/ 60.9%

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

       2. neg-mul-1 60.9%

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

   13. Simplified 60.9%

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

   14. Taylor expanded in a around 0 60.9%

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

       1. +-commutative 60.9%

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

       2. mul-1-neg 60.9%

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

       3. sub-neg 60.9%

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

       4. div-sub 60.9%

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

   16. Simplified 60.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.9 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-287}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-192}:\\ \;\;\;\;\frac{z}{\frac{t - a}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -6.8e+25)
     t_2
     (if (<= a 6.4e-287)
       t_1
       (if (<= a 3.2e-189)
         (* z (/ (- y x) (- a t)))
         (if (<= a 1.6e+96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -6.8e+25) {
		tmp = t_2;
	} else if (a <= 6.4e-287) {
		tmp = t_1;
	} else if (a <= 3.2e-189) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.6e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-6.8d+25)) then
        tmp = t_2
    else if (a <= 6.4d-287) then
        tmp = t_1
    else if (a <= 3.2d-189) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.6d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -6.8e+25) {
		tmp = t_2;
	} else if (a <= 6.4e-287) {
		tmp = t_1;
	} else if (a <= 3.2e-189) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.6e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -6.8e+25:
		tmp = t_2
	elif a <= 6.4e-287:
		tmp = t_1
	elif a <= 3.2e-189:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.6e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -6.8e+25)
		tmp = t_2;
	elseif (a <= 6.4e-287)
		tmp = t_1;
	elseif (a <= 3.2e-189)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.6e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -6.8e+25)
		tmp = t_2;
	elseif (a <= 6.4e-287)
		tmp = t_1;
	elseif (a <= 3.2e-189)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.6e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+25], t$95$2, If[LessEqual[a, 6.4e-287], t$95$1, If[LessEqual[a, 3.2e-189], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.79999999999999967e25 or 1.60000000000000003e96 < a

   1. Initial program 76.4%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 74.6%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   if -6.79999999999999967e25 < a < 6.40000000000000037e-287 or 3.2000000000000001e-189 < a < 1.60000000000000003e96

   1. Initial program 73.1%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 55.0%

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

      1. associate-*r/ 68.6%

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

   6. Simplified 68.6%

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

   if 6.40000000000000037e-287 < a < 3.2000000000000001e-189

   1. Initial program 62.1%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in z around inf 67.6%

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

      1. div-sub 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-287}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 13: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -5.3e+25)
     t_2
     (if (<= a -3.6e-200)
       t_1
       (if (<= a 3.9e-191)
         (* (- y x) (/ z (- a t)))
         (if (<= a 4e+96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.3e+25) {
		tmp = t_2;
	} else if (a <= -3.6e-200) {
		tmp = t_1;
	} else if (a <= 3.9e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-5.3d+25)) then
        tmp = t_2
    else if (a <= (-3.6d-200)) then
        tmp = t_1
    else if (a <= 3.9d-191) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 4d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.3e+25) {
		tmp = t_2;
	} else if (a <= -3.6e-200) {
		tmp = t_1;
	} else if (a <= 3.9e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 4e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -5.3e+25:
		tmp = t_2
	elif a <= -3.6e-200:
		tmp = t_1
	elif a <= 3.9e-191:
		tmp = (y - x) * (z / (a - t))
	elif a <= 4e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -5.3e+25)
		tmp = t_2;
	elseif (a <= -3.6e-200)
		tmp = t_1;
	elseif (a <= 3.9e-191)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 4e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -5.3e+25)
		tmp = t_2;
	elseif (a <= -3.6e-200)
		tmp = t_1;
	elseif (a <= 3.9e-191)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 4e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e+25], t$95$2, If[LessEqual[a, -3.6e-200], t$95$1, If[LessEqual[a, 3.9e-191], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.29999999999999986e25 or 4.0000000000000002e96 < a

   1. Initial program 76.4%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 74.6%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   if -5.29999999999999986e25 < a < -3.6000000000000002e-200 or 3.8999999999999999e-191 < a < 4.0000000000000002e96

   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* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around 0 54.8%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if -3.6000000000000002e-200 < a < 3.8999999999999999e-191

   1. Initial program 74.1%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. associate-/l* 74.1%

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

      2. clear-num 74.0%

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

      3. inv-pow 74.0%

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

   5. Applied egg-rr 74.0%

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

      1. unpow-1 74.0%

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

      2. associate-/r* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in z around -inf 67.2%

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

      1. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 75.0%

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

   12. Applied egg-rr 75.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 14: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ z (/ a (- y x))))))
   (if (<= a -3.7e+25)
     t_2
     (if (<= a -1.26e-198)
       t_1
       (if (<= a 1.85e-191)
         (* (- y x) (/ z (- a t)))
         (if (<= a 3.6e+48) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -3.7e+25) {
		tmp = t_2;
	} else if (a <= -1.26e-198) {
		tmp = t_1;
	} else if (a <= 1.85e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 3.6e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (z / (a / (y - x)))
    if (a <= (-3.7d+25)) then
        tmp = t_2
    else if (a <= (-1.26d-198)) then
        tmp = t_1
    else if (a <= 1.85d-191) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 3.6d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z / (a / (y - x)));
	double tmp;
	if (a <= -3.7e+25) {
		tmp = t_2;
	} else if (a <= -1.26e-198) {
		tmp = t_1;
	} else if (a <= 1.85e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 3.6e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (z / (a / (y - x)))
	tmp = 0
	if a <= -3.7e+25:
		tmp = t_2
	elif a <= -1.26e-198:
		tmp = t_1
	elif a <= 1.85e-191:
		tmp = (y - x) * (z / (a - t))
	elif a <= 3.6e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -3.7e+25)
		tmp = t_2;
	elseif (a <= -1.26e-198)
		tmp = t_1;
	elseif (a <= 1.85e-191)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 3.6e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (z / (a / (y - x)));
	tmp = 0.0;
	if (a <= -3.7e+25)
		tmp = t_2;
	elseif (a <= -1.26e-198)
		tmp = t_1;
	elseif (a <= 1.85e-191)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 3.6e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+25], t$95$2, If[LessEqual[a, -1.26e-198], t$95$1, If[LessEqual[a, 1.85e-191], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6999999999999999e25 or 3.59999999999999983e48 < a

   1. Initial program 73.8%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

   if -3.6999999999999999e25 < a < -1.25999999999999992e-198 or 1.8499999999999998e-191 < a < 3.59999999999999983e48

   1. Initial program 74.2%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 60.4%

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

      1. associate-*r/ 71.3%

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

   6. Simplified 71.3%

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

   if -1.25999999999999992e-198 < a < 1.8499999999999998e-191

   1. Initial program 74.1%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. associate-/l* 74.1%

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

      2. clear-num 74.0%

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

      3. inv-pow 74.0%

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

   5. Applied egg-rr 74.0%

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

      1. unpow-1 74.0%

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

      2. associate-/r* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in z around -inf 67.2%

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

      1. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 75.0%

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

   12. Applied egg-rr 75.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 15: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -2.02 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -2.02e+24)
     (+ x (/ z (/ a (- y x))))
     (if (<= a -3.9e-199)
       t_1
       (if (<= a 3.5e-191)
         (* (- y x) (/ z (- a t)))
         (if (<= a 1.85e+96) t_1 (- x (/ (* y (- t z)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -2.02e+24) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -3.9e-199) {
		tmp = t_1;
	} else if (a <= 3.5e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.85e+96) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-2.02d+24)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-3.9d-199)) then
        tmp = t_1
    else if (a <= 3.5d-191) then
        tmp = (y - x) * (z / (a - t))
    else if (a <= 1.85d+96) then
        tmp = t_1
    else
        tmp = 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 t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -2.02e+24) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -3.9e-199) {
		tmp = t_1;
	} else if (a <= 3.5e-191) {
		tmp = (y - x) * (z / (a - t));
	} else if (a <= 1.85e+96) {
		tmp = t_1;
	} else {
		tmp = x - ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -2.02e+24:
		tmp = x + (z / (a / (y - x)))
	elif a <= -3.9e-199:
		tmp = t_1
	elif a <= 3.5e-191:
		tmp = (y - x) * (z / (a - t))
	elif a <= 1.85e+96:
		tmp = t_1
	else:
		tmp = x - ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -2.02e+24)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -3.9e-199)
		tmp = t_1;
	elseif (a <= 3.5e-191)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif (a <= 1.85e+96)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -2.02e+24)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -3.9e-199)
		tmp = t_1;
	elseif (a <= 3.5e-191)
		tmp = (y - x) * (z / (a - t));
	elseif (a <= 1.85e+96)
		tmp = t_1;
	else
		tmp = x - ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.02e+24], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e-199], t$95$1, If[LessEqual[a, 3.5e-191], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+96], t$95$1, N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.0199999999999999e24

   1. Initial program 67.7%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

   if -2.0199999999999999e24 < a < -3.9000000000000001e-199 or 3.50000000000000007e-191 < a < 1.84999999999999996e96

   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* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around 0 54.8%

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

      1. associate-*r/ 69.3%

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

   6. Simplified 69.3%

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

   if -3.9000000000000001e-199 < a < 3.50000000000000007e-191

   1. Initial program 74.1%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. associate-/l* 74.1%

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

      2. clear-num 74.0%

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

      3. inv-pow 74.0%

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

   5. Applied egg-rr 74.0%

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

      1. unpow-1 74.0%

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

      2. associate-/r* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in z around -inf 67.2%

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

      1. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 75.0%

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

   12. Applied egg-rr 75.0%

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

   if 1.84999999999999996e96 < a

   1. Initial program 88.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in a around inf 90.4%

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

   5. Taylor expanded in x around 0 81.0%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.02 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-191}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]

Alternative 16: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -1.55e-31)
     y
     (if (<= t -6.3e-115)
       x
       (if (<= t -3.8e-247)
         t_1
         (if (<= t 1.25e-258)
           x
           (if (<= t 3.4e-143) t_1 (if (<= t 5.2e+136) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -1.55e-31) {
		tmp = y;
	} else if (t <= -6.3e-115) {
		tmp = x;
	} else if (t <= -3.8e-247) {
		tmp = t_1;
	} else if (t <= 1.25e-258) {
		tmp = x;
	} else if (t <= 3.4e-143) {
		tmp = t_1;
	} else if (t <= 5.2e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (t <= (-1.55d-31)) then
        tmp = y
    else if (t <= (-6.3d-115)) then
        tmp = x
    else if (t <= (-3.8d-247)) then
        tmp = t_1
    else if (t <= 1.25d-258) then
        tmp = x
    else if (t <= 3.4d-143) then
        tmp = t_1
    else if (t <= 5.2d+136) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -1.55e-31) {
		tmp = y;
	} else if (t <= -6.3e-115) {
		tmp = x;
	} else if (t <= -3.8e-247) {
		tmp = t_1;
	} else if (t <= 1.25e-258) {
		tmp = x;
	} else if (t <= 3.4e-143) {
		tmp = t_1;
	} else if (t <= 5.2e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -1.55e-31:
		tmp = y
	elif t <= -6.3e-115:
		tmp = x
	elif t <= -3.8e-247:
		tmp = t_1
	elif t <= 1.25e-258:
		tmp = x
	elif t <= 3.4e-143:
		tmp = t_1
	elif t <= 5.2e+136:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -1.55e-31)
		tmp = y;
	elseif (t <= -6.3e-115)
		tmp = x;
	elseif (t <= -3.8e-247)
		tmp = t_1;
	elseif (t <= 1.25e-258)
		tmp = x;
	elseif (t <= 3.4e-143)
		tmp = t_1;
	elseif (t <= 5.2e+136)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -1.55e-31)
		tmp = y;
	elseif (t <= -6.3e-115)
		tmp = x;
	elseif (t <= -3.8e-247)
		tmp = t_1;
	elseif (t <= 1.25e-258)
		tmp = x;
	elseif (t <= 3.4e-143)
		tmp = t_1;
	elseif (t <= 5.2e+136)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-31], y, If[LessEqual[t, -6.3e-115], x, If[LessEqual[t, -3.8e-247], t$95$1, If[LessEqual[t, 1.25e-258], x, If[LessEqual[t, 3.4e-143], t$95$1, If[LessEqual[t, 5.2e+136], x, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e-31 or 5.2000000000000003e136 < t

   1. Initial program 50.4%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around inf 40.2%

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

   if -1.55e-31 < t < -6.2999999999999996e-115 or -3.79999999999999988e-247 < t < 1.25e-258 or 3.39999999999999983e-143 < t < 5.2000000000000003e136

   1. Initial program 90.2%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in a around inf 44.6%

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

   if -6.2999999999999996e-115 < t < -3.79999999999999988e-247 or 1.25e-258 < t < 3.39999999999999983e-143

   1. Initial program 89.0%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 88.9%

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

   5. Taylor expanded in y around inf 57.5%

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

      1. div-sub 57.5%

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

      2. *-commutative 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in z around inf 52.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e-32)
   y
   (if (<= t -1.5e-116)
     x
     (if (<= t -6.5e-247)
       (/ y (/ a z))
       (if (<= t 4.8e-258)
         x
         (if (<= t 2e-147) (* y (/ z a)) (if (<= t 4.6e+136) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e-32) {
		tmp = y;
	} else if (t <= -1.5e-116) {
		tmp = x;
	} else if (t <= -6.5e-247) {
		tmp = y / (a / z);
	} else if (t <= 4.8e-258) {
		tmp = x;
	} else if (t <= 2e-147) {
		tmp = y * (z / a);
	} else if (t <= 4.6e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.8d-32)) then
        tmp = y
    else if (t <= (-1.5d-116)) then
        tmp = x
    else if (t <= (-6.5d-247)) then
        tmp = y / (a / z)
    else if (t <= 4.8d-258) then
        tmp = x
    else if (t <= 2d-147) then
        tmp = y * (z / a)
    else if (t <= 4.6d+136) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e-32) {
		tmp = y;
	} else if (t <= -1.5e-116) {
		tmp = x;
	} else if (t <= -6.5e-247) {
		tmp = y / (a / z);
	} else if (t <= 4.8e-258) {
		tmp = x;
	} else if (t <= 2e-147) {
		tmp = y * (z / a);
	} else if (t <= 4.6e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e-32:
		tmp = y
	elif t <= -1.5e-116:
		tmp = x
	elif t <= -6.5e-247:
		tmp = y / (a / z)
	elif t <= 4.8e-258:
		tmp = x
	elif t <= 2e-147:
		tmp = y * (z / a)
	elif t <= 4.6e+136:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e-32)
		tmp = y;
	elseif (t <= -1.5e-116)
		tmp = x;
	elseif (t <= -6.5e-247)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 4.8e-258)
		tmp = x;
	elseif (t <= 2e-147)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4.6e+136)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.8e-32)
		tmp = y;
	elseif (t <= -1.5e-116)
		tmp = x;
	elseif (t <= -6.5e-247)
		tmp = y / (a / z);
	elseif (t <= 4.8e-258)
		tmp = x;
	elseif (t <= 2e-147)
		tmp = y * (z / a);
	elseif (t <= 4.6e+136)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e-32], y, If[LessEqual[t, -1.5e-116], x, If[LessEqual[t, -6.5e-247], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-258], x, If[LessEqual[t, 2e-147], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+136], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.7999999999999996e-32 or 4.6e136 < t

   1. Initial program 50.4%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around inf 40.2%

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

   if -9.7999999999999996e-32 < t < -1.50000000000000013e-116 or -6.4999999999999996e-247 < t < 4.8000000000000003e-258 or 1.9999999999999999e-147 < t < 4.6e136

   1. Initial program 90.2%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in a around inf 44.6%

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

   if -1.50000000000000013e-116 < t < -6.4999999999999996e-247

   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* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in a around inf 86.6%

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

   5. Taylor expanded in y around inf 56.6%

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

      1. div-sub 56.6%

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

      2. *-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in z around inf 50.0%

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

      1. associate-/l* 53.3%

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

   10. Simplified 53.3%

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

   if 4.8000000000000003e-258 < t < 1.9999999999999999e-147

   1. Initial program 88.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 91.8%

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

   5. Taylor expanded in y around inf 58.8%

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

      1. div-sub 58.8%

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

      2. *-commutative 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 50.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+124}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.1e+124)
   y
   (if (<= t -8.8e-43)
     (/ z (/ (- t) (- y x)))
     (if (<= t 9e-60)
       (+ x (/ y (/ a z)))
       (if (<= t 4.6e+136) (- x (/ (* y t) a)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e+124) {
		tmp = y;
	} else if (t <= -8.8e-43) {
		tmp = z / (-t / (y - x));
	} else if (t <= 9e-60) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.6e+136) {
		tmp = x - ((y * t) / a);
	} 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 <= (-4.1d+124)) then
        tmp = y
    else if (t <= (-8.8d-43)) then
        tmp = z / (-t / (y - x))
    else if (t <= 9d-60) then
        tmp = x + (y / (a / z))
    else if (t <= 4.6d+136) then
        tmp = x - ((y * t) / a)
    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 <= -4.1e+124) {
		tmp = y;
	} else if (t <= -8.8e-43) {
		tmp = z / (-t / (y - x));
	} else if (t <= 9e-60) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.6e+136) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.1e+124:
		tmp = y
	elif t <= -8.8e-43:
		tmp = z / (-t / (y - x))
	elif t <= 9e-60:
		tmp = x + (y / (a / z))
	elif t <= 4.6e+136:
		tmp = x - ((y * t) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.1e+124)
		tmp = y;
	elseif (t <= -8.8e-43)
		tmp = Float64(z / Float64(Float64(-t) / Float64(y - x)));
	elseif (t <= 9e-60)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.6e+136)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.1e+124)
		tmp = y;
	elseif (t <= -8.8e-43)
		tmp = z / (-t / (y - x));
	elseif (t <= 9e-60)
		tmp = x + (y / (a / z));
	elseif (t <= 4.6e+136)
		tmp = x - ((y * t) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.1e+124], y, If[LessEqual[t, -8.8e-43], N[(z / N[((-t) / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-60], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+136], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.10000000000000001e124 or 4.6e136 < t

   1. Initial program 34.9%

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

      1. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around inf 53.0%

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

   if -4.10000000000000001e124 < t < -8.79999999999999989e-43

   1. Initial program 75.5%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. associate-/l* 75.5%

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

      2. clear-num 75.4%

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

      3. inv-pow 75.4%

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

   5. Applied egg-rr 75.4%

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

      1. unpow-1 75.4%

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

      2. associate-/r* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in z around -inf 42.4%

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

      1. associate-/l* 57.7%

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

   10. Simplified 57.7%

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

   11. Taylor expanded in a around 0 48.1%

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

       1. neg-mul-1 48.1%

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

       2. distribute-neg-frac 48.1%

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

   13. Simplified 48.1%

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

   if -8.79999999999999989e-43 < t < 9.00000000000000001e-60

   1. Initial program 92.0%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 83.9%

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

   5. Taylor expanded in y around inf 64.4%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if 9.00000000000000001e-60 < t < 4.6e136

   1. Initial program 80.6%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 60.1%

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

      1. fma-def 60.1%

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

      2. associate-*r/ 60.3%

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

      3. fma-def 60.3%

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

      4. neg-mul-1 60.3%

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

      5. +-commutative 60.3%

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

      6. unsub-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y around inf 59.6%

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

   8. Taylor expanded in t around 0 52.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+124}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.19 \lor \neg \left(a \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.19) (not (<= a 6.5e-63)))
   (+ x (/ (- y x) (/ a (- z t))))
   (- y (/ (* (- x y) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.19) || !(a <= 6.5e-63)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.19d0)) .or. (.not. (a <= 6.5d-63))) then
        tmp = x + ((y - x) / (a / (z - t)))
    else
        tmp = y - (((x - y) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.19) || !(a <= 6.5e-63)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.19) or not (a <= 6.5e-63):
		tmp = x + ((y - x) / (a / (z - t)))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.19) || !(a <= 6.5e-63))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.19) || ~((a <= 6.5e-63)))
		tmp = x + ((y - x) / (a / (z - t)));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.19], N[Not[LessEqual[a, 6.5e-63]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.19 or 6.4999999999999998e-63 < a

   1. Initial program 74.0%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 77.5%

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

   if -0.19 < a < 6.4999999999999998e-63

   1. Initial program 73.8%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in t around -inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. div-sub 72.4%

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

      4. *-commutative 72.4%

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

      5. div-sub 73.4%

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

      6. distribute-rgt-out-- 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.19 \lor \neg \left(a \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 20: 53.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a - t}{t}}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ (- a t) t))))
   (if (<= t -1.7e+127)
     t_1
     (if (<= t -8.8e-43)
       (/ z (/ (- t) (- y x)))
       (if (<= t 5.5e-31) (+ x (/ y (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a - t) / t);
	double tmp;
	if (t <= -1.7e+127) {
		tmp = t_1;
	} else if (t <= -8.8e-43) {
		tmp = z / (-t / (y - x));
	} else if (t <= 5.5e-31) {
		tmp = x + (y / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y / ((a - t) / t)
    if (t <= (-1.7d+127)) then
        tmp = t_1
    else if (t <= (-8.8d-43)) then
        tmp = z / (-t / (y - x))
    else if (t <= 5.5d-31) then
        tmp = x + (y / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a - t) / t);
	double tmp;
	if (t <= -1.7e+127) {
		tmp = t_1;
	} else if (t <= -8.8e-43) {
		tmp = z / (-t / (y - x));
	} else if (t <= 5.5e-31) {
		tmp = x + (y / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((a - t) / t)
	tmp = 0
	if t <= -1.7e+127:
		tmp = t_1
	elif t <= -8.8e-43:
		tmp = z / (-t / (y - x))
	elif t <= 5.5e-31:
		tmp = x + (y / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(a - t) / t))
	tmp = 0.0
	if (t <= -1.7e+127)
		tmp = t_1;
	elseif (t <= -8.8e-43)
		tmp = Float64(z / Float64(Float64(-t) / Float64(y - x)));
	elseif (t <= 5.5e-31)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((a - t) / t);
	tmp = 0.0;
	if (t <= -1.7e+127)
		tmp = t_1;
	elseif (t <= -8.8e-43)
		tmp = z / (-t / (y - x));
	elseif (t <= 5.5e-31)
		tmp = x + (y / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+127], t$95$1, If[LessEqual[t, -8.8e-43], N[(z / N[((-t) / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-31], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.69999999999999989e127 or 5.49999999999999958e-31 < t

   1. Initial program 48.3%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around 0 34.7%

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

      1. fma-def 34.7%

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

      2. associate-*r/ 51.4%

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

      3. fma-def 51.4%

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

      4. neg-mul-1 51.4%

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

      5. +-commutative 51.4%

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

      6. unsub-neg 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in x around 0 32.7%

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

      1. mul-1-neg 32.7%

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

      2. associate-/l* 51.7%

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

      3. distribute-neg-frac 51.7%

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

   9. Simplified 51.7%

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

   if -1.69999999999999989e127 < t < -8.79999999999999989e-43

   1. Initial program 73.8%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. associate-/l* 73.8%

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

      2. clear-num 73.7%

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

      3. inv-pow 73.7%

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

   5. Applied egg-rr 73.7%

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

      1. unpow-1 73.7%

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

      2. associate-/r* 89.1%

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

   7. Simplified 89.1%

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

   8. Taylor expanded in z around -inf 41.4%

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

      1. associate-/l* 56.4%

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

   10. Simplified 56.4%

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

   11. Taylor expanded in a around 0 47.1%

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

       1. neg-mul-1 47.1%

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

       2. distribute-neg-frac 47.1%

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

   13. Simplified 47.1%

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

   if -8.79999999999999989e-43 < t < 5.49999999999999958e-31

   1. Initial program 91.6%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 83.8%

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

   5. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{-y}{\frac{a - t}{t}}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a - t}{t}}\\ \end{array} \]

Alternative 21: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+128}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.6e+128)
   y
   (if (<= t 8e-60)
     (+ x (/ y (/ a z)))
     (if (<= t 8.4e+136) (- x (/ (* y t) a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.6e+128) {
		tmp = y;
	} else if (t <= 8e-60) {
		tmp = x + (y / (a / z));
	} else if (t <= 8.4e+136) {
		tmp = x - ((y * t) / a);
	} 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 <= (-9.6d+128)) then
        tmp = y
    else if (t <= 8d-60) then
        tmp = x + (y / (a / z))
    else if (t <= 8.4d+136) then
        tmp = x - ((y * t) / a)
    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 <= -9.6e+128) {
		tmp = y;
	} else if (t <= 8e-60) {
		tmp = x + (y / (a / z));
	} else if (t <= 8.4e+136) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.6e+128:
		tmp = y
	elif t <= 8e-60:
		tmp = x + (y / (a / z))
	elif t <= 8.4e+136:
		tmp = x - ((y * t) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.6e+128)
		tmp = y;
	elseif (t <= 8e-60)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 8.4e+136)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.6e+128)
		tmp = y;
	elseif (t <= 8e-60)
		tmp = x + (y / (a / z));
	elseif (t <= 8.4e+136)
		tmp = x - ((y * t) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.6e+128], y, If[LessEqual[t, 8e-60], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+136], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.6000000000000007e128 or 8.3999999999999996e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -9.6000000000000007e128 < t < 7.9999999999999998e-60

   1. Initial program 87.4%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around 0 71.4%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if 7.9999999999999998e-60 < t < 8.3999999999999996e136

   1. Initial program 80.6%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 60.1%

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

      1. fma-def 60.1%

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

      2. associate-*r/ 60.3%

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

      3. fma-def 60.3%

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

      4. neg-mul-1 60.3%

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

      5. +-commutative 60.3%

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

      6. unsub-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y around inf 59.6%

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

   8. Taylor expanded in t around 0 52.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+128}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+131) y (if (<= t 4.6e+136) (+ x (* z (/ y a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+131) {
		tmp = y;
	} else if (t <= 4.6e+136) {
		tmp = x + (z * (y / a));
	} 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 <= (-1.22d+131)) then
        tmp = y
    else if (t <= 4.6d+136) then
        tmp = x + (z * (y / a))
    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 <= -1.22e+131) {
		tmp = y;
	} else if (t <= 4.6e+136) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e+131:
		tmp = y
	elif t <= 4.6e+136:
		tmp = x + (z * (y / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+131)
		tmp = y;
	elseif (t <= 4.6e+136)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e+131)
		tmp = y;
	elseif (t <= 4.6e+136)
		tmp = x + (z * (y / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+131], y, If[LessEqual[t, 4.6e+136], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22e131 or 4.6e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -1.22e131 < t < 4.6e136

   1. Initial program 86.4%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around 0 66.8%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. associate-/l* 55.7%

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

      2. associate-/r/ 53.4%

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

   7. Simplified 53.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+136}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 52.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.32e+132) y (if (<= t 7.5e+136) (+ x (/ y (/ a z))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+132) {
		tmp = y;
	} else if (t <= 7.5e+136) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.32d+132)) then
        tmp = y
    else if (t <= 7.5d+136) then
        tmp = x + (y / (a / z))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.32e+132) {
		tmp = y;
	} else if (t <= 7.5e+136) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.32e+132:
		tmp = y
	elif t <= 7.5e+136:
		tmp = x + (y / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.32e+132)
		tmp = y;
	elseif (t <= 7.5e+136)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.32e+132)
		tmp = y;
	elseif (t <= 7.5e+136)
		tmp = x + (y / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.32e+132], y, If[LessEqual[t, 7.5e+136], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3199999999999999e132 or 7.5000000000000002e136 < t

   1. Initial program 34.3%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -1.3199999999999999e132 < t < 7.5000000000000002e136

   1. Initial program 86.4%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around 0 66.8%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. associate-/l* 55.7%

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

   7. Simplified 55.7%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 24: 37.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e-33) y (if (<= t 5.2e+136) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e-33) {
		tmp = y;
	} else if (t <= 5.2e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.8d-33)) then
        tmp = y
    else if (t <= 5.2d+136) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e-33) {
		tmp = y;
	} else if (t <= 5.2e+136) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e-33:
		tmp = y
	elif t <= 5.2e+136:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e-33)
		tmp = y;
	elseif (t <= 5.2e+136)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e-33)
		tmp = y;
	elseif (t <= 5.2e+136)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e-33], y, If[LessEqual[t, 5.2e+136], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000005e-33 or 5.2000000000000003e136 < t

   1. Initial program 50.4%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around inf 40.2%

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

   if -5.80000000000000005e-33 < t < 5.2000000000000003e136

   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* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in a around inf 36.8%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25: 24.7% 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 74.0%

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

   1. associate-/l* 90.1%

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

3. Simplified 90.1%

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

4. Taylor expanded in a around inf 27.9%

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

5. Final simplification 27.9%

   \[\leadsto x \]

Developer target: 86.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023230 
(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))))