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

Percentage Accurate: 67.6% → 89.9%

Time: 16.3s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-230} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-230) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (+ (* (- y x) a) (* z (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-230) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-230) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-230], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-230 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 89.0%

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

      3. fma-define 89.0%

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

   3. Simplified 89.0%

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

   if -1.00000000000000005e-230 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in t around -inf 99.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-230} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- z t) (- a t)))
     (if (<= t_1 -1e-230)
       t_1
       (if (<= t_1 0.0)
         (- y (* (/ x t) (- a z)))
         (if (<= t_1 1e+293) t_1 (+ y (* (/ (- y x) t) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - ((x / t) * (a - z));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - ((x / t) * (a - z));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z - t) / (a - t))
	elif t_1 <= -1e-230:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - ((x / t) * (a - z))
	elif t_1 <= 1e+293:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t_1 <= -1e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z - t) / (a - t));
	elseif (t_1 <= -1e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - ((x / t) * (a - z));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-230], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 30.3%

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

      1. +-commutative 30.3%

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

      2. associate-/l* 80.1%

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

      3. fma-define 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. unpow-1 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around inf 65.3%

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

       1. div-sub 65.3%

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

   11. Simplified 65.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-230 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999992e292

   1. Initial program 96.4%

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

   if -1.00000000000000005e-230 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. associate-/l* 89.0%

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

      8. associate-/l* 89.0%

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

      9. distribute-rgt-out-- 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac2 89.3%

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

   8. Simplified 89.3%

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

   if 9.9999999999999992e292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 31.9%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. associate--l+ 40.8%

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

      2. distribute-lft-out-- 40.8%

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

      3. div-sub 43.0%

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

      4. mul-1-neg 43.0%

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

      5. unsub-neg 43.0%

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

      6. div-sub 40.8%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 65.8%

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

      9. distribute-rgt-out-- 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{-1}{\frac{t}{\left(y - x\right) \cdot \left(z - a\right)}}\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- z t) (- a t)))
     (if (<= t_1 -1e-230)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ -1.0 (/ t (* (- y x) (- z a)))))
         (if (<= t_1 1e+293) t_1 (+ y (* (/ (- y x) t) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z - t) / (a - t))
	elif t_1 <= -1e-230:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))))
	elif t_1 <= 1e+293:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t_1 <= -1e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(-1.0 / Float64(t / Float64(Float64(y - x) * Float64(z - a)))));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z - t) / (a - t));
	elseif (t_1 <= -1e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-230], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(-1.0 / N[(t / N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 30.3%

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

      1. +-commutative 30.3%

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

      2. associate-/l* 80.1%

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

      3. fma-define 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. unpow-1 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around inf 65.3%

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

       1. div-sub 65.3%

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

   11. Simplified 65.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-230 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999992e292

   1. Initial program 96.4%

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

   if -1.00000000000000005e-230 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. associate-/l* 89.0%

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

      8. associate-/l* 89.0%

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

      9. distribute-rgt-out-- 89.3%

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

   5. Simplified 89.3%

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

      1. associate-*l/ 99.9%

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

      2. distribute-rgt-out-- 99.9%

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

      3. clear-num 99.7%

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

      4. distribute-rgt-out-- 99.7%

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

   7. Applied egg-rr 99.7%

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

   if 9.9999999999999992e292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 31.9%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. associate--l+ 40.8%

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

      2. distribute-lft-out-- 40.8%

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

      3. div-sub 43.0%

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

      4. mul-1-neg 43.0%

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

      5. unsub-neg 43.0%

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

      6. div-sub 40.8%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 65.8%

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

      9. distribute-rgt-out-- 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{-1}{\frac{t}{\left(y - x\right) \cdot \left(z - a\right)}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{-1}{\frac{t}{\left(y - x\right) \cdot \left(z - a\right)}}\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- z t) (- a t)))
     (if (<= t_1 -1e-230)
       (+ x (/ -1.0 (/ (- a t) (* (- y x) (- t z)))))
       (if (<= t_1 0.0)
         (+ y (/ -1.0 (/ t (* (- y x) (- z a)))))
         (if (<= t_1 1e+293) t_1 (+ y (* (/ (- y x) t) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else if (t_1 <= 0.0) {
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else if (t_1 <= 0.0) {
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z - t) / (a - t))
	elif t_1 <= -1e-230:
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))))
	elif t_1 <= 0.0:
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))))
	elif t_1 <= 1e+293:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t_1 <= -1e-230)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / Float64(Float64(y - x) * Float64(t - z)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(-1.0 / Float64(t / Float64(Float64(y - x) * Float64(z - a)))));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z - t) / (a - t));
	elseif (t_1 <= -1e-230)
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	elseif (t_1 <= 0.0)
		tmp = y + (-1.0 / (t / ((y - x) * (z - a))));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-230], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(-1.0 / N[(t / N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 30.3%

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

      1. +-commutative 30.3%

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

      2. associate-/l* 80.1%

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

      3. fma-define 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. unpow-1 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around inf 65.3%

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

       1. div-sub 65.3%

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

   11. Simplified 65.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-230

   1. Initial program 97.2%

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

      1. clear-num 97.3%

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

      2. inv-pow 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-/r* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

      2. associate-/l/ 97.3%

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

      3. *-commutative 97.3%

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

   6. Simplified 97.3%

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

   if -1.00000000000000005e-230 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. div-sub 99.9%

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

      7. associate-/l* 89.0%

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

      8. associate-/l* 89.0%

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

      9. distribute-rgt-out-- 89.3%

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

   5. Simplified 89.3%

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

      1. associate-*l/ 99.9%

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

      2. distribute-rgt-out-- 99.9%

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

      3. clear-num 99.7%

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

      4. distribute-rgt-out-- 99.7%

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

   7. Applied egg-rr 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999992e292

   1. Initial program 95.7%

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

   if 9.9999999999999992e292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 31.9%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. associate--l+ 40.8%

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

      2. distribute-lft-out-- 40.8%

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

      3. div-sub 43.0%

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

      4. mul-1-neg 43.0%

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

      5. unsub-neg 43.0%

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

      6. div-sub 40.8%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 65.8%

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

      9. distribute-rgt-out-- 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{-1}{\frac{t}{\left(y - x\right) \cdot \left(z - a\right)}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (- z t) (- a t)))
     (if (<= t_1 -1e-230)
       (+ x (/ -1.0 (/ (- a t) (* (- y x) (- t z)))))
       (if (<= t_1 0.0)
         (+ y (/ (+ (* (- y x) a) (* z (- x y))) t))
         (if (<= t_1 1e+293) t_1 (+ y (* (/ (- y x) t) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else if (t_1 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / (a - t));
	} else if (t_1 <= -1e-230) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else if (t_1 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (t_1 <= 1e+293) {
		tmp = t_1;
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((z - t) / (a - t))
	elif t_1 <= -1e-230:
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))))
	elif t_1 <= 0.0:
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
	elif t_1 <= 1e+293:
		tmp = t_1
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t_1 <= -1e-230)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / Float64(Float64(y - x) * Float64(t - z)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((z - t) / (a - t));
	elseif (t_1 <= -1e-230)
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	elseif (t_1 <= 0.0)
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	elseif (t_1 <= 1e+293)
		tmp = t_1;
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-230], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], t$95$1, N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 30.3%

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

      1. +-commutative 30.3%

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

      2. associate-/l* 80.1%

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

      3. fma-define 80.1%

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

   3. Simplified 80.1%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. unpow-1 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in y around inf 65.3%

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

       1. div-sub 65.3%

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

   11. Simplified 65.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-230

   1. Initial program 97.2%

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

      1. clear-num 97.3%

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

      2. inv-pow 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-/r* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

      2. associate-/l/ 97.3%

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

      3. *-commutative 97.3%

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

   6. Simplified 97.3%

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

   if -1.00000000000000005e-230 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in t around -inf 99.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999992e292

   1. Initial program 95.7%

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

   if 9.9999999999999992e292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 31.9%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. associate--l+ 40.8%

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

      2. distribute-lft-out-- 40.8%

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

      3. div-sub 43.0%

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

      4. mul-1-neg 43.0%

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

      5. unsub-neg 43.0%

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

      6. div-sub 40.8%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 65.8%

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

      9. distribute-rgt-out-- 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.2e+179)
     y
     (if (<= t -2.25e+92)
       (/ (* x (- z a)) t)
       (if (<= t -4.3e+86)
         y
         (if (<= t 1.15e-303)
           t_1
           (if (<= t 5.4e-281) (* y (/ z a)) (if (<= t 2.5e+40) 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 <= -7.2e+179) {
		tmp = y;
	} else if (t <= -2.25e+92) {
		tmp = (x * (z - a)) / t;
	} else if (t <= -4.3e+86) {
		tmp = y;
	} else if (t <= 1.15e-303) {
		tmp = t_1;
	} else if (t <= 5.4e-281) {
		tmp = y * (z / a);
	} else if (t <= 2.5e+40) {
		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 <= (-7.2d+179)) then
        tmp = y
    else if (t <= (-2.25d+92)) then
        tmp = (x * (z - a)) / t
    else if (t <= (-4.3d+86)) then
        tmp = y
    else if (t <= 1.15d-303) then
        tmp = t_1
    else if (t <= 5.4d-281) then
        tmp = y * (z / a)
    else if (t <= 2.5d+40) 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 <= -7.2e+179) {
		tmp = y;
	} else if (t <= -2.25e+92) {
		tmp = (x * (z - a)) / t;
	} else if (t <= -4.3e+86) {
		tmp = y;
	} else if (t <= 1.15e-303) {
		tmp = t_1;
	} else if (t <= 5.4e-281) {
		tmp = y * (z / a);
	} else if (t <= 2.5e+40) {
		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 <= -7.2e+179:
		tmp = y
	elif t <= -2.25e+92:
		tmp = (x * (z - a)) / t
	elif t <= -4.3e+86:
		tmp = y
	elif t <= 1.15e-303:
		tmp = t_1
	elif t <= 5.4e-281:
		tmp = y * (z / a)
	elif t <= 2.5e+40:
		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 <= -7.2e+179)
		tmp = y;
	elseif (t <= -2.25e+92)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	elseif (t <= -4.3e+86)
		tmp = y;
	elseif (t <= 1.15e-303)
		tmp = t_1;
	elseif (t <= 5.4e-281)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.5e+40)
		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 <= -7.2e+179)
		tmp = y;
	elseif (t <= -2.25e+92)
		tmp = (x * (z - a)) / t;
	elseif (t <= -4.3e+86)
		tmp = y;
	elseif (t <= 1.15e-303)
		tmp = t_1;
	elseif (t <= 5.4e-281)
		tmp = y * (z / a);
	elseif (t <= 2.5e+40)
		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, -7.2e+179], y, If[LessEqual[t, -2.25e+92], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -4.3e+86], y, If[LessEqual[t, 1.15e-303], t$95$1, If[LessEqual[t, 5.4e-281], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+40], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.1999999999999995e179 or -2.25e92 < t < -4.3000000000000002e86 or 2.50000000000000002e40 < t

   1. Initial program 41.8%

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

   3. Taylor expanded in t around inf 56.3%

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

   if -7.1999999999999995e179 < t < -2.25e92

   1. Initial program 52.0%

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

   3. Taylor expanded in x around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. unsub-neg 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in t around inf 34.8%

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

      1. associate-*r/ 34.8%

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

      2. associate-*r* 34.8%

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

      3. neg-mul-1 34.8%

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

      4. mul-1-neg 34.8%

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

      5. sub-neg 34.8%

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

   8. Simplified 34.8%

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

   9. Taylor expanded in a around 0 34.8%

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

       1. +-commutative 34.8%

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

       2. neg-mul-1 34.8%

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

       3. *-commutative 34.8%

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

       4. distribute-rgt-neg-in 34.8%

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

       5. mul-1-neg 34.8%

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

       6. distribute-lft-in 34.8%

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

       7. mul-1-neg 34.8%

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

       8. sub-neg 34.8%

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

   11. Simplified 34.8%

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

   if -4.3000000000000002e86 < t < 1.14999999999999998e-303 or 5.39999999999999979e-281 < t < 2.50000000000000002e40

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in t around 0 54.8%

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

   if 1.14999999999999998e-303 < t < 5.39999999999999979e-281

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around -inf 84.4%

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

   10. Taylor expanded in t around 0 69.7%

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

       1. associate-/l* 85.3%

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

   12. Simplified 85.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128} \lor \neg \left(a \leq 280\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= a -3e+18)
     t_1
     (if (<= a -1.25e-88)
       (- y (* (/ x t) (- a z)))
       (if (or (<= a -1.3e-128) (not (<= a 280.0)))
         t_1
         (+ y (* (/ z t) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -3e+18) {
		tmp = t_1;
	} else if (a <= -1.25e-88) {
		tmp = y - ((x / t) * (a - z));
	} else if ((a <= -1.3e-128) || !(a <= 280.0)) {
		tmp = t_1;
	} else {
		tmp = y + ((z / t) * (x - 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 + (y * ((z - t) / (a - t)))
    if (a <= (-3d+18)) then
        tmp = t_1
    else if (a <= (-1.25d-88)) then
        tmp = y - ((x / t) * (a - z))
    else if ((a <= (-1.3d-128)) .or. (.not. (a <= 280.0d0))) then
        tmp = t_1
    else
        tmp = y + ((z / t) * (x - 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 + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -3e+18) {
		tmp = t_1;
	} else if (a <= -1.25e-88) {
		tmp = y - ((x / t) * (a - z));
	} else if ((a <= -1.3e-128) || !(a <= 280.0)) {
		tmp = t_1;
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if a <= -3e+18:
		tmp = t_1
	elif a <= -1.25e-88:
		tmp = y - ((x / t) * (a - z))
	elif (a <= -1.3e-128) or not (a <= 280.0):
		tmp = t_1
	else:
		tmp = y + ((z / t) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a <= -3e+18)
		tmp = t_1;
	elseif (a <= -1.25e-88)
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	elseif ((a <= -1.3e-128) || !(a <= 280.0))
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a <= -3e+18)
		tmp = t_1;
	elseif (a <= -1.25e-88)
		tmp = y - ((x / t) * (a - z));
	elseif ((a <= -1.3e-128) || ~((a <= 280.0)))
		tmp = t_1;
	else
		tmp = y + ((z / t) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+18], t$95$1, If[LessEqual[a, -1.25e-88], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.3e-128], N[Not[LessEqual[a, 280.0]], $MachinePrecision]], t$95$1, N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3e18 or -1.25000000000000002e-88 < a < -1.2999999999999999e-128 or 280 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 70.0%

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

      1. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

   if -3e18 < a < -1.25000000000000002e-88

   1. Initial program 51.6%

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

   3. Taylor expanded in t around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. distribute-lft-out-- 74.7%

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

      3. div-sub 75.1%

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

      4. mul-1-neg 75.1%

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

      5. unsub-neg 75.1%

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

      6. div-sub 74.7%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 78.8%

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

      9. distribute-rgt-out-- 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around 0 75.1%

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

      1. neg-mul-1 75.1%

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

      2. distribute-neg-frac2 75.1%

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

   8. Simplified 75.1%

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

   if -1.2999999999999999e-128 < a < 280

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. distribute-lft-out-- 75.1%

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

      3. div-sub 77.2%

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

      4. mul-1-neg 77.2%

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

      5. unsub-neg 77.2%

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

      6. div-sub 75.1%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 70.9%

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

      9. distribute-rgt-out-- 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-88}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128} \lor \neg \left(a \leq 280\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-90}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 370:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= a -2.05e+18)
     t_1
     (if (<= a -9.2e-90)
       (- y (* (/ x t) (- a z)))
       (if (<= a -1.3e-128)
         (+ x (/ (* y (- z t)) (- a t)))
         (if (<= a 370.0) (+ y (* (/ z t) (- x y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -2.05e+18) {
		tmp = t_1;
	} else if (a <= -9.2e-90) {
		tmp = y - ((x / t) * (a - z));
	} else if (a <= -1.3e-128) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 370.0) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (a <= (-2.05d+18)) then
        tmp = t_1
    else if (a <= (-9.2d-90)) then
        tmp = y - ((x / t) * (a - z))
    else if (a <= (-1.3d-128)) then
        tmp = x + ((y * (z - t)) / (a - t))
    else if (a <= 370.0d0) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -2.05e+18) {
		tmp = t_1;
	} else if (a <= -9.2e-90) {
		tmp = y - ((x / t) * (a - z));
	} else if (a <= -1.3e-128) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 370.0) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if a <= -2.05e+18:
		tmp = t_1
	elif a <= -9.2e-90:
		tmp = y - ((x / t) * (a - z))
	elif a <= -1.3e-128:
		tmp = x + ((y * (z - t)) / (a - t))
	elif a <= 370.0:
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a <= -2.05e+18)
		tmp = t_1;
	elseif (a <= -9.2e-90)
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	elseif (a <= -1.3e-128)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	elseif (a <= 370.0)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a <= -2.05e+18)
		tmp = t_1;
	elseif (a <= -9.2e-90)
		tmp = y - ((x / t) * (a - z));
	elseif (a <= -1.3e-128)
		tmp = x + ((y * (z - t)) / (a - t));
	elseif (a <= 370.0)
		tmp = y + ((z / t) * (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e+18], t$95$1, If[LessEqual[a, -9.2e-90], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-128], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 370.0], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.05e18 or 370 < a

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 86.2%

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

   5. Simplified 86.2%

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

   if -2.05e18 < a < -9.1999999999999992e-90

   1. Initial program 51.6%

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

   3. Taylor expanded in t around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. distribute-lft-out-- 74.7%

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

      3. div-sub 75.1%

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

      4. mul-1-neg 75.1%

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

      5. unsub-neg 75.1%

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

      6. div-sub 74.7%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 78.8%

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

      9. distribute-rgt-out-- 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around 0 75.1%

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

      1. neg-mul-1 75.1%

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

      2. distribute-neg-frac2 75.1%

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

   8. Simplified 75.1%

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

   if -9.1999999999999992e-90 < a < -1.2999999999999999e-128

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -1.2999999999999999e-128 < a < 370

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. distribute-lft-out-- 75.1%

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

      3. div-sub 77.2%

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

      4. mul-1-neg 77.2%

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

      5. unsub-neg 77.2%

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

      6. div-sub 75.1%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 70.9%

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

      9. distribute-rgt-out-- 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-90}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 370:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-90}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 750:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= a -2.2e+52)
     t_1
     (if (<= a -4.2e-90)
       (+ y (* (/ (- y x) t) (- a z)))
       (if (<= a -1.12e-128)
         (+ x (/ (* y (- z t)) (- a t)))
         (if (<= a 750.0) (+ y (* (/ z t) (- x y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -2.2e+52) {
		tmp = t_1;
	} else if (a <= -4.2e-90) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (a <= -1.12e-128) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 750.0) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (a <= (-2.2d+52)) then
        tmp = t_1
    else if (a <= (-4.2d-90)) then
        tmp = y + (((y - x) / t) * (a - z))
    else if (a <= (-1.12d-128)) then
        tmp = x + ((y * (z - t)) / (a - t))
    else if (a <= 750.0d0) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -2.2e+52) {
		tmp = t_1;
	} else if (a <= -4.2e-90) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (a <= -1.12e-128) {
		tmp = x + ((y * (z - t)) / (a - t));
	} else if (a <= 750.0) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if a <= -2.2e+52:
		tmp = t_1
	elif a <= -4.2e-90:
		tmp = y + (((y - x) / t) * (a - z))
	elif a <= -1.12e-128:
		tmp = x + ((y * (z - t)) / (a - t))
	elif a <= 750.0:
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a <= -2.2e+52)
		tmp = t_1;
	elseif (a <= -4.2e-90)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (a <= -1.12e-128)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	elseif (a <= 750.0)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a <= -2.2e+52)
		tmp = t_1;
	elseif (a <= -4.2e-90)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (a <= -1.12e-128)
		tmp = x + ((y * (z - t)) / (a - t));
	elseif (a <= 750.0)
		tmp = y + ((z / t) * (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+52], t$95$1, If[LessEqual[a, -4.2e-90], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e-128], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 750.0], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2e52 or 750 < a

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

   if -2.2e52 < a < -4.1999999999999998e-90

   1. Initial program 59.7%

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

   3. Taylor expanded in t around inf 74.1%

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

      1. associate--l+ 74.1%

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

      2. distribute-lft-out-- 74.1%

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

      3. div-sub 74.4%

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

      4. mul-1-neg 74.4%

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

      5. unsub-neg 74.4%

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

      6. div-sub 74.1%

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

      7. associate-/l* 77.3%

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

      8. associate-/l* 77.2%

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

      9. distribute-rgt-out-- 77.5%

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

   5. Simplified 77.5%

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

   if -4.1999999999999998e-90 < a < -1.12e-128

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -1.12e-128 < a < 750

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. distribute-lft-out-- 75.1%

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

      3. div-sub 77.2%

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

      4. mul-1-neg 77.2%

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

      5. unsub-neg 77.2%

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

      6. div-sub 75.1%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 70.9%

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

      9. distribute-rgt-out-- 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-/l* 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-90}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;a \leq 750:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e+86)
   y
   (if (<= t -4e-234)
     x
     (if (<= t 2.9e-264)
       (* y (/ z a))
       (if (<= t 1.35e-67) (* x (+ 1.0 (/ t a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+86) {
		tmp = y;
	} else if (t <= -4e-234) {
		tmp = x;
	} else if (t <= 2.9e-264) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-67) {
		tmp = x * (1.0 + (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 <= (-9.8d+86)) then
        tmp = y
    else if (t <= (-4d-234)) then
        tmp = x
    else if (t <= 2.9d-264) then
        tmp = y * (z / a)
    else if (t <= 1.35d-67) then
        tmp = x * (1.0d0 + (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 <= -9.8e+86) {
		tmp = y;
	} else if (t <= -4e-234) {
		tmp = x;
	} else if (t <= 2.9e-264) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-67) {
		tmp = x * (1.0 + (t / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e+86:
		tmp = y
	elif t <= -4e-234:
		tmp = x
	elif t <= 2.9e-264:
		tmp = y * (z / a)
	elif t <= 1.35e-67:
		tmp = x * (1.0 + (t / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e+86)
		tmp = y;
	elseif (t <= -4e-234)
		tmp = x;
	elseif (t <= 2.9e-264)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.35e-67)
		tmp = Float64(x * Float64(1.0 + Float64(t / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.8e+86)
		tmp = y;
	elseif (t <= -4e-234)
		tmp = x;
	elseif (t <= 2.9e-264)
		tmp = y * (z / a);
	elseif (t <= 1.35e-67)
		tmp = x * (1.0 + (t / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e+86], y, If[LessEqual[t, -4e-234], x, If[LessEqual[t, 2.9e-264], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-67], N[(x * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.7999999999999999e86 or 1.35000000000000008e-67 < t

   1. Initial program 47.6%

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

   3. Taylor expanded in t around inf 46.2%

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

   if -9.7999999999999999e86 < t < -3.9999999999999998e-234

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 43.0%

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

   if -3.9999999999999998e-234 < t < 2.8999999999999999e-264

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-/l* 91.9%

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

      3. fma-define 91.9%

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

   3. Simplified 91.9%

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

      1. clear-num 91.8%

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

      2. inv-pow 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. unpow-1 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in y around -inf 49.3%

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

   10. Taylor expanded in t around 0 41.4%

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

       1. associate-/l* 50.0%

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

   12. Simplified 50.0%

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

   if 2.8999999999999999e-264 < t < 1.35000000000000008e-67

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. unsub-neg 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 48.6%

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

      1. +-commutative 48.6%

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

   8. Simplified 48.6%

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

   9. Taylor expanded in t around 0 49.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.2e+86)
     y
     (if (<= t 3.2e-301)
       t_1
       (if (<= t 5.5e-279) (* y (/ z a)) (if (<= t 7.5e+33) 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 <= -7.2e+86) {
		tmp = y;
	} else if (t <= 3.2e-301) {
		tmp = t_1;
	} else if (t <= 5.5e-279) {
		tmp = y * (z / a);
	} else if (t <= 7.5e+33) {
		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 <= (-7.2d+86)) then
        tmp = y
    else if (t <= 3.2d-301) then
        tmp = t_1
    else if (t <= 5.5d-279) then
        tmp = y * (z / a)
    else if (t <= 7.5d+33) 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 <= -7.2e+86) {
		tmp = y;
	} else if (t <= 3.2e-301) {
		tmp = t_1;
	} else if (t <= 5.5e-279) {
		tmp = y * (z / a);
	} else if (t <= 7.5e+33) {
		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 <= -7.2e+86:
		tmp = y
	elif t <= 3.2e-301:
		tmp = t_1
	elif t <= 5.5e-279:
		tmp = y * (z / a)
	elif t <= 7.5e+33:
		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 <= -7.2e+86)
		tmp = y;
	elseif (t <= 3.2e-301)
		tmp = t_1;
	elseif (t <= 5.5e-279)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7.5e+33)
		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 <= -7.2e+86)
		tmp = y;
	elseif (t <= 3.2e-301)
		tmp = t_1;
	elseif (t <= 5.5e-279)
		tmp = y * (z / a);
	elseif (t <= 7.5e+33)
		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, -7.2e+86], y, If[LessEqual[t, 3.2e-301], t$95$1, If[LessEqual[t, 5.5e-279], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+33], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000011e86 or 7.50000000000000046e33 < t

   1. Initial program 43.7%

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

   3. Taylor expanded in t around inf 48.9%

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

   if -7.20000000000000011e86 < t < 3.1999999999999999e-301 or 5.5000000000000002e-279 < t < 7.50000000000000046e33

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in t around 0 54.8%

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

   if 3.1999999999999999e-301 < t < 5.5000000000000002e-279

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around -inf 84.4%

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

   10. Taylor expanded in t around 0 69.7%

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

       1. associate-/l* 85.3%

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

   12. Simplified 85.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.4e+28)
     (* t (/ y (- t a)))
     (if (<= t 3.2e-301)
       t_1
       (if (<= t 2.5e-275) (* y (/ z a)) (if (<= t 1e+42) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.4e+28) {
		tmp = t * (y / (t - a));
	} else if (t <= 3.2e-301) {
		tmp = t_1;
	} else if (t <= 2.5e-275) {
		tmp = y * (z / a);
	} else if (t <= 1e+42) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-3.4d+28)) then
        tmp = t * (y / (t - a))
    else if (t <= 3.2d-301) then
        tmp = t_1
    else if (t <= 2.5d-275) then
        tmp = y * (z / a)
    else if (t <= 1d+42) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.4e+28) {
		tmp = t * (y / (t - a));
	} else if (t <= 3.2e-301) {
		tmp = t_1;
	} else if (t <= 2.5e-275) {
		tmp = y * (z / a);
	} else if (t <= 1e+42) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.4e+28:
		tmp = t * (y / (t - a))
	elif t <= 3.2e-301:
		tmp = t_1
	elif t <= 2.5e-275:
		tmp = y * (z / a)
	elif t <= 1e+42:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.4e+28)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	elseif (t <= 3.2e-301)
		tmp = t_1;
	elseif (t <= 2.5e-275)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1e+42)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.4e+28)
		tmp = t * (y / (t - a));
	elseif (t <= 3.2e-301)
		tmp = t_1;
	elseif (t <= 2.5e-275)
		tmp = y * (z / a);
	elseif (t <= 1e+42)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+28], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-301], t$95$1, If[LessEqual[t, 2.5e-275], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+42], t$95$1, y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.4e28

   1. Initial program 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-/l* 72.0%

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

      3. fma-define 72.1%

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

   3. Simplified 72.1%

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

      1. clear-num 72.0%

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

      2. inv-pow 72.0%

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

   6. Applied egg-rr 72.0%

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

      1. unpow-1 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in y around -inf 39.1%

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

   10. Taylor expanded in z around 0 31.4%

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

       1. mul-1-neg 31.4%

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

       2. associate-/l* 43.9%

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

       3. distribute-rgt-neg-in 43.9%

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

       4. distribute-neg-frac2 43.9%

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

   12. Simplified 43.9%

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

   if -3.4e28 < t < 3.1999999999999999e-301 or 2.49999999999999992e-275 < t < 1.00000000000000004e42

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in t around 0 57.8%

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

   if 3.1999999999999999e-301 < t < 2.49999999999999992e-275

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around -inf 84.4%

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

   10. Taylor expanded in t around 0 69.7%

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

       1. associate-/l* 85.3%

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

   12. Simplified 85.3%

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

   if 1.00000000000000004e42 < t

   1. Initial program 41.6%

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

   3. Taylor expanded in t around inf 53.6%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 10^{+42}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ (- t z) t))))
   (if (<= t -3.8e+86)
     t_2
     (if (<= t 2.2e-301)
       t_1
       (if (<= t 6.2e-279) (* y (/ z a)) (if (<= t 3.3e-68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((t - z) / t);
	double tmp;
	if (t <= -3.8e+86) {
		tmp = t_2;
	} else if (t <= 2.2e-301) {
		tmp = t_1;
	} else if (t <= 6.2e-279) {
		tmp = y * (z / a);
	} else if (t <= 3.3e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * ((t - z) / t)
    if (t <= (-3.8d+86)) then
        tmp = t_2
    else if (t <= 2.2d-301) then
        tmp = t_1
    else if (t <= 6.2d-279) then
        tmp = y * (z / a)
    else if (t <= 3.3d-68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((t - z) / t);
	double tmp;
	if (t <= -3.8e+86) {
		tmp = t_2;
	} else if (t <= 2.2e-301) {
		tmp = t_1;
	} else if (t <= 6.2e-279) {
		tmp = y * (z / a);
	} else if (t <= 3.3e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * ((t - z) / t)
	tmp = 0
	if t <= -3.8e+86:
		tmp = t_2
	elif t <= 2.2e-301:
		tmp = t_1
	elif t <= 6.2e-279:
		tmp = y * (z / a)
	elif t <= 3.3e-68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (t <= -3.8e+86)
		tmp = t_2;
	elseif (t <= 2.2e-301)
		tmp = t_1;
	elseif (t <= 6.2e-279)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.3e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * ((t - z) / t);
	tmp = 0.0;
	if (t <= -3.8e+86)
		tmp = t_2;
	elseif (t <= 2.2e-301)
		tmp = t_1;
	elseif (t <= 6.2e-279)
		tmp = y * (z / a);
	elseif (t <= 3.3e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+86], t$95$2, If[LessEqual[t, 2.2e-301], t$95$1, If[LessEqual[t, 6.2e-279], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999978e86 or 3.2999999999999998e-68 < t

   1. Initial program 47.6%

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

      1. +-commutative 47.6%

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

      2. associate-/l* 75.5%

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

      3. fma-define 75.6%

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

   3. Simplified 75.6%

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

      1. clear-num 75.5%

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

      2. inv-pow 75.5%

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

   6. Applied egg-rr 75.5%

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

      1. unpow-1 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in y around -inf 43.2%

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

   10. Taylor expanded in a around 0 38.6%

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

       1. mul-1-neg 38.6%

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

       2. associate-/l* 57.5%

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

       3. distribute-lft-neg-in 57.5%

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

   12. Simplified 57.5%

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

   if -3.79999999999999978e86 < t < 2.2e-301 or 6.1999999999999998e-279 < t < 3.2999999999999998e-68

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in t around 0 57.5%

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

   if 2.2e-301 < t < 6.1999999999999998e-279

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around -inf 84.4%

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

   10. Taylor expanded in t around 0 69.7%

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

       1. associate-/l* 85.3%

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

   12. Simplified 85.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+245}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5200000:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+245)
   (- y (* (/ x t) (- a z)))
   (if (<= t -1.32e+26)
     (* y (/ (- z t) (- a t)))
     (if (<= t 5200000.0)
       (+ x (* z (/ (- y x) a)))
       (+ y (* (/ z t) (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+245) {
		tmp = y - ((x / t) * (a - z));
	} else if (t <= -1.32e+26) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 5200000.0) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + ((z / t) * (x - 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 <= (-3.9d+245)) then
        tmp = y - ((x / t) * (a - z))
    else if (t <= (-1.32d+26)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 5200000.0d0) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = y + ((z / t) * (x - 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 <= -3.9e+245) {
		tmp = y - ((x / t) * (a - z));
	} else if (t <= -1.32e+26) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 5200000.0) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + ((z / t) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+245:
		tmp = y - ((x / t) * (a - z))
	elif t <= -1.32e+26:
		tmp = y * ((z - t) / (a - t))
	elif t <= 5200000.0:
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y + ((z / t) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+245)
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	elseif (t <= -1.32e+26)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 5200000.0)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.9e+245)
		tmp = y - ((x / t) * (a - z));
	elseif (t <= -1.32e+26)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 5200000.0)
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y + ((z / t) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+245], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.32e+26], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5200000.0], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8999999999999998e245

   1. Initial program 15.3%

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

   3. Taylor expanded in t around inf 40.3%

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

      1. associate--l+ 40.3%

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

      2. distribute-lft-out-- 40.3%

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

      3. div-sub 40.3%

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

      4. mul-1-neg 40.3%

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

      5. unsub-neg 40.3%

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

      6. div-sub 40.3%

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

      7. associate-/l* 64.1%

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

      8. associate-/l* 88.3%

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

      9. distribute-rgt-out-- 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in y around 0 88.3%

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

      1. neg-mul-1 88.3%

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

      2. distribute-neg-frac2 88.3%

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

   8. Simplified 88.3%

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

   if -3.8999999999999998e245 < t < -1.32e26

   1. Initial program 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 78.6%

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

      3. fma-define 78.7%

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

   3. Simplified 78.7%

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

      1. clear-num 78.6%

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

      2. inv-pow 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow-1 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in y around inf 65.4%

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

       1. div-sub 65.4%

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

   11. Simplified 65.4%

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

   if -1.32e26 < t < 5.2e6

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if 5.2e6 < t

   1. Initial program 44.4%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate--l+ 64.1%

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

      2. distribute-lft-out-- 64.1%

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

      3. div-sub 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

      6. div-sub 64.1%

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

      7. associate-/l* 73.5%

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

      8. associate-/l* 82.7%

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

      9. distribute-rgt-out-- 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in z around inf 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-/l* 78.8%

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

   8. Simplified 78.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+245}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5200000:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+86)
   y
   (if (<= t -3e-239)
     x
     (if (<= t 2.9e-263) (* y (/ z a)) (if (<= t 1.35e-67) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+86) {
		tmp = y;
	} else if (t <= -3e-239) {
		tmp = x;
	} else if (t <= 2.9e-263) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-67) {
		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 <= (-3.8d+86)) then
        tmp = y
    else if (t <= (-3d-239)) then
        tmp = x
    else if (t <= 2.9d-263) then
        tmp = y * (z / a)
    else if (t <= 1.35d-67) 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 <= -3.8e+86) {
		tmp = y;
	} else if (t <= -3e-239) {
		tmp = x;
	} else if (t <= 2.9e-263) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+86:
		tmp = y
	elif t <= -3e-239:
		tmp = x
	elif t <= 2.9e-263:
		tmp = y * (z / a)
	elif t <= 1.35e-67:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+86)
		tmp = y;
	elseif (t <= -3e-239)
		tmp = x;
	elseif (t <= 2.9e-263)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.35e-67)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+86)
		tmp = y;
	elseif (t <= -3e-239)
		tmp = x;
	elseif (t <= 2.9e-263)
		tmp = y * (z / a);
	elseif (t <= 1.35e-67)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+86], y, If[LessEqual[t, -3e-239], x, If[LessEqual[t, 2.9e-263], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-67], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999978e86 or 1.35000000000000008e-67 < t

   1. Initial program 47.6%

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

   3. Taylor expanded in t around inf 46.2%

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

   if -3.79999999999999978e86 < t < -2.9999999999999998e-239 or 2.90000000000000004e-263 < t < 1.35000000000000008e-67

   1. Initial program 84.5%

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

   3. Taylor expanded in a around inf 45.2%

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

   if -2.9999999999999998e-239 < t < 2.90000000000000004e-263

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-/l* 91.9%

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

      3. fma-define 91.9%

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

   3. Simplified 91.9%

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

      1. clear-num 91.8%

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

      2. inv-pow 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. unpow-1 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in y around -inf 49.3%

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

   10. Taylor expanded in t around 0 41.4%

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

       1. associate-/l* 50.0%

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

   12. Simplified 50.0%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.007 \lor \neg \left(y \leq 3.5 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.007) (not (<= y 3.5e+36)))
   (* y (/ (- z t) (- a t)))
   (* x (- 1.0 (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.007) || !(y <= 3.5e+36)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-0.007d0)) .or. (.not. (y <= 3.5d+36))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.007) || !(y <= 3.5e+36)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.007) or not (y <= 3.5e+36):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.007) || !(y <= 3.5e+36))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -0.007) || ~((y <= 3.5e+36)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.007], N[Not[LessEqual[y, 3.5e+36]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00700000000000000015 or 3.4999999999999998e36 < y

   1. Initial program 61.5%

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

      1. +-commutative 61.5%

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

      2. associate-/l* 92.2%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

      1. clear-num 92.2%

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

      2. inv-pow 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. unpow-1 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in y around inf 82.8%

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

       1. div-sub 82.8%

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

   11. Simplified 82.8%

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

   if -0.00700000000000000015 < y < 3.4999999999999998e36

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in t around 0 50.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.007 \lor \neg \left(y \leq 3.5 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+27} \lor \neg \left(t \leq 8.6 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e+27) (not (<= t 8.6e-101)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+27) || !(t <= 8.6e-101)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.25d+27)) .or. (.not. (t <= 8.6d-101))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+27) || !(t <= 8.6e-101)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e+27) or not (t <= 8.6e-101):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e+27) || !(t <= 8.6e-101))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e+27) || ~((t <= 8.6e-101)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e+27], N[Not[LessEqual[t, 8.6e-101]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999995e27 or 8.5999999999999995e-101 < t

   1. Initial program 50.9%

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

      1. +-commutative 50.9%

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

      2. associate-/l* 75.8%

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

      3. fma-define 75.9%

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

   3. Simplified 75.9%

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

      1. clear-num 75.9%

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

      2. inv-pow 75.9%

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

   6. Applied egg-rr 75.9%

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

      1. unpow-1 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in y around inf 64.7%

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

       1. div-sub 64.7%

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

   11. Simplified 64.7%

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

   if -1.24999999999999995e27 < t < 8.5999999999999995e-101

   1. Initial program 88.0%

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

   3. Taylor expanded in t around 0 72.5%

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

      1. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+27} \lor \neg \left(t \leq 8.6 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+25} \lor \neg \left(t \leq 15500000000\right):\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e+25) (not (<= t 15500000000.0)))
   (+ y (* (/ z t) (- x y)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+25) || !(t <= 15500000000.0)) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.1d+25)) .or. (.not. (t <= 15500000000.0d0))) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = x + (z * ((y - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+25) || !(t <= 15500000000.0)) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e+25) or not (t <= 15500000000.0):
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e+25) || !(t <= 15500000000.0))
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.1e+25) || ~((t <= 15500000000.0)))
		tmp = y + ((z / t) * (x - y));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e+25], N[Not[LessEqual[t, 15500000000.0]], $MachinePrecision]], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0999999999999998e25 or 1.55e10 < t

   1. Initial program 47.8%

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

   3. Taylor expanded in t around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. distribute-lft-out-- 62.3%

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

      3. div-sub 62.3%

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

      4. mul-1-neg 62.3%

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

      5. unsub-neg 62.3%

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

      6. div-sub 62.3%

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

      7. associate-/l* 70.1%

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

      8. associate-/l* 76.3%

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

      9. distribute-rgt-out-- 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in z around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-/l* 70.5%

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

   8. Simplified 70.5%

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

   if -3.0999999999999998e25 < t < 1.55e10

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+25} \lor \neg \left(t \leq 15500000000\right):\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+86) y (if (<= t 1.35e-67) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+86) {
		tmp = y;
	} else if (t <= 1.35e-67) {
		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 <= (-4.4d+86)) then
        tmp = y
    else if (t <= 1.35d-67) 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 <= -4.4e+86) {
		tmp = y;
	} else if (t <= 1.35e-67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+86:
		tmp = y
	elif t <= 1.35e-67:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+86)
		tmp = y;
	elseif (t <= 1.35e-67)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+86)
		tmp = y;
	elseif (t <= 1.35e-67)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+86], y, If[LessEqual[t, 1.35e-67], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.40000000000000006e86 or 1.35000000000000008e-67 < t

   1. Initial program 47.6%

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

   3. Taylor expanded in t around inf 46.2%

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

   if -4.40000000000000006e86 < t < 1.35000000000000008e-67

   1. Initial program 85.8%

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

   3. Taylor expanded in a around inf 41.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

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

3. Taylor expanded in a around inf 27.4%

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

4. Final simplification 27.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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