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

Percentage Accurate: 68.0% → 90.8%

Time: 26.4s

Alternatives: 28

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-291}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+272}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ (- x y) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 -2e+287)
     t_1
     (if (<= t_2 -2e-292)
       t_2
       (if (<= t_2 5e-291)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 2e+272) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+287) {
		tmp = t_1;
	} else if (t_2 <= -2e-292) {
		tmp = t_2;
	} else if (t_2 <= 5e-291) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+272) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((z - t) * ((x - y) / (a - t)))
    t_2 = x - (((y - x) * (t - z)) / (a - t))
    if (t_2 <= (-2d+287)) then
        tmp = t_1
    else if (t_2 <= (-2d-292)) then
        tmp = t_2
    else if (t_2 <= 5d-291) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t_2 <= 2d+272) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((x - y) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+287) {
		tmp = t_1;
	} else if (t_2 <= -2e-292) {
		tmp = t_2;
	} else if (t_2 <= 5e-291) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+272) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * ((x - y) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -2e+287:
		tmp = t_1
	elif t_2 <= -2e-292:
		tmp = t_2
	elif t_2 <= 5e-291:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 2e+272:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e+287)
		tmp = t_1;
	elseif (t_2 <= -2e-292)
		tmp = t_2;
	elseif (t_2 <= 5e-291)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 2e+272)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - t) * ((x - y) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e+287)
		tmp = t_1;
	elseif (t_2 <= -2e-292)
		tmp = t_2;
	elseif (t_2 <= 5e-291)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 2e+272)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+287], t$95$1, If[LessEqual[t$95$2, -2e-292], t$95$2, If[LessEqual[t$95$2, 5e-291], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+272], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000002e287 or 2.0000000000000001e272 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 52.3%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   if -2.0000000000000002e287 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-292 or 5.0000000000000003e-291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.0000000000000001e272

   1. Initial program 97.5%

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

   if -2.0000000000000001e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000003e-291

   1. Initial program 7.2%

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

      1. +-commutative 7.2%

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

      2. associate-*l/ 3.7%

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

      3. fma-def 3.7%

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

   3. Simplified 3.7%

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

      1. fma-udef 3.7%

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

      2. associate-/r/ 7.2%

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

      3. div-inv 7.2%

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

      4. clear-num 7.2%

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

   6. Applied egg-rr 7.2%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. associate-*r/ 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{+287}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{-291}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+272}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(t_1, y - x, x\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-291}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 -2e-292)
     (fma t_1 (- y x) x)
     (if (<= t_2 5e-291)
       (+ y (/ (* (- y x) (- a z)) t))
       (+ x (* (- y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e-292) {
		tmp = fma(t_1, (y - x), x);
	} else if (t_2 <= 5e-291) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-292)
		tmp = fma(t_1, Float64(y - x), x);
	elseif (t_2 <= 5e-291)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-292], N[(t$95$1 * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 5e-291], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-292

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-/l* 85.9%

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

      4. associate-/r/ 92.8%

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

      5. fma-def 92.8%

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

   3. Simplified 92.8%

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

   if -2.0000000000000001e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000003e-291

   1. Initial program 7.2%

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

      1. +-commutative 7.2%

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

      2. associate-*l/ 3.7%

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

      3. fma-def 3.7%

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

   3. Simplified 3.7%

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

      1. fma-udef 3.7%

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

      2. associate-/r/ 7.2%

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

      3. div-inv 7.2%

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

      4. clear-num 7.2%

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

   6. Applied egg-rr 7.2%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. associate-*r/ 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 100.0%

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

   9. Simplified 100.0%

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

   if 5.0000000000000003e-291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 79.5%

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

      1. +-commutative 79.5%

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

      2. associate-*l/ 87.4%

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

      3. fma-def 87.5%

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

   3. Simplified 87.5%

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

      1. fma-udef 87.4%

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

      2. associate-/r/ 91.1%

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

      3. div-inv 91.0%

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

      4. clear-num 91.0%

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

   6. Applied egg-rr 91.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{-291}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := \left(z - a\right) \cdot \frac{x}{t}\\ t_3 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a))))
        (t_2 (* (- z a) (/ x t)))
        (t_3 (* z (/ y (- a t)))))
   (if (<= t -1.9e+161)
     y
     (if (<= t -7.2e+71)
       t_2
       (if (<= t -9.2e-32)
         t_1
         (if (<= t -9.4e-153)
           t_3
           (if (<= t 1.1e-183)
             t_1
             (if (<= t 3e-161)
               t_3
               (if (<= t 3e+52)
                 t_1
                 (if (<= t 6.2e+126) t_3 (if (<= t 1.7e+162) t_2 y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = (z - a) * (x / t);
	double t_3 = z * (y / (a - t));
	double tmp;
	if (t <= -1.9e+161) {
		tmp = y;
	} else if (t <= -7.2e+71) {
		tmp = t_2;
	} else if (t <= -9.2e-32) {
		tmp = t_1;
	} else if (t <= -9.4e-153) {
		tmp = t_3;
	} else if (t <= 1.1e-183) {
		tmp = t_1;
	} else if (t <= 3e-161) {
		tmp = t_3;
	} else if (t <= 3e+52) {
		tmp = t_1;
	} else if (t <= 6.2e+126) {
		tmp = t_3;
	} else if (t <= 1.7e+162) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = (z - a) * (x / t)
    t_3 = z * (y / (a - t))
    if (t <= (-1.9d+161)) then
        tmp = y
    else if (t <= (-7.2d+71)) then
        tmp = t_2
    else if (t <= (-9.2d-32)) then
        tmp = t_1
    else if (t <= (-9.4d-153)) then
        tmp = t_3
    else if (t <= 1.1d-183) then
        tmp = t_1
    else if (t <= 3d-161) then
        tmp = t_3
    else if (t <= 3d+52) then
        tmp = t_1
    else if (t <= 6.2d+126) then
        tmp = t_3
    else if (t <= 1.7d+162) then
        tmp = t_2
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = (z - a) * (x / t);
	double t_3 = z * (y / (a - t));
	double tmp;
	if (t <= -1.9e+161) {
		tmp = y;
	} else if (t <= -7.2e+71) {
		tmp = t_2;
	} else if (t <= -9.2e-32) {
		tmp = t_1;
	} else if (t <= -9.4e-153) {
		tmp = t_3;
	} else if (t <= 1.1e-183) {
		tmp = t_1;
	} else if (t <= 3e-161) {
		tmp = t_3;
	} else if (t <= 3e+52) {
		tmp = t_1;
	} else if (t <= 6.2e+126) {
		tmp = t_3;
	} else if (t <= 1.7e+162) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = (z - a) * (x / t)
	t_3 = z * (y / (a - t))
	tmp = 0
	if t <= -1.9e+161:
		tmp = y
	elif t <= -7.2e+71:
		tmp = t_2
	elif t <= -9.2e-32:
		tmp = t_1
	elif t <= -9.4e-153:
		tmp = t_3
	elif t <= 1.1e-183:
		tmp = t_1
	elif t <= 3e-161:
		tmp = t_3
	elif t <= 3e+52:
		tmp = t_1
	elif t <= 6.2e+126:
		tmp = t_3
	elif t <= 1.7e+162:
		tmp = t_2
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(Float64(z - a) * Float64(x / t))
	t_3 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.9e+161)
		tmp = y;
	elseif (t <= -7.2e+71)
		tmp = t_2;
	elseif (t <= -9.2e-32)
		tmp = t_1;
	elseif (t <= -9.4e-153)
		tmp = t_3;
	elseif (t <= 1.1e-183)
		tmp = t_1;
	elseif (t <= 3e-161)
		tmp = t_3;
	elseif (t <= 3e+52)
		tmp = t_1;
	elseif (t <= 6.2e+126)
		tmp = t_3;
	elseif (t <= 1.7e+162)
		tmp = t_2;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = (z - a) * (x / t);
	t_3 = z * (y / (a - t));
	tmp = 0.0;
	if (t <= -1.9e+161)
		tmp = y;
	elseif (t <= -7.2e+71)
		tmp = t_2;
	elseif (t <= -9.2e-32)
		tmp = t_1;
	elseif (t <= -9.4e-153)
		tmp = t_3;
	elseif (t <= 1.1e-183)
		tmp = t_1;
	elseif (t <= 3e-161)
		tmp = t_3;
	elseif (t <= 3e+52)
		tmp = t_1;
	elseif (t <= 6.2e+126)
		tmp = t_3;
	elseif (t <= 1.7e+162)
		tmp = t_2;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+161], y, If[LessEqual[t, -7.2e+71], t$95$2, If[LessEqual[t, -9.2e-32], t$95$1, If[LessEqual[t, -9.4e-153], t$95$3, If[LessEqual[t, 1.1e-183], t$95$1, If[LessEqual[t, 3e-161], t$95$3, If[LessEqual[t, 3e+52], t$95$1, If[LessEqual[t, 6.2e+126], t$95$3, If[LessEqual[t, 1.7e+162], t$95$2, y]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9000000000000001e161 or 1.70000000000000001e162 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in t around inf 57.9%

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

   if -1.9000000000000001e161 < t < -7.1999999999999999e71 or 6.2e126 < t < 1.70000000000000001e162

   1. Initial program 76.5%

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

      1. associate-*l/ 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in t around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. associate-*r/ 66.5%

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

      3. associate-*r/ 66.5%

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

      4. div-sub 66.5%

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

      5. distribute-lft-out-- 66.5%

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

      6. associate-*r/ 66.5%

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

      7. mul-1-neg 66.5%

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

      8. unsub-neg 66.5%

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

      9. distribute-rgt-out-- 66.5%

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

      10. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in y around 0 47.0%

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

      1. associate-*l/ 53.2%

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

   10. Simplified 53.2%

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

   if -7.1999999999999999e71 < t < -9.2000000000000002e-32 or -9.3999999999999998e-153 < t < 1.1e-183 or 2.99999999999999989e-161 < t < 3e52

   1. Initial program 88.9%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in t around 0 71.0%

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

      1. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in x around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. unsub-neg 62.8%

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

   10. Simplified 62.8%

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

   if -9.2000000000000002e-32 < t < -9.3999999999999998e-153 or 1.1e-183 < t < 2.99999999999999989e-161 or 3e52 < t < 6.2e126

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 85.9%

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

      3. fma-def 86.1%

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

   3. Simplified 86.1%

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

      1. fma-udef 85.9%

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

      2. associate-/r/ 85.2%

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

      3. div-inv 83.7%

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

      4. clear-num 83.8%

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

   6. Applied egg-rr 83.8%

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

   7. Taylor expanded in y around inf 73.9%

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

      1. div-sub 73.9%

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

   9. Simplified 73.9%

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

   10. Taylor expanded in z around inf 49.6%

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

       1. associate-/l* 57.5%

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

       2. associate-/r/ 58.3%

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

   12. Simplified 58.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+71}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+162}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-292} \lor \neg \left(t_1 \leq 5 \cdot 10^{-291}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-292) (not (<= t_1 5e-291)))
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-292) || !(t_1 <= 5e-291)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - x) * (t - z)) / (a - t))
    if ((t_1 <= (-2d-292)) .or. (.not. (t_1 <= 5d-291))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-292) || !(t_1 <= 5e-291)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-292) or not (t_1 <= 5e-291):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-292) || !(t_1 <= 5e-291))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-292) || ~((t_1 <= 5e-291)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-292], N[Not[LessEqual[t$95$1, 5e-291]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-292 or 5.0000000000000003e-291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-*l/ 87.3%

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

      3. fma-def 87.4%

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

   3. Simplified 87.4%

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

      1. fma-udef 87.3%

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

      2. associate-/r/ 92.2%

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

      3. div-inv 91.8%

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

      4. clear-num 91.9%

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

   6. Applied egg-rr 91.9%

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

   if -2.0000000000000001e-292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000003e-291

   1. Initial program 7.2%

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

      1. +-commutative 7.2%

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

      2. associate-*l/ 3.7%

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

      3. fma-def 3.7%

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

   3. Simplified 3.7%

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

      1. fma-udef 3.7%

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

      2. associate-/r/ 7.2%

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

      3. div-inv 7.2%

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

      4. clear-num 7.2%

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

   6. Applied egg-rr 7.2%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. div-sub 99.9%

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

      5. distribute-lft-out-- 99.9%

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

      6. associate-*r/ 99.9%

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

      7. mul-1-neg 99.9%

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

      8. unsub-neg 99.9%

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

      9. distribute-rgt-out-- 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-292} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{-291}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= t -1.45e+107)
     y
     (if (<= t -2.35e-22)
       x
       (if (<= t -1.9e-271)
         t_1
         (if (<= t 1.4e-268)
           x
           (if (<= t 3e-233)
             t_1
             (if (<= t 1.12e-184)
               x
               (if (<= t 1.3e-152) t_1 (if (<= t 6e+64) x y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (t <= -1.45e+107) {
		tmp = y;
	} else if (t <= -2.35e-22) {
		tmp = x;
	} else if (t <= -1.9e-271) {
		tmp = t_1;
	} else if (t <= 1.4e-268) {
		tmp = x;
	} else if (t <= 3e-233) {
		tmp = t_1;
	} else if (t <= 1.12e-184) {
		tmp = x;
	} else if (t <= 1.3e-152) {
		tmp = t_1;
	} else if (t <= 6e+64) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / z)
    if (t <= (-1.45d+107)) then
        tmp = y
    else if (t <= (-2.35d-22)) then
        tmp = x
    else if (t <= (-1.9d-271)) then
        tmp = t_1
    else if (t <= 1.4d-268) then
        tmp = x
    else if (t <= 3d-233) then
        tmp = t_1
    else if (t <= 1.12d-184) then
        tmp = x
    else if (t <= 1.3d-152) then
        tmp = t_1
    else if (t <= 6d+64) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (t <= -1.45e+107) {
		tmp = y;
	} else if (t <= -2.35e-22) {
		tmp = x;
	} else if (t <= -1.9e-271) {
		tmp = t_1;
	} else if (t <= 1.4e-268) {
		tmp = x;
	} else if (t <= 3e-233) {
		tmp = t_1;
	} else if (t <= 1.12e-184) {
		tmp = x;
	} else if (t <= 1.3e-152) {
		tmp = t_1;
	} else if (t <= 6e+64) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if t <= -1.45e+107:
		tmp = y
	elif t <= -2.35e-22:
		tmp = x
	elif t <= -1.9e-271:
		tmp = t_1
	elif t <= 1.4e-268:
		tmp = x
	elif t <= 3e-233:
		tmp = t_1
	elif t <= 1.12e-184:
		tmp = x
	elif t <= 1.3e-152:
		tmp = t_1
	elif t <= 6e+64:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (t <= -1.45e+107)
		tmp = y;
	elseif (t <= -2.35e-22)
		tmp = x;
	elseif (t <= -1.9e-271)
		tmp = t_1;
	elseif (t <= 1.4e-268)
		tmp = x;
	elseif (t <= 3e-233)
		tmp = t_1;
	elseif (t <= 1.12e-184)
		tmp = x;
	elseif (t <= 1.3e-152)
		tmp = t_1;
	elseif (t <= 6e+64)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (t <= -1.45e+107)
		tmp = y;
	elseif (t <= -2.35e-22)
		tmp = x;
	elseif (t <= -1.9e-271)
		tmp = t_1;
	elseif (t <= 1.4e-268)
		tmp = x;
	elseif (t <= 3e-233)
		tmp = t_1;
	elseif (t <= 1.12e-184)
		tmp = x;
	elseif (t <= 1.3e-152)
		tmp = t_1;
	elseif (t <= 6e+64)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+107], y, If[LessEqual[t, -2.35e-22], x, If[LessEqual[t, -1.9e-271], t$95$1, If[LessEqual[t, 1.4e-268], x, If[LessEqual[t, 3e-233], t$95$1, If[LessEqual[t, 1.12e-184], x, If[LessEqual[t, 1.3e-152], t$95$1, If[LessEqual[t, 6e+64], x, y]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999994e107 or 6.0000000000000004e64 < t

   1. Initial program 47.0%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in t around inf 45.2%

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

   if -1.44999999999999994e107 < t < -2.3500000000000001e-22 or -1.90000000000000005e-271 < t < 1.40000000000000008e-268 or 2.99999999999999999e-233 < t < 1.11999999999999997e-184 or 1.30000000000000006e-152 < t < 6.0000000000000004e64

   1. Initial program 86.3%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around inf 43.3%

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

   if -2.3500000000000001e-22 < t < -1.90000000000000005e-271 or 1.40000000000000008e-268 < t < 2.99999999999999999e-233 or 1.11999999999999997e-184 < t < 1.30000000000000006e-152

   1. Initial program 89.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around -inf 71.8%

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

   6. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in a around inf 49.0%

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

       1. associate-/l* 48.4%

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

   11. Simplified 48.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-273}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)))
   (if (<= t -2.9e+107)
     y
     (if (<= t -1.15e-21)
       x
       (if (<= t -2.55e-273)
         (/ y (/ a z))
         (if (<= t 2.9e-267)
           x
           (if (<= t 8e-234)
             t_1
             (if (<= t 1.05e-183)
               x
               (if (<= t 4e-154) t_1 (if (<= t 4e+68) x y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (t <= -2.9e+107) {
		tmp = y;
	} else if (t <= -1.15e-21) {
		tmp = x;
	} else if (t <= -2.55e-273) {
		tmp = y / (a / z);
	} else if (t <= 2.9e-267) {
		tmp = x;
	} else if (t <= 8e-234) {
		tmp = t_1;
	} else if (t <= 1.05e-183) {
		tmp = x;
	} else if (t <= 4e-154) {
		tmp = t_1;
	} else if (t <= 4e+68) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / a
    if (t <= (-2.9d+107)) then
        tmp = y
    else if (t <= (-1.15d-21)) then
        tmp = x
    else if (t <= (-2.55d-273)) then
        tmp = y / (a / z)
    else if (t <= 2.9d-267) then
        tmp = x
    else if (t <= 8d-234) then
        tmp = t_1
    else if (t <= 1.05d-183) then
        tmp = x
    else if (t <= 4d-154) then
        tmp = t_1
    else if (t <= 4d+68) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (t <= -2.9e+107) {
		tmp = y;
	} else if (t <= -1.15e-21) {
		tmp = x;
	} else if (t <= -2.55e-273) {
		tmp = y / (a / z);
	} else if (t <= 2.9e-267) {
		tmp = x;
	} else if (t <= 8e-234) {
		tmp = t_1;
	} else if (t <= 1.05e-183) {
		tmp = x;
	} else if (t <= 4e-154) {
		tmp = t_1;
	} else if (t <= 4e+68) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	tmp = 0
	if t <= -2.9e+107:
		tmp = y
	elif t <= -1.15e-21:
		tmp = x
	elif t <= -2.55e-273:
		tmp = y / (a / z)
	elif t <= 2.9e-267:
		tmp = x
	elif t <= 8e-234:
		tmp = t_1
	elif t <= 1.05e-183:
		tmp = x
	elif t <= 4e-154:
		tmp = t_1
	elif t <= 4e+68:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (t <= -2.9e+107)
		tmp = y;
	elseif (t <= -1.15e-21)
		tmp = x;
	elseif (t <= -2.55e-273)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 2.9e-267)
		tmp = x;
	elseif (t <= 8e-234)
		tmp = t_1;
	elseif (t <= 1.05e-183)
		tmp = x;
	elseif (t <= 4e-154)
		tmp = t_1;
	elseif (t <= 4e+68)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	tmp = 0.0;
	if (t <= -2.9e+107)
		tmp = y;
	elseif (t <= -1.15e-21)
		tmp = x;
	elseif (t <= -2.55e-273)
		tmp = y / (a / z);
	elseif (t <= 2.9e-267)
		tmp = x;
	elseif (t <= 8e-234)
		tmp = t_1;
	elseif (t <= 1.05e-183)
		tmp = x;
	elseif (t <= 4e-154)
		tmp = t_1;
	elseif (t <= 4e+68)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -2.9e+107], y, If[LessEqual[t, -1.15e-21], x, If[LessEqual[t, -2.55e-273], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-267], x, If[LessEqual[t, 8e-234], t$95$1, If[LessEqual[t, 1.05e-183], x, If[LessEqual[t, 4e-154], t$95$1, If[LessEqual[t, 4e+68], x, y]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.89999999999999988e107 or 3.99999999999999981e68 < t

   1. Initial program 47.0%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in t around inf 45.2%

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

   if -2.89999999999999988e107 < t < -1.15e-21 or -2.54999999999999983e-273 < t < 2.90000000000000021e-267 or 7.9999999999999997e-234 < t < 1.0500000000000001e-183 or 3.9999999999999999e-154 < t < 3.99999999999999981e68

   1. Initial program 86.3%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around inf 43.3%

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

   if -1.15e-21 < t < -2.54999999999999983e-273

   1. Initial program 87.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around -inf 64.9%

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

   6. Taylor expanded in y around inf 48.5%

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

      1. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in a around inf 38.6%

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

       1. associate-/l* 42.8%

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

   11. Simplified 42.8%

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

   if 2.90000000000000021e-267 < t < 7.9999999999999997e-234 or 1.0500000000000001e-183 < t < 3.9999999999999999e-154

   1. Initial program 94.8%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in z around -inf 85.1%

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

   6. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in a around inf 69.2%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-273}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-154}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-157}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= z -7.6e+143)
     (/ (- y) (/ t z))
     (if (<= z -2.7e-21)
       t_1
       (if (<= z -4.5e-157)
         y
         (if (<= z 2.6e-119)
           x
           (if (<= z 3.9e-41)
             y
             (if (<= z 1.2e+63)
               x
               (if (<= z 3.7e+193) t_1 (/ (- x) (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (z <= -7.6e+143) {
		tmp = -y / (t / z);
	} else if (z <= -2.7e-21) {
		tmp = t_1;
	} else if (z <= -4.5e-157) {
		tmp = y;
	} else if (z <= 2.6e-119) {
		tmp = x;
	} else if (z <= 3.9e-41) {
		tmp = y;
	} else if (z <= 1.2e+63) {
		tmp = x;
	} else if (z <= 3.7e+193) {
		tmp = t_1;
	} else {
		tmp = -x / (a / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / z)
    if (z <= (-7.6d+143)) then
        tmp = -y / (t / z)
    else if (z <= (-2.7d-21)) then
        tmp = t_1
    else if (z <= (-4.5d-157)) then
        tmp = y
    else if (z <= 2.6d-119) then
        tmp = x
    else if (z <= 3.9d-41) then
        tmp = y
    else if (z <= 1.2d+63) then
        tmp = x
    else if (z <= 3.7d+193) then
        tmp = t_1
    else
        tmp = -x / (a / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (z <= -7.6e+143) {
		tmp = -y / (t / z);
	} else if (z <= -2.7e-21) {
		tmp = t_1;
	} else if (z <= -4.5e-157) {
		tmp = y;
	} else if (z <= 2.6e-119) {
		tmp = x;
	} else if (z <= 3.9e-41) {
		tmp = y;
	} else if (z <= 1.2e+63) {
		tmp = x;
	} else if (z <= 3.7e+193) {
		tmp = t_1;
	} else {
		tmp = -x / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if z <= -7.6e+143:
		tmp = -y / (t / z)
	elif z <= -2.7e-21:
		tmp = t_1
	elif z <= -4.5e-157:
		tmp = y
	elif z <= 2.6e-119:
		tmp = x
	elif z <= 3.9e-41:
		tmp = y
	elif z <= 1.2e+63:
		tmp = x
	elif z <= 3.7e+193:
		tmp = t_1
	else:
		tmp = -x / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (z <= -7.6e+143)
		tmp = Float64(Float64(-y) / Float64(t / z));
	elseif (z <= -2.7e-21)
		tmp = t_1;
	elseif (z <= -4.5e-157)
		tmp = y;
	elseif (z <= 2.6e-119)
		tmp = x;
	elseif (z <= 3.9e-41)
		tmp = y;
	elseif (z <= 1.2e+63)
		tmp = x;
	elseif (z <= 3.7e+193)
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (z <= -7.6e+143)
		tmp = -y / (t / z);
	elseif (z <= -2.7e-21)
		tmp = t_1;
	elseif (z <= -4.5e-157)
		tmp = y;
	elseif (z <= 2.6e-119)
		tmp = x;
	elseif (z <= 3.9e-41)
		tmp = y;
	elseif (z <= 1.2e+63)
		tmp = x;
	elseif (z <= 3.7e+193)
		tmp = t_1;
	else
		tmp = -x / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e+143], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-21], t$95$1, If[LessEqual[z, -4.5e-157], y, If[LessEqual[z, 2.6e-119], x, If[LessEqual[z, 3.9e-41], y, If[LessEqual[z, 1.2e+63], x, If[LessEqual[z, 3.7e+193], t$95$1, N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.60000000000000001e143

   1. Initial program 77.2%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around -inf 64.0%

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

   6. Taylor expanded in y around inf 40.5%

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

      1. *-commutative 40.5%

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

   8. Simplified 40.5%

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

   9. Taylor expanded in a around 0 43.7%

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

       1. mul-1-neg 43.7%

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

       2. associate-/l* 50.0%

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

       3. distribute-neg-frac 50.0%

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

   11. Simplified 50.0%

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

   if -7.60000000000000001e143 < z < -2.7000000000000001e-21 or 1.2e63 < z < 3.7000000000000003e193

   1. Initial program 75.4%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in z around -inf 60.2%

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

   6. Taylor expanded in y around inf 37.7%

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

      1. *-commutative 37.7%

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

   8. Simplified 37.7%

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

   9. Taylor expanded in a around inf 32.8%

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

       1. associate-/l* 37.9%

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

   11. Simplified 37.9%

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

   if -2.7000000000000001e-21 < z < -4.49999999999999999e-157 or 2.60000000000000012e-119 < z < 3.89999999999999991e-41

   1. Initial program 59.7%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 46.7%

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

   if -4.49999999999999999e-157 < z < 2.60000000000000012e-119 or 3.89999999999999991e-41 < z < 1.2e63

   1. Initial program 74.9%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in a around inf 48.3%

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

   if 3.7000000000000003e193 < z

   1. Initial program 87.9%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 62.1%

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

      1. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in x around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

   10. Simplified 55.8%

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

   11. Taylor expanded in z around inf 40.7%

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

       1. mul-1-neg 40.7%

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

       2. associate-/l* 52.8%

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

       3. distribute-neg-frac 52.8%

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

   13. Simplified 52.8%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-157}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+193}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= t -2.25e+138)
     t_1
     (if (<= t -3.2e+66)
       (* z (/ (- y x) (- a t)))
       (if (<= t -1.52e-97)
         t_2
         (if (<= t 1.65e-68)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 1.22e-8)
             t_2
             (if (<= t 4.6e+49) (+ x (/ z (- (/ a x)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2.25e+138) {
		tmp = t_1;
	} else if (t <= -3.2e+66) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.52e-97) {
		tmp = t_2;
	} else if (t <= 1.65e-68) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.22e-8) {
		tmp = t_2;
	} else if (t <= 4.6e+49) {
		tmp = x + (z / -(a / 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) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = (z - t) * (y / (a - t))
    if (t <= (-2.25d+138)) then
        tmp = t_1
    else if (t <= (-3.2d+66)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-1.52d-97)) then
        tmp = t_2
    else if (t <= 1.65d-68) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 1.22d-8) then
        tmp = t_2
    else if (t <= 4.6d+49) then
        tmp = x + (z / -(a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2.25e+138) {
		tmp = t_1;
	} else if (t <= -3.2e+66) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -1.52e-97) {
		tmp = t_2;
	} else if (t <= 1.65e-68) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.22e-8) {
		tmp = t_2;
	} else if (t <= 4.6e+49) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = (z - t) * (y / (a - t))
	tmp = 0
	if t <= -2.25e+138:
		tmp = t_1
	elif t <= -3.2e+66:
		tmp = z * ((y - x) / (a - t))
	elif t <= -1.52e-97:
		tmp = t_2
	elif t <= 1.65e-68:
		tmp = x + (z / (a / (y - x)))
	elif t <= 1.22e-8:
		tmp = t_2
	elif t <= 4.6e+49:
		tmp = x + (z / -(a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.25e+138)
		tmp = t_1;
	elseif (t <= -3.2e+66)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -1.52e-97)
		tmp = t_2;
	elseif (t <= 1.65e-68)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 1.22e-8)
		tmp = t_2;
	elseif (t <= 4.6e+49)
		tmp = Float64(x + Float64(z / Float64(-Float64(a / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (t <= -2.25e+138)
		tmp = t_1;
	elseif (t <= -3.2e+66)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -1.52e-97)
		tmp = t_2;
	elseif (t <= 1.65e-68)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 1.22e-8)
		tmp = t_2;
	elseif (t <= 4.6e+49)
		tmp = x + (z / -(a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+138], t$95$1, If[LessEqual[t, -3.2e+66], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.52e-97], t$95$2, If[LessEqual[t, 1.65e-68], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-8], t$95$2, If[LessEqual[t, 4.6e+49], N[(x + N[(z / (-N[(a / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.24999999999999991e138 or 4.60000000000000004e49 < t

   1. Initial program 45.6%

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

      1. +-commutative 45.6%

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

      2. associate-*l/ 64.6%

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

      3. fma-def 64.7%

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

   3. Simplified 64.7%

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

      1. fma-udef 64.6%

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

      2. associate-/r/ 71.2%

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

      3. div-inv 71.2%

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

      4. clear-num 71.2%

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

   6. Applied egg-rr 71.2%

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

   7. Taylor expanded in y around inf 67.9%

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

      1. div-sub 67.9%

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

   9. Simplified 67.9%

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

   if -2.24999999999999991e138 < t < -3.2e66

   1. Initial program 83.7%

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

      1. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. div-sub 61.7%

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

   7. Simplified 61.7%

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

   if -3.2e66 < t < -1.5200000000000001e-97 or 1.6499999999999999e-68 < t < 1.22e-8

   1. Initial program 78.3%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 61.5%

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

      2. associate-/r/ 63.6%

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

   7. Simplified 63.6%

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

   if -1.5200000000000001e-97 < t < 1.6499999999999999e-68

   1. Initial program 93.8%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around 0 86.3%

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

      1. associate-/l* 85.8%

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

   7. Simplified 85.8%

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

   if 1.22e-8 < t < 4.60000000000000004e49

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-97}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 0.000235:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= t -2.25e+138)
     t_1
     (if (<= t -3.3e+66)
       (* z (/ (- y x) (- a t)))
       (if (<= t -2.45e-98)
         t_2
         (if (<= t 1.42e-67)
           (- x (/ (* z (- x y)) a))
           (if (<= t 0.000235)
             t_2
             (if (<= t 1.45e+50) (+ x (/ z (- (/ a x)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2.25e+138) {
		tmp = t_1;
	} else if (t <= -3.3e+66) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -2.45e-98) {
		tmp = t_2;
	} else if (t <= 1.42e-67) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 0.000235) {
		tmp = t_2;
	} else if (t <= 1.45e+50) {
		tmp = x + (z / -(a / 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) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = (z - t) * (y / (a - t))
    if (t <= (-2.25d+138)) then
        tmp = t_1
    else if (t <= (-3.3d+66)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-2.45d-98)) then
        tmp = t_2
    else if (t <= 1.42d-67) then
        tmp = x - ((z * (x - y)) / a)
    else if (t <= 0.000235d0) then
        tmp = t_2
    else if (t <= 1.45d+50) then
        tmp = x + (z / -(a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -2.25e+138) {
		tmp = t_1;
	} else if (t <= -3.3e+66) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -2.45e-98) {
		tmp = t_2;
	} else if (t <= 1.42e-67) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 0.000235) {
		tmp = t_2;
	} else if (t <= 1.45e+50) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = (z - t) * (y / (a - t))
	tmp = 0
	if t <= -2.25e+138:
		tmp = t_1
	elif t <= -3.3e+66:
		tmp = z * ((y - x) / (a - t))
	elif t <= -2.45e-98:
		tmp = t_2
	elif t <= 1.42e-67:
		tmp = x - ((z * (x - y)) / a)
	elif t <= 0.000235:
		tmp = t_2
	elif t <= 1.45e+50:
		tmp = x + (z / -(a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.25e+138)
		tmp = t_1;
	elseif (t <= -3.3e+66)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -2.45e-98)
		tmp = t_2;
	elseif (t <= 1.42e-67)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	elseif (t <= 0.000235)
		tmp = t_2;
	elseif (t <= 1.45e+50)
		tmp = Float64(x + Float64(z / Float64(-Float64(a / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (t <= -2.25e+138)
		tmp = t_1;
	elseif (t <= -3.3e+66)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -2.45e-98)
		tmp = t_2;
	elseif (t <= 1.42e-67)
		tmp = x - ((z * (x - y)) / a);
	elseif (t <= 0.000235)
		tmp = t_2;
	elseif (t <= 1.45e+50)
		tmp = x + (z / -(a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+138], t$95$1, If[LessEqual[t, -3.3e+66], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.45e-98], t$95$2, If[LessEqual[t, 1.42e-67], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.000235], t$95$2, If[LessEqual[t, 1.45e+50], N[(x + N[(z / (-N[(a / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.24999999999999991e138 or 1.45e50 < t

   1. Initial program 45.6%

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

      1. +-commutative 45.6%

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

      2. associate-*l/ 64.6%

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

      3. fma-def 64.7%

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

   3. Simplified 64.7%

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

      1. fma-udef 64.6%

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

      2. associate-/r/ 71.2%

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

      3. div-inv 71.2%

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

      4. clear-num 71.2%

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

   6. Applied egg-rr 71.2%

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

   7. Taylor expanded in y around inf 67.9%

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

      1. div-sub 67.9%

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

   9. Simplified 67.9%

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

   if -2.24999999999999991e138 < t < -3.3000000000000001e66

   1. Initial program 83.7%

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

      1. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. div-sub 61.7%

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

   7. Simplified 61.7%

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

   if -3.3000000000000001e66 < t < -2.45000000000000007e-98 or 1.42000000000000004e-67 < t < 2.34999999999999993e-4

   1. Initial program 78.3%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 61.5%

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

      2. associate-/r/ 63.6%

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

   7. Simplified 63.6%

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

   if -2.45000000000000007e-98 < t < 1.42000000000000004e-67

   1. Initial program 93.8%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around 0 86.3%

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

   if 2.34999999999999993e-4 < t < 1.45e50

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-98}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 0.000235:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -32000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= t -3.5e+44)
     t_1
     (if (<= t -32000.0)
       (+ x (/ (* y z) a))
       (if (<= t -2.1e-65)
         t_2
         (if (<= t 8.2e-69)
           (- x (/ (* z (- x y)) a))
           (if (<= t 4.5e-11)
             t_2
             (if (<= t 5.5e+49) (+ x (/ z (- (/ a x)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -3.5e+44) {
		tmp = t_1;
	} else if (t <= -32000.0) {
		tmp = x + ((y * z) / a);
	} else if (t <= -2.1e-65) {
		tmp = t_2;
	} else if (t <= 8.2e-69) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 4.5e-11) {
		tmp = t_2;
	} else if (t <= 5.5e+49) {
		tmp = x + (z / -(a / 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) :: t_2
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / z))
    t_2 = (z - t) * (y / (a - t))
    if (t <= (-3.5d+44)) then
        tmp = t_1
    else if (t <= (-32000.0d0)) then
        tmp = x + ((y * z) / a)
    else if (t <= (-2.1d-65)) then
        tmp = t_2
    else if (t <= 8.2d-69) then
        tmp = x - ((z * (x - y)) / a)
    else if (t <= 4.5d-11) then
        tmp = t_2
    else if (t <= 5.5d+49) then
        tmp = x + (z / -(a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (t <= -3.5e+44) {
		tmp = t_1;
	} else if (t <= -32000.0) {
		tmp = x + ((y * z) / a);
	} else if (t <= -2.1e-65) {
		tmp = t_2;
	} else if (t <= 8.2e-69) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= 4.5e-11) {
		tmp = t_2;
	} else if (t <= 5.5e+49) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = (z - t) * (y / (a - t))
	tmp = 0
	if t <= -3.5e+44:
		tmp = t_1
	elif t <= -32000.0:
		tmp = x + ((y * z) / a)
	elif t <= -2.1e-65:
		tmp = t_2
	elif t <= 8.2e-69:
		tmp = x - ((z * (x - y)) / a)
	elif t <= 4.5e-11:
		tmp = t_2
	elif t <= 5.5e+49:
		tmp = x + (z / -(a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.5e+44)
		tmp = t_1;
	elseif (t <= -32000.0)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= -2.1e-65)
		tmp = t_2;
	elseif (t <= 8.2e-69)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	elseif (t <= 4.5e-11)
		tmp = t_2;
	elseif (t <= 5.5e+49)
		tmp = Float64(x + Float64(z / Float64(-Float64(a / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (t <= -3.5e+44)
		tmp = t_1;
	elseif (t <= -32000.0)
		tmp = x + ((y * z) / a);
	elseif (t <= -2.1e-65)
		tmp = t_2;
	elseif (t <= 8.2e-69)
		tmp = x - ((z * (x - y)) / a);
	elseif (t <= 4.5e-11)
		tmp = t_2;
	elseif (t <= 5.5e+49)
		tmp = x + (z / -(a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+44], t$95$1, If[LessEqual[t, -32000.0], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-65], t$95$2, If[LessEqual[t, 8.2e-69], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-11], t$95$2, If[LessEqual[t, 5.5e+49], N[(x + N[(z / (-N[(a / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.4999999999999999e44 or 5.50000000000000042e49 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. div-sub 68.5%

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

      5. distribute-lft-out-- 68.5%

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

      6. associate-*r/ 68.5%

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

      7. mul-1-neg 68.5%

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

      8. unsub-neg 68.5%

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

      9. distribute-rgt-out-- 68.6%

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

      10. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in z around inf 73.8%

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

   if -3.4999999999999999e44 < t < -32000

   1. Initial program 56.4%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in y around inf 68.2%

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

   if -32000 < t < -2.10000000000000003e-65 or 8.1999999999999998e-69 < t < 4.5e-11

   1. Initial program 80.4%

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

      1. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in x around 0 65.0%

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

      1. associate-/l* 65.1%

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

      2. associate-/r/ 68.9%

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

   7. Simplified 68.9%

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

   if -2.10000000000000003e-65 < t < 8.1999999999999998e-69

   1. Initial program 94.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around 0 85.2%

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

   if 4.5e-11 < t < 5.50000000000000042e49

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+44}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -32000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-65}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+127}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z a) (/ x t))))
   (if (<= t -1.05e+160)
     y
     (if (<= t -9e+65)
       t_1
       (if (<= t 4.6e-117)
         (+ x (/ z (/ a y)))
         (if (<= t 4e+54)
           (* x (- 1.0 (/ z a)))
           (if (<= t 1.05e+127)
             (* z (/ y (- a t)))
             (if (<= t 7e+159) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - a) * (x / t);
	double tmp;
	if (t <= -1.05e+160) {
		tmp = y;
	} else if (t <= -9e+65) {
		tmp = t_1;
	} else if (t <= 4.6e-117) {
		tmp = x + (z / (a / y));
	} else if (t <= 4e+54) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.05e+127) {
		tmp = z * (y / (a - t));
	} else if (t <= 7e+159) {
		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 = (z - a) * (x / t)
    if (t <= (-1.05d+160)) then
        tmp = y
    else if (t <= (-9d+65)) then
        tmp = t_1
    else if (t <= 4.6d-117) then
        tmp = x + (z / (a / y))
    else if (t <= 4d+54) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.05d+127) then
        tmp = z * (y / (a - t))
    else if (t <= 7d+159) 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 = (z - a) * (x / t);
	double tmp;
	if (t <= -1.05e+160) {
		tmp = y;
	} else if (t <= -9e+65) {
		tmp = t_1;
	} else if (t <= 4.6e-117) {
		tmp = x + (z / (a / y));
	} else if (t <= 4e+54) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.05e+127) {
		tmp = z * (y / (a - t));
	} else if (t <= 7e+159) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - a) * (x / t)
	tmp = 0
	if t <= -1.05e+160:
		tmp = y
	elif t <= -9e+65:
		tmp = t_1
	elif t <= 4.6e-117:
		tmp = x + (z / (a / y))
	elif t <= 4e+54:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.05e+127:
		tmp = z * (y / (a - t))
	elif t <= 7e+159:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - a) * Float64(x / t))
	tmp = 0.0
	if (t <= -1.05e+160)
		tmp = y;
	elseif (t <= -9e+65)
		tmp = t_1;
	elseif (t <= 4.6e-117)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 4e+54)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.05e+127)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= 7e+159)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - a) * (x / t);
	tmp = 0.0;
	if (t <= -1.05e+160)
		tmp = y;
	elseif (t <= -9e+65)
		tmp = t_1;
	elseif (t <= 4.6e-117)
		tmp = x + (z / (a / y));
	elseif (t <= 4e+54)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.05e+127)
		tmp = z * (y / (a - t));
	elseif (t <= 7e+159)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+160], y, If[LessEqual[t, -9e+65], t$95$1, If[LessEqual[t, 4.6e-117], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+54], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+127], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+159], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.04999999999999998e160 or 6.9999999999999999e159 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in t around inf 57.9%

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

   if -1.04999999999999998e160 < t < -9e65 or 1.04999999999999996e127 < t < 6.9999999999999999e159

   1. Initial program 79.3%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. associate-*r/ 67.4%

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

      3. associate-*r/ 67.4%

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

      4. div-sub 67.4%

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

      5. distribute-lft-out-- 67.4%

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

      6. associate-*r/ 67.4%

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

      7. mul-1-neg 67.4%

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

      8. unsub-neg 67.4%

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

      9. distribute-rgt-out-- 67.4%

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

      10. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in y around 0 47.6%

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

      1. associate-*l/ 53.0%

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

   10. Simplified 53.0%

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

   if -9e65 < t < 4.59999999999999989e-117

   1. Initial program 90.2%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 66.1%

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

   if 4.59999999999999989e-117 < t < 4.0000000000000003e54

   1. Initial program 78.4%

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

      1. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around 0 49.3%

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

      1. associate-/l* 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   10. Simplified 59.9%

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

   if 4.0000000000000003e54 < t < 1.04999999999999996e127

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-*l/ 86.8%

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

      3. fma-def 86.9%

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

   3. Simplified 86.9%

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

      1. fma-udef 86.8%

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

      2. associate-/r/ 87.0%

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

      3. div-inv 87.0%

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

      4. clear-num 87.0%

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in y around inf 80.9%

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

      1. div-sub 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in z around inf 29.7%

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

       1. associate-/l* 48.1%

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

       2. associate-/r/ 48.0%

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

   12. Simplified 48.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+65}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+127}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+159}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z a) (/ x t))))
   (if (<= t -2.55e+160)
     y
     (if (<= t -3.4e+64)
       t_1
       (if (<= t 5.5e-117)
         (+ x (/ (* y z) a))
         (if (<= t 2.4e+57)
           (* x (- 1.0 (/ z a)))
           (if (<= t 6.2e+126)
             (* z (/ y (- a t)))
             (if (<= t 2.45e+160) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - a) * (x / t);
	double tmp;
	if (t <= -2.55e+160) {
		tmp = y;
	} else if (t <= -3.4e+64) {
		tmp = t_1;
	} else if (t <= 5.5e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.4e+57) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+126) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.45e+160) {
		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 = (z - a) * (x / t)
    if (t <= (-2.55d+160)) then
        tmp = y
    else if (t <= (-3.4d+64)) then
        tmp = t_1
    else if (t <= 5.5d-117) then
        tmp = x + ((y * z) / a)
    else if (t <= 2.4d+57) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6.2d+126) then
        tmp = z * (y / (a - t))
    else if (t <= 2.45d+160) 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 = (z - a) * (x / t);
	double tmp;
	if (t <= -2.55e+160) {
		tmp = y;
	} else if (t <= -3.4e+64) {
		tmp = t_1;
	} else if (t <= 5.5e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.4e+57) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e+126) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.45e+160) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - a) * (x / t)
	tmp = 0
	if t <= -2.55e+160:
		tmp = y
	elif t <= -3.4e+64:
		tmp = t_1
	elif t <= 5.5e-117:
		tmp = x + ((y * z) / a)
	elif t <= 2.4e+57:
		tmp = x * (1.0 - (z / a))
	elif t <= 6.2e+126:
		tmp = z * (y / (a - t))
	elif t <= 2.45e+160:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - a) * Float64(x / t))
	tmp = 0.0
	if (t <= -2.55e+160)
		tmp = y;
	elseif (t <= -3.4e+64)
		tmp = t_1;
	elseif (t <= 5.5e-117)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 2.4e+57)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.2e+126)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= 2.45e+160)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - a) * (x / t);
	tmp = 0.0;
	if (t <= -2.55e+160)
		tmp = y;
	elseif (t <= -3.4e+64)
		tmp = t_1;
	elseif (t <= 5.5e-117)
		tmp = x + ((y * z) / a);
	elseif (t <= 2.4e+57)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6.2e+126)
		tmp = z * (y / (a - t));
	elseif (t <= 2.45e+160)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+160], y, If[LessEqual[t, -3.4e+64], t$95$1, If[LessEqual[t, 5.5e-117], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+57], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+126], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+160], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5500000000000001e160 or 2.4500000000000001e160 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in t around inf 57.9%

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

   if -2.5500000000000001e160 < t < -3.4000000000000002e64 or 6.2e126 < t < 2.4500000000000001e160

   1. Initial program 79.3%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. associate-*r/ 67.4%

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

      3. associate-*r/ 67.4%

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

      4. div-sub 67.4%

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

      5. distribute-lft-out-- 67.4%

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

      6. associate-*r/ 67.4%

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

      7. mul-1-neg 67.4%

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

      8. unsub-neg 67.4%

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

      9. distribute-rgt-out-- 67.4%

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

      10. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in y around 0 47.6%

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

      1. associate-*l/ 53.0%

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

   10. Simplified 53.0%

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

   if -3.4000000000000002e64 < t < 5.50000000000000025e-117

   1. Initial program 90.2%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 67.1%

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

   if 5.50000000000000025e-117 < t < 2.40000000000000005e57

   1. Initial program 78.4%

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

      1. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around 0 49.3%

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

      1. associate-/l* 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   10. Simplified 59.9%

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

   if 2.40000000000000005e57 < t < 6.2e126

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-*l/ 86.8%

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

      3. fma-def 86.9%

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

   3. Simplified 86.9%

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

      1. fma-udef 86.8%

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

      2. associate-/r/ 87.0%

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

      3. div-inv 87.0%

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

      4. clear-num 87.0%

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in y around inf 80.9%

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

      1. div-sub 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in z around inf 29.7%

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

       1. associate-/l* 48.1%

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

       2. associate-/r/ 48.0%

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

   12. Simplified 48.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+64}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+160}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z a) (/ x t))))
   (if (<= t -3.1e+159)
     y
     (if (<= t -1e+65)
       t_1
       (if (<= t 7.2e-117)
         (+ x (/ (* y z) a))
         (if (<= t 5.8e+56)
           (* x (- 1.0 (/ z a)))
           (if (<= t 1.1e+127)
             (/ y (/ (- a t) z))
             (if (<= t 6.1e+159) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - a) * (x / t);
	double tmp;
	if (t <= -3.1e+159) {
		tmp = y;
	} else if (t <= -1e+65) {
		tmp = t_1;
	} else if (t <= 7.2e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5.8e+56) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.1e+127) {
		tmp = y / ((a - t) / z);
	} else if (t <= 6.1e+159) {
		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 = (z - a) * (x / t)
    if (t <= (-3.1d+159)) then
        tmp = y
    else if (t <= (-1d+65)) then
        tmp = t_1
    else if (t <= 7.2d-117) then
        tmp = x + ((y * z) / a)
    else if (t <= 5.8d+56) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.1d+127) then
        tmp = y / ((a - t) / z)
    else if (t <= 6.1d+159) 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 = (z - a) * (x / t);
	double tmp;
	if (t <= -3.1e+159) {
		tmp = y;
	} else if (t <= -1e+65) {
		tmp = t_1;
	} else if (t <= 7.2e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5.8e+56) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.1e+127) {
		tmp = y / ((a - t) / z);
	} else if (t <= 6.1e+159) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - a) * (x / t)
	tmp = 0
	if t <= -3.1e+159:
		tmp = y
	elif t <= -1e+65:
		tmp = t_1
	elif t <= 7.2e-117:
		tmp = x + ((y * z) / a)
	elif t <= 5.8e+56:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.1e+127:
		tmp = y / ((a - t) / z)
	elif t <= 6.1e+159:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - a) * Float64(x / t))
	tmp = 0.0
	if (t <= -3.1e+159)
		tmp = y;
	elseif (t <= -1e+65)
		tmp = t_1;
	elseif (t <= 7.2e-117)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 5.8e+56)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.1e+127)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= 6.1e+159)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - a) * (x / t);
	tmp = 0.0;
	if (t <= -3.1e+159)
		tmp = y;
	elseif (t <= -1e+65)
		tmp = t_1;
	elseif (t <= 7.2e-117)
		tmp = x + ((y * z) / a);
	elseif (t <= 5.8e+56)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.1e+127)
		tmp = y / ((a - t) / z);
	elseif (t <= 6.1e+159)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+159], y, If[LessEqual[t, -1e+65], t$95$1, If[LessEqual[t, 7.2e-117], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+56], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+127], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e+159], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.0999999999999998e159 or 6.1e159 < t

   1. Initial program 32.0%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in t around inf 57.9%

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

   if -3.0999999999999998e159 < t < -9.9999999999999999e64 or 1.1000000000000001e127 < t < 6.1e159

   1. Initial program 79.3%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. associate-*r/ 67.4%

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

      3. associate-*r/ 67.4%

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

      4. div-sub 67.4%

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

      5. distribute-lft-out-- 67.4%

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

      6. associate-*r/ 67.4%

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

      7. mul-1-neg 67.4%

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

      8. unsub-neg 67.4%

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

      9. distribute-rgt-out-- 67.4%

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

      10. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in y around 0 47.6%

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

      1. associate-*l/ 53.0%

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

   10. Simplified 53.0%

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

   if -9.9999999999999999e64 < t < 7.2000000000000001e-117

   1. Initial program 90.2%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 67.1%

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

   if 7.2000000000000001e-117 < t < 5.80000000000000014e56

   1. Initial program 78.4%

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

      1. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around 0 49.3%

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

      1. associate-/l* 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   10. Simplified 59.9%

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

   if 5.80000000000000014e56 < t < 1.1000000000000001e127

   1. Initial program 68.6%

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

      1. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in z around -inf 29.8%

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

   6. Taylor expanded in y around inf 29.7%

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

      1. associate-/l* 48.1%

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

   8. Simplified 48.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+65}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+159}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -0.104:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-40}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+189}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (/ a z))))
   (if (<= z -0.104)
     t_1
     (if (<= z -1.45e-155)
       y
       (if (<= z 1.36e-117)
         x
         (if (<= z 2.5e-40)
           y
           (if (<= z 2.85e+57) x (if (<= z 8e+189) (/ y (/ a z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (a / z);
	double tmp;
	if (z <= -0.104) {
		tmp = t_1;
	} else if (z <= -1.45e-155) {
		tmp = y;
	} else if (z <= 1.36e-117) {
		tmp = x;
	} else if (z <= 2.5e-40) {
		tmp = y;
	} else if (z <= 2.85e+57) {
		tmp = x;
	} else if (z <= 8e+189) {
		tmp = y / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (a / z)
    if (z <= (-0.104d0)) then
        tmp = t_1
    else if (z <= (-1.45d-155)) then
        tmp = y
    else if (z <= 1.36d-117) then
        tmp = x
    else if (z <= 2.5d-40) then
        tmp = y
    else if (z <= 2.85d+57) then
        tmp = x
    else if (z <= 8d+189) then
        tmp = y / (a / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (a / z);
	double tmp;
	if (z <= -0.104) {
		tmp = t_1;
	} else if (z <= -1.45e-155) {
		tmp = y;
	} else if (z <= 1.36e-117) {
		tmp = x;
	} else if (z <= 2.5e-40) {
		tmp = y;
	} else if (z <= 2.85e+57) {
		tmp = x;
	} else if (z <= 8e+189) {
		tmp = y / (a / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (a / z)
	tmp = 0
	if z <= -0.104:
		tmp = t_1
	elif z <= -1.45e-155:
		tmp = y
	elif z <= 1.36e-117:
		tmp = x
	elif z <= 2.5e-40:
		tmp = y
	elif z <= 2.85e+57:
		tmp = x
	elif z <= 8e+189:
		tmp = y / (a / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(a / z))
	tmp = 0.0
	if (z <= -0.104)
		tmp = t_1;
	elseif (z <= -1.45e-155)
		tmp = y;
	elseif (z <= 1.36e-117)
		tmp = x;
	elseif (z <= 2.5e-40)
		tmp = y;
	elseif (z <= 2.85e+57)
		tmp = x;
	elseif (z <= 8e+189)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (a / z);
	tmp = 0.0;
	if (z <= -0.104)
		tmp = t_1;
	elseif (z <= -1.45e-155)
		tmp = y;
	elseif (z <= 1.36e-117)
		tmp = x;
	elseif (z <= 2.5e-40)
		tmp = y;
	elseif (z <= 2.85e+57)
		tmp = x;
	elseif (z <= 8e+189)
		tmp = y / (a / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.104], t$95$1, If[LessEqual[z, -1.45e-155], y, If[LessEqual[z, 1.36e-117], x, If[LessEqual[z, 2.5e-40], y, If[LessEqual[z, 2.85e+57], x, If[LessEqual[z, 8e+189], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.103999999999999995 or 8.0000000000000002e189 < z

   1. Initial program 82.1%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 52.1%

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

      1. associate-/l* 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in x around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. unsub-neg 45.3%

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

   10. Simplified 45.3%

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

   11. Taylor expanded in z around inf 31.1%

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

       1. mul-1-neg 31.1%

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

       2. associate-/l* 37.5%

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

       3. distribute-neg-frac 37.5%

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

   13. Simplified 37.5%

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

   if -0.103999999999999995 < z < -1.45000000000000005e-155 or 1.35999999999999996e-117 < z < 2.49999999999999982e-40

   1. Initial program 60.9%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in t around inf 43.7%

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

   if -1.45000000000000005e-155 < z < 1.35999999999999996e-117 or 2.49999999999999982e-40 < z < 2.8499999999999999e57

   1. Initial program 74.9%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in a around inf 48.3%

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

   if 2.8499999999999999e57 < z < 8.0000000000000002e189

   1. Initial program 69.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around -inf 58.1%

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

   6. Taylor expanded in y around inf 42.3%

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

      1. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in a around inf 38.6%

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

       1. associate-/l* 46.1%

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

   11. Simplified 46.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.104:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-40}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+189}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1e+160)
     y
     (if (<= t -1.4e+73)
       (* (- z a) (/ x t))
       (if (<= t -900.0)
         t_1
         (if (<= t -3.2e-149)
           (* y (/ (- z t) a))
           (if (<= t 8.5e+70) 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 <= -1e+160) {
		tmp = y;
	} else if (t <= -1.4e+73) {
		tmp = (z - a) * (x / t);
	} else if (t <= -900.0) {
		tmp = t_1;
	} else if (t <= -3.2e-149) {
		tmp = y * ((z - t) / a);
	} else if (t <= 8.5e+70) {
		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 <= (-1d+160)) then
        tmp = y
    else if (t <= (-1.4d+73)) then
        tmp = (z - a) * (x / t)
    else if (t <= (-900.0d0)) then
        tmp = t_1
    else if (t <= (-3.2d-149)) then
        tmp = y * ((z - t) / a)
    else if (t <= 8.5d+70) 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 <= -1e+160) {
		tmp = y;
	} else if (t <= -1.4e+73) {
		tmp = (z - a) * (x / t);
	} else if (t <= -900.0) {
		tmp = t_1;
	} else if (t <= -3.2e-149) {
		tmp = y * ((z - t) / a);
	} else if (t <= 8.5e+70) {
		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 <= -1e+160:
		tmp = y
	elif t <= -1.4e+73:
		tmp = (z - a) * (x / t)
	elif t <= -900.0:
		tmp = t_1
	elif t <= -3.2e-149:
		tmp = y * ((z - t) / a)
	elif t <= 8.5e+70:
		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 <= -1e+160)
		tmp = y;
	elseif (t <= -1.4e+73)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= -900.0)
		tmp = t_1;
	elseif (t <= -3.2e-149)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 8.5e+70)
		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 <= -1e+160)
		tmp = y;
	elseif (t <= -1.4e+73)
		tmp = (z - a) * (x / t);
	elseif (t <= -900.0)
		tmp = t_1;
	elseif (t <= -3.2e-149)
		tmp = y * ((z - t) / a);
	elseif (t <= 8.5e+70)
		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, -1e+160], y, If[LessEqual[t, -1.4e+73], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -900.0], t$95$1, If[LessEqual[t, -3.2e-149], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+70], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.00000000000000001e160 or 8.4999999999999996e70 < t

   1. Initial program 43.7%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around inf 49.2%

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

   if -1.00000000000000001e160 < t < -1.40000000000000004e73

   1. Initial program 72.1%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in t around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-*r/ 67.6%

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

      7. mul-1-neg 67.6%

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

      8. unsub-neg 67.6%

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

      9. distribute-rgt-out-- 67.6%

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

      10. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 49.6%

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

      1. associate-*l/ 53.7%

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

   10. Simplified 53.7%

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

   if -1.40000000000000004e73 < t < -900 or -3.20000000000000002e-149 < t < 8.4999999999999996e70

   1. Initial program 88.3%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in t around 0 71.8%

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

      1. associate-/l* 73.6%

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

   7. Simplified 73.6%

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

   8. Taylor expanded in x around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   10. Simplified 61.6%

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

   if -900 < t < -3.20000000000000002e-149

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*l/ 89.4%

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

      3. fma-def 89.7%

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

   3. Simplified 89.7%

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

      1. fma-udef 89.4%

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

      2. associate-/r/ 88.3%

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

      3. div-inv 86.0%

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

      4. clear-num 86.1%

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

   6. Applied egg-rr 86.1%

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

   7. Taylor expanded in y around inf 64.2%

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

      1. div-sub 64.2%

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

   9. Simplified 64.2%

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

   10. Taylor expanded in a around inf 48.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+160}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -900:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= t -1.55e+107)
     y
     (if (<= t -5.8e-22)
       x
       (if (<= t -9e-273)
         t_1
         (if (<= t 2.55e-183)
           x
           (if (<= t 2.1e-152) t_1 (if (<= t 2.7e+63) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (t <= -1.55e+107) {
		tmp = y;
	} else if (t <= -5.8e-22) {
		tmp = x;
	} else if (t <= -9e-273) {
		tmp = t_1;
	} else if (t <= 2.55e-183) {
		tmp = x;
	} else if (t <= 2.1e-152) {
		tmp = t_1;
	} else if (t <= 2.7e+63) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / a)
    if (t <= (-1.55d+107)) then
        tmp = y
    else if (t <= (-5.8d-22)) then
        tmp = x
    else if (t <= (-9d-273)) then
        tmp = t_1
    else if (t <= 2.55d-183) then
        tmp = x
    else if (t <= 2.1d-152) then
        tmp = t_1
    else if (t <= 2.7d+63) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (t <= -1.55e+107) {
		tmp = y;
	} else if (t <= -5.8e-22) {
		tmp = x;
	} else if (t <= -9e-273) {
		tmp = t_1;
	} else if (t <= 2.55e-183) {
		tmp = x;
	} else if (t <= 2.1e-152) {
		tmp = t_1;
	} else if (t <= 2.7e+63) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if t <= -1.55e+107:
		tmp = y
	elif t <= -5.8e-22:
		tmp = x
	elif t <= -9e-273:
		tmp = t_1
	elif t <= 2.55e-183:
		tmp = x
	elif t <= 2.1e-152:
		tmp = t_1
	elif t <= 2.7e+63:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (t <= -1.55e+107)
		tmp = y;
	elseif (t <= -5.8e-22)
		tmp = x;
	elseif (t <= -9e-273)
		tmp = t_1;
	elseif (t <= 2.55e-183)
		tmp = x;
	elseif (t <= 2.1e-152)
		tmp = t_1;
	elseif (t <= 2.7e+63)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	tmp = 0.0;
	if (t <= -1.55e+107)
		tmp = y;
	elseif (t <= -5.8e-22)
		tmp = x;
	elseif (t <= -9e-273)
		tmp = t_1;
	elseif (t <= 2.55e-183)
		tmp = x;
	elseif (t <= 2.1e-152)
		tmp = t_1;
	elseif (t <= 2.7e+63)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+107], y, If[LessEqual[t, -5.8e-22], x, If[LessEqual[t, -9e-273], t$95$1, If[LessEqual[t, 2.55e-183], x, If[LessEqual[t, 2.1e-152], t$95$1, If[LessEqual[t, 2.7e+63], x, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000013e107 or 2.70000000000000017e63 < t

   1. Initial program 47.0%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in t around inf 45.2%

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

   if -1.55000000000000013e107 < t < -5.8000000000000003e-22 or -8.99999999999999921e-273 < t < 2.55e-183 or 2.09999999999999999e-152 < t < 2.70000000000000017e63

   1. Initial program 87.6%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 40.9%

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

   if -5.8000000000000003e-22 < t < -8.99999999999999921e-273 or 2.55e-183 < t < 2.09999999999999999e-152

   1. Initial program 86.9%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around 0 70.6%

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

      1. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in z around inf 59.1%

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

   9. Taylor expanded in y around inf 46.0%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -1.35e+45)
     t_1
     (if (<= t 2.4e-69)
       (- x (/ (- x y) (/ a (- z t))))
       (if (<= t 8.8e-8)
         (* (- z t) (/ y (- a t)))
         (if (<= t 5e+49) (+ x (/ z (- (/ a x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -1.35e+45) {
		tmp = t_1;
	} else if (t <= 2.4e-69) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 8.8e-8) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 5e+49) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / (z - a)))
    if (t <= (-1.35d+45)) then
        tmp = t_1
    else if (t <= 2.4d-69) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (t <= 8.8d-8) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 5d+49) then
        tmp = x + (z / -(a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -1.35e+45) {
		tmp = t_1;
	} else if (t <= 2.4e-69) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 8.8e-8) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 5e+49) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -1.35e+45:
		tmp = t_1
	elif t <= 2.4e-69:
		tmp = x - ((x - y) / (a / (z - t)))
	elif t <= 8.8e-8:
		tmp = (z - t) * (y / (a - t))
	elif t <= 5e+49:
		tmp = x + (z / -(a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -1.35e+45)
		tmp = t_1;
	elseif (t <= 2.4e-69)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (t <= 8.8e-8)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 5e+49)
		tmp = Float64(x + Float64(z / Float64(-Float64(a / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -1.35e+45)
		tmp = t_1;
	elseif (t <= 2.4e-69)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (t <= 8.8e-8)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 5e+49)
		tmp = x + (z / -(a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+45], t$95$1, If[LessEqual[t, 2.4e-69], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-8], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+49], N[(x + N[(z / (-N[(a / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.34999999999999992e45 or 5.0000000000000004e49 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. div-sub 68.5%

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

      5. distribute-lft-out-- 68.5%

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

      6. associate-*r/ 68.5%

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

      7. mul-1-neg 68.5%

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

      8. unsub-neg 68.5%

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

      9. distribute-rgt-out-- 68.6%

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

      10. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

   if -1.34999999999999992e45 < t < 2.4000000000000001e-69

   1. Initial program 90.6%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in a around inf 80.5%

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

      1. associate-/l* 84.0%

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

   7. Simplified 84.0%

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

   if 2.4000000000000001e-69 < t < 8.7999999999999994e-8

   1. Initial program 73.2%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. associate-/l* 64.8%

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

      2. associate-/r/ 73.5%

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

   7. Simplified 73.5%

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

   if 8.7999999999999994e-8 < t < 5.0000000000000004e49

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 0.00022:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))))
   (if (<= t -2.4e+45)
     t_1
     (if (<= t 3.6e-67)
       (- x (/ (- x y) (/ a (- z t))))
       (if (<= t 0.00022)
         (* (- z t) (/ y (- a t)))
         (if (<= t 6.5e+52) (+ x (/ z (- (/ a x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -2.4e+45) {
		tmp = t_1;
	} else if (t <= 3.6e-67) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 0.00022) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 6.5e+52) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / z))
    if (t <= (-2.4d+45)) then
        tmp = t_1
    else if (t <= 3.6d-67) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (t <= 0.00022d0) then
        tmp = (z - t) * (y / (a - t))
    else if (t <= 6.5d+52) then
        tmp = x + (z / -(a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -2.4e+45) {
		tmp = t_1;
	} else if (t <= 3.6e-67) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (t <= 0.00022) {
		tmp = (z - t) * (y / (a - t));
	} else if (t <= 6.5e+52) {
		tmp = x + (z / -(a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	tmp = 0
	if t <= -2.4e+45:
		tmp = t_1
	elif t <= 3.6e-67:
		tmp = x - ((x - y) / (a / (z - t)))
	elif t <= 0.00022:
		tmp = (z - t) * (y / (a - t))
	elif t <= 6.5e+52:
		tmp = x + (z / -(a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (t <= -2.4e+45)
		tmp = t_1;
	elseif (t <= 3.6e-67)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (t <= 0.00022)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (t <= 6.5e+52)
		tmp = Float64(x + Float64(z / Float64(-Float64(a / x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	tmp = 0.0;
	if (t <= -2.4e+45)
		tmp = t_1;
	elseif (t <= 3.6e-67)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (t <= 0.00022)
		tmp = (z - t) * (y / (a - t));
	elseif (t <= 6.5e+52)
		tmp = x + (z / -(a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+45], t$95$1, If[LessEqual[t, 3.6e-67], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00022], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+52], N[(x + N[(z / (-N[(a / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.39999999999999989e45 or 6.49999999999999996e52 < t

   1. Initial program 53.8%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. div-sub 68.5%

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

      5. distribute-lft-out-- 68.5%

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

      6. associate-*r/ 68.5%

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

      7. mul-1-neg 68.5%

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

      8. unsub-neg 68.5%

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

      9. distribute-rgt-out-- 68.6%

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

      10. associate-/l* 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in z around inf 73.8%

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

   if -2.39999999999999989e45 < t < 3.59999999999999999e-67

   1. Initial program 90.6%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in a around inf 80.5%

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

      1. associate-/l* 84.0%

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

   7. Simplified 84.0%

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

   if 3.59999999999999999e-67 < t < 2.20000000000000008e-4

   1. Initial program 73.2%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. associate-/l* 64.8%

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

      2. associate-/r/ 73.5%

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

   7. Simplified 73.5%

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

   if 2.20000000000000008e-4 < t < 6.49999999999999996e52

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 0.00022:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{z}{-\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{t} + -1}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+64}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (+ (/ a t) -1.0))))
   (if (<= t -3.2e+161)
     t_1
     (if (<= t -2e+64)
       (* (- z a) (/ x t))
       (if (<= t 6.1e-117)
         (+ x (/ (* y z) a))
         (if (<= t 7.2e+62) (* x (- 1.0 (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double tmp;
	if (t <= -3.2e+161) {
		tmp = t_1;
	} else if (t <= -2e+64) {
		tmp = (z - a) * (x / t);
	} else if (t <= 6.1e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 7.2e+62) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y / ((a / t) + (-1.0d0))
    if (t <= (-3.2d+161)) then
        tmp = t_1
    else if (t <= (-2d+64)) then
        tmp = (z - a) * (x / t)
    else if (t <= 6.1d-117) then
        tmp = x + ((y * z) / a)
    else if (t <= 7.2d+62) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double tmp;
	if (t <= -3.2e+161) {
		tmp = t_1;
	} else if (t <= -2e+64) {
		tmp = (z - a) * (x / t);
	} else if (t <= 6.1e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 7.2e+62) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((a / t) + -1.0)
	tmp = 0
	if t <= -3.2e+161:
		tmp = t_1
	elif t <= -2e+64:
		tmp = (z - a) * (x / t)
	elif t <= 6.1e-117:
		tmp = x + ((y * z) / a)
	elif t <= 7.2e+62:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(a / t) + -1.0))
	tmp = 0.0
	if (t <= -3.2e+161)
		tmp = t_1;
	elseif (t <= -2e+64)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= 6.1e-117)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 7.2e+62)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((a / t) + -1.0);
	tmp = 0.0;
	if (t <= -3.2e+161)
		tmp = t_1;
	elseif (t <= -2e+64)
		tmp = (z - a) * (x / t);
	elseif (t <= 6.1e-117)
		tmp = x + ((y * z) / a);
	elseif (t <= 7.2e+62)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+161], t$95$1, If[LessEqual[t, -2e+64], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e-117], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+62], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.20000000000000002e161 or 7.2e62 < t

   1. Initial program 43.7%

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

      1. +-commutative 43.7%

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

      2. associate-*l/ 64.7%

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

      3. fma-def 64.7%

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

   3. Simplified 64.7%

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

      1. fma-udef 64.7%

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

      2. associate-/r/ 72.0%

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

      3. div-inv 72.0%

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

      4. clear-num 72.0%

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

   6. Applied egg-rr 72.0%

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

   7. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   10. Taylor expanded in z around 0 37.4%

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

       1. mul-1-neg 37.4%

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

       2. *-commutative 37.4%

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

       3. associate-/l* 52.9%

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

       4. div-sub 52.9%

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

       5. sub-neg 52.9%

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

       6. *-inverses 52.9%

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

       7. metadata-eval 52.9%

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

   12. Simplified 52.9%

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

   if -3.20000000000000002e161 < t < -2.00000000000000004e64

   1. Initial program 76.5%

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

      1. associate-*l/ 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in t around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. associate-*r/ 68.7%

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

      3. associate-*r/ 68.7%

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

      4. div-sub 68.7%

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

      5. distribute-lft-out-- 68.7%

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

      6. associate-*r/ 68.7%

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

      7. mul-1-neg 68.7%

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

      8. unsub-neg 68.7%

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

      9. distribute-rgt-out-- 68.7%

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

      10. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in y around 0 50.0%

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

      1. associate-*l/ 53.4%

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

   10. Simplified 53.4%

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

   if -2.00000000000000004e64 < t < 6.10000000000000002e-117

   1. Initial program 90.2%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 67.1%

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

   if 6.10000000000000002e-117 < t < 7.2e62

   1. Initial program 79.6%

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

      1. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in t around 0 49.3%

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

      1. associate-/l* 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in x around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   10. Simplified 59.4%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+161}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+64}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{t} + -1}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (+ (/ a t) -1.0))))
   (if (<= t -8.4e+189)
     t_1
     (if (<= t -1.2e+45)
       (/ (- z) (/ t (- y x)))
       (if (<= t 6e-117)
         (+ x (/ (* y z) a))
         (if (<= t 2.2e+71) (* x (- 1.0 (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double tmp;
	if (t <= -8.4e+189) {
		tmp = t_1;
	} else if (t <= -1.2e+45) {
		tmp = -z / (t / (y - x));
	} else if (t <= 6e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.2e+71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y / ((a / t) + (-1.0d0))
    if (t <= (-8.4d+189)) then
        tmp = t_1
    else if (t <= (-1.2d+45)) then
        tmp = -z / (t / (y - x))
    else if (t <= 6d-117) then
        tmp = x + ((y * z) / a)
    else if (t <= 2.2d+71) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double tmp;
	if (t <= -8.4e+189) {
		tmp = t_1;
	} else if (t <= -1.2e+45) {
		tmp = -z / (t / (y - x));
	} else if (t <= 6e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.2e+71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((a / t) + -1.0)
	tmp = 0
	if t <= -8.4e+189:
		tmp = t_1
	elif t <= -1.2e+45:
		tmp = -z / (t / (y - x))
	elif t <= 6e-117:
		tmp = x + ((y * z) / a)
	elif t <= 2.2e+71:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(a / t) + -1.0))
	tmp = 0.0
	if (t <= -8.4e+189)
		tmp = t_1;
	elseif (t <= -1.2e+45)
		tmp = Float64(Float64(-z) / Float64(t / Float64(y - x)));
	elseif (t <= 6e-117)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 2.2e+71)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((a / t) + -1.0);
	tmp = 0.0;
	if (t <= -8.4e+189)
		tmp = t_1;
	elseif (t <= -1.2e+45)
		tmp = -z / (t / (y - x));
	elseif (t <= 6e-117)
		tmp = x + ((y * z) / a);
	elseif (t <= 2.2e+71)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.4e+189], t$95$1, If[LessEqual[t, -1.2e+45], N[((-z) / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-117], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+71], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.3999999999999997e189 or 2.19999999999999995e71 < t

   1. Initial program 43.9%

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

      1. +-commutative 43.9%

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

      2. associate-*l/ 66.8%

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

      3. fma-def 66.8%

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

   3. Simplified 66.8%

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

      1. fma-udef 66.8%

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

      2. associate-/r/ 73.8%

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

      3. div-inv 73.8%

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

      4. clear-num 73.8%

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

   6. Applied egg-rr 73.8%

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

   7. Taylor expanded in y around inf 67.7%

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

      1. div-sub 67.7%

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

   9. Simplified 67.7%

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

   10. Taylor expanded in z around 0 38.1%

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

       1. mul-1-neg 38.1%

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

       2. *-commutative 38.1%

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

       3. associate-/l* 55.1%

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

       4. div-sub 55.1%

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

       5. sub-neg 55.1%

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

       6. *-inverses 55.1%

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

       7. metadata-eval 55.1%

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

   12. Simplified 55.1%

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

   if -8.3999999999999997e189 < t < -1.19999999999999995e45

   1. Initial program 69.7%

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

      1. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in t around inf 67.5%

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

      1. associate--l+ 67.5%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

      6. associate-*r/ 67.5%

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

      7. mul-1-neg 67.5%

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

      8. unsub-neg 67.5%

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

      9. distribute-rgt-out-- 67.5%

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

      10. associate-/l* 75.3%

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

   7. Simplified 75.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

      2. associate-/l* 49.0%

         \[\leadsto -\color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   10. Simplified 49.0%

       \[\leadsto \color{blue}{-\frac{z}{\frac{t}{y - x}}} \]

   if -1.19999999999999995e45 < t < 5.99999999999999982e-117

   1. Initial program 90.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 78.5%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 78.9%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in y around inf 68.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]

   if 5.99999999999999982e-117 < t < 2.19999999999999995e71

   1. Initial program 79.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.3%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.0%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 54.0%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 59.4%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 59.4%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+189}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 46.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -240:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.25e+138)
     y
     (if (<= t -240.0)
       t_1
       (if (<= t -5.5e-149) (* y (/ (- z t) a)) (if (<= t 1.6e+71) 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 <= -2.25e+138) {
		tmp = y;
	} else if (t <= -240.0) {
		tmp = t_1;
	} else if (t <= -5.5e-149) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.6e+71) {
		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 <= (-2.25d+138)) then
        tmp = y
    else if (t <= (-240.0d0)) then
        tmp = t_1
    else if (t <= (-5.5d-149)) then
        tmp = y * ((z - t) / a)
    else if (t <= 1.6d+71) 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 <= -2.25e+138) {
		tmp = y;
	} else if (t <= -240.0) {
		tmp = t_1;
	} else if (t <= -5.5e-149) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.6e+71) {
		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 <= -2.25e+138:
		tmp = y
	elif t <= -240.0:
		tmp = t_1
	elif t <= -5.5e-149:
		tmp = y * ((z - t) / a)
	elif t <= 1.6e+71:
		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 <= -2.25e+138)
		tmp = y;
	elseif (t <= -240.0)
		tmp = t_1;
	elseif (t <= -5.5e-149)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 1.6e+71)
		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 <= -2.25e+138)
		tmp = y;
	elseif (t <= -240.0)
		tmp = t_1;
	elseif (t <= -5.5e-149)
		tmp = y * ((z - t) / a);
	elseif (t <= 1.6e+71)
		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, -2.25e+138], y, If[LessEqual[t, -240.0], t$95$1, If[LessEqual[t, -5.5e-149], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+71], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.24999999999999991e138 or 1.60000000000000012e71 < t

   1. Initial program 44.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.1%

      \[\leadsto \color{blue}{y} \]

   if -2.24999999999999991e138 < t < -240 or -5.50000000000000043e-149 < t < 1.60000000000000012e71

   1. Initial program 87.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.7%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 69.6%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 69.6%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 58.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 58.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -240 < t < -5.50000000000000043e-149

   1. Initial program 86.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 86.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 89.4%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 89.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 89.4%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 88.3%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 86.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 86.1%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 86.1%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 64.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 64.2%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 64.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in a around inf 48.9%

       \[\leadsto y \cdot \color{blue}{\frac{z - t}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -240:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= t -2e+161)
     t_1
     (if (<= t -6.5e+63)
       (* (- z a) (/ x t))
       (if (<= t 4.5e-117)
         (+ x (/ (* y z) a))
         (if (<= t 1.55e+50) (* x (- 1.0 (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -2e+161) {
		tmp = t_1;
	} else if (t <= -6.5e+63) {
		tmp = (z - a) * (x / t);
	} else if (t <= 4.5e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.55e+50) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (t <= (-2d+161)) then
        tmp = t_1
    else if (t <= (-6.5d+63)) then
        tmp = (z - a) * (x / t)
    else if (t <= 4.5d-117) then
        tmp = x + ((y * z) / a)
    else if (t <= 1.55d+50) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -2e+161) {
		tmp = t_1;
	} else if (t <= -6.5e+63) {
		tmp = (z - a) * (x / t);
	} else if (t <= 4.5e-117) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.55e+50) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if t <= -2e+161:
		tmp = t_1
	elif t <= -6.5e+63:
		tmp = (z - a) * (x / t)
	elif t <= 4.5e-117:
		tmp = x + ((y * z) / a)
	elif t <= 1.55e+50:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (t <= -2e+161)
		tmp = t_1;
	elseif (t <= -6.5e+63)
		tmp = Float64(Float64(z - a) * Float64(x / t));
	elseif (t <= 4.5e-117)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 1.55e+50)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (t <= -2e+161)
		tmp = t_1;
	elseif (t <= -6.5e+63)
		tmp = (z - a) * (x / t);
	elseif (t <= 4.5e-117)
		tmp = x + ((y * z) / a);
	elseif (t <= 1.55e+50)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+161], t$95$1, If[LessEqual[t, -6.5e+63], N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-117], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+50], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0000000000000001e161 or 1.55000000000000001e50 < t

   1. Initial program 45.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 65.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 65.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 72.8%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 72.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 72.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 69.2%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in a around 0 64.2%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{t}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 64.2%

          \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot \left(z - t\right)}{t}} \]

       2. neg-mul-1 64.2%

          \[\leadsto y \cdot \frac{\color{blue}{-\left(z - t\right)}}{t} \]

   12. Simplified 64.2%

       \[\leadsto y \cdot \color{blue}{\frac{-\left(z - t\right)}{t}} \]

   if -2.0000000000000001e161 < t < -6.49999999999999992e63

   1. Initial program 76.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 68.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 68.7%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 68.7%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 68.7%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 68.7%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 68.7%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 68.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 68.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 68.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 72.5%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in y around 0 50.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*l/ 53.4%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \left(z - a\right)} \]

   10. Simplified 53.4%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot \left(z - a\right)} \]

   if -6.49999999999999992e63 < t < 4.49999999999999969e-117

   1. Initial program 90.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 76.8%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 78.0%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 78.0%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in y around inf 67.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]

   if 4.49999999999999969e-117 < t < 1.55000000000000001e50

   1. Initial program 78.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.3%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.1%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 54.1%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 59.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 59.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 59.9%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+63}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.55e-27)
     t_1
     (if (<= x 2.5e+38)
       (* y (/ (- z t) (- a t)))
       (if (<= x 1.25e+79)
         (/ (- z) (/ t (- y x)))
         (if (<= x 3.45e+115) (* y (/ (- t z) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.55e-27) {
		tmp = t_1;
	} else if (x <= 2.5e+38) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.25e+79) {
		tmp = -z / (t / (y - x));
	} else if (x <= 3.45e+115) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-1.55d-27)) then
        tmp = t_1
    else if (x <= 2.5d+38) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 1.25d+79) then
        tmp = -z / (t / (y - x))
    else if (x <= 3.45d+115) then
        tmp = y * ((t - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.55e-27) {
		tmp = t_1;
	} else if (x <= 2.5e+38) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.25e+79) {
		tmp = -z / (t / (y - x));
	} else if (x <= 3.45e+115) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.55e-27:
		tmp = t_1
	elif x <= 2.5e+38:
		tmp = y * ((z - t) / (a - t))
	elif x <= 1.25e+79:
		tmp = -z / (t / (y - x))
	elif x <= 3.45e+115:
		tmp = y * ((t - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.55e-27)
		tmp = t_1;
	elseif (x <= 2.5e+38)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 1.25e+79)
		tmp = Float64(Float64(-z) / Float64(t / Float64(y - x)));
	elseif (x <= 3.45e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.55e-27)
		tmp = t_1;
	elseif (x <= 2.5e+38)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 1.25e+79)
		tmp = -z / (t / (y - x));
	elseif (x <= 3.45e+115)
		tmp = y * ((t - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e-27], t$95$1, If[LessEqual[x, 2.5e+38], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+79], N[((-z) / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.45e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.5499999999999999e-27 or 3.44999999999999983e115 < x

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 56.5%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.8%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 62.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 62.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 62.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -1.5499999999999999e-27 < x < 2.49999999999999985e38

   1. Initial program 84.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 86.4%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 86.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 86.4%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 92.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 91.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 92.0%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 92.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 74.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 74.9%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 74.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 2.49999999999999985e38 < x < 1.25e79

   1. Initial program 42.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 60.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 62.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 62.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 62.0%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 62.0%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 62.0%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 62.0%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 62.0%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 62.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 62.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 62.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 80.5%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(y - x\right)}{t}} \]

      2. associate-/l* 62.1%

         \[\leadsto -\color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   10. Simplified 62.1%

       \[\leadsto \color{blue}{-\frac{z}{\frac{t}{y - x}}} \]

   if 1.25e79 < x < 3.44999999999999983e115

   1. Initial program 23.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 23.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 22.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 21.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 21.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 22.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 41.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 41.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 41.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 41.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 81.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 81.6%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 81.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in a around 0 81.6%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{t}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 81.6%

          \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot \left(z - t\right)}{t}} \]

       2. neg-mul-1 81.6%

          \[\leadsto y \cdot \frac{\color{blue}{-\left(z - t\right)}}{t} \]

   12. Simplified 81.6%

       \[\leadsto y \cdot \color{blue}{\frac{-\left(z - t\right)}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.3e-27)
     t_1
     (if (<= x 1.1e+36)
       (* y (/ (- z t) (- a t)))
       (if (<= x 1.26e+81)
         (* z (/ (- y x) (- a t)))
         (if (<= x 2.1e+115) (* y (/ (- t z) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.3e-27) {
		tmp = t_1;
	} else if (x <= 1.1e+36) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.26e+81) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 2.1e+115) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (x <= (-1.3d-27)) then
        tmp = t_1
    else if (x <= 1.1d+36) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 1.26d+81) then
        tmp = z * ((y - x) / (a - t))
    else if (x <= 2.1d+115) then
        tmp = y * ((t - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.3e-27) {
		tmp = t_1;
	} else if (x <= 1.1e+36) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.26e+81) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 2.1e+115) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.3e-27:
		tmp = t_1
	elif x <= 1.1e+36:
		tmp = y * ((z - t) / (a - t))
	elif x <= 1.26e+81:
		tmp = z * ((y - x) / (a - t))
	elif x <= 2.1e+115:
		tmp = y * ((t - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.3e-27)
		tmp = t_1;
	elseif (x <= 1.1e+36)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 1.26e+81)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (x <= 2.1e+115)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.3e-27)
		tmp = t_1;
	elseif (x <= 1.1e+36)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 1.26e+81)
		tmp = z * ((y - x) / (a - t));
	elseif (x <= 2.1e+115)
		tmp = y * ((t - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e-27], t$95$1, If[LessEqual[x, 1.1e+36], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.26e+81], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+115], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000009e-27 or 2.10000000000000003e115 < x

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 56.5%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.8%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 62.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 62.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 62.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -1.30000000000000009e-27 < x < 1.1e36

   1. Initial program 83.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 83.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 86.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 86.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 86.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 92.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 91.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 91.9%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 74.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 74.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 74.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 1.1e36 < x < 1.25999999999999996e81

   1. Initial program 52.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 67.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.5%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 75.5%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 75.5%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if 1.25999999999999996e81 < x < 2.10000000000000003e115

   1. Initial program 23.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 23.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 22.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 21.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 21.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 22.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 41.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 41.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 41.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 41.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 81.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 81.6%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 81.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   10. Taylor expanded in a around 0 81.6%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{t}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 81.6%

          \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot \left(z - t\right)}{t}} \]

       2. neg-mul-1 81.6%

          \[\leadsto y \cdot \frac{\color{blue}{-\left(z - t\right)}}{t} \]

   12. Simplified 81.6%

       \[\leadsto y \cdot \color{blue}{\frac{-\left(z - t\right)}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-196} \lor \neg \left(a \leq 2.45 \cdot 10^{-127}\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.55e-196) (not (<= a 2.45e-127)))
   (- x (* (- z t) (/ (- x y) (- a t))))
   (+ y (/ (- x y) (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.55e-196) || !(a <= 2.45e-127)) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.55d-196)) .or. (.not. (a <= 2.45d-127))) then
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.55e-196) || !(a <= 2.45e-127)) {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.55e-196) or not (a <= 2.45e-127):
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.55e-196) || !(a <= 2.45e-127))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.55e-196) || ~((a <= 2.45e-127)))
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.55e-196], N[Not[LessEqual[a, 2.45e-127]], $MachinePrecision]], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.55000000000000001e-196 or 2.45e-127 < a

   1. Initial program 77.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   if -2.55000000000000001e-196 < a < 2.45e-127

   1. Initial program 62.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 88.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 88.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 88.4%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 88.4%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 88.4%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 88.4%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 88.4%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 88.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 88.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 88.4%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 93.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 93.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-196} \lor \neg \left(a \leq 2.45 \cdot 10^{-127}\right):\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+138) y (if (<= t 2.6e+71) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+138) {
		tmp = y;
	} else if (t <= 2.6e+71) {
		tmp = x * (1.0 - (z / 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 <= (-2.3d+138)) then
        tmp = y
    else if (t <= 2.6d+71) then
        tmp = x * (1.0d0 - (z / 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 <= -2.3e+138) {
		tmp = y;
	} else if (t <= 2.6e+71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+138:
		tmp = y
	elif t <= 2.6e+71:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+138)
		tmp = y;
	elseif (t <= 2.6e+71)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+138)
		tmp = y;
	elseif (t <= 2.6e+71)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+138], y, If[LessEqual[t, 2.6e+71], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000008e138 or 2.59999999999999991e71 < t

   1. Initial program 44.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.1%

      \[\leadsto \color{blue}{y} \]

   if -2.30000000000000008e138 < t < 2.59999999999999991e71

   1. Initial program 87.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.2%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.5%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 68.5%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in x around inf 54.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 54.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   10. Simplified 54.3%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+110) y (if (<= t 5.5e+66) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+110) {
		tmp = y;
	} else if (t <= 5.5e+66) {
		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 <= (-2.8d+110)) then
        tmp = y
    else if (t <= 5.5d+66) 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 <= -2.8e+110) {
		tmp = y;
	} else if (t <= 5.5e+66) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+110:
		tmp = y
	elif t <= 5.5e+66:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+110)
		tmp = y;
	elseif (t <= 5.5e+66)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+110)
		tmp = y;
	elseif (t <= 5.5e+66)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+110], y, If[LessEqual[t, 5.5e+66], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999987e110 or 5.5e66 < t

   1. Initial program 47.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.2%

      \[\leadsto \color{blue}{y} \]

   if -2.79999999999999987e110 < t < 5.5e66

   1. Initial program 87.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 34.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 24.5% 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 73.8%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 80.5%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 80.5%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 26.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 26.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 87.0% 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 2024023 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))