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

Percentage Accurate: 68.9% → 85.9%

Time: 16.8s

Alternatives: 26

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: 68.9% 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: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+186}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+120} \lor \neg \left(t \leq 1.35 \cdot 10^{+138}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -1.75e+258)
     t_1
     (if (<= t -1.05e+186)
       (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a)))))
       (if (or (<= t -3.2e+120) (not (<= t 1.35e+138)))
         t_1
         (- x (/ (- z t) (/ (- a t) (- x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.75e+258) {
		tmp = t_1;
	} else if (t <= -1.05e+186) {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	} else if ((t <= -3.2e+120) || !(t <= 1.35e+138)) {
		tmp = t_1;
	} else {
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z - a) * ((x - y) / t))
    if (t <= (-1.75d+258)) then
        tmp = t_1
    else if (t <= (-1.05d+186)) then
        tmp = x + ((z - t) * ((y - x) * ((-1.0d0) / (t - a))))
    else if ((t <= (-3.2d+120)) .or. (.not. (t <= 1.35d+138))) then
        tmp = t_1
    else
        tmp = x - ((z - t) / ((a - t) / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.75e+258) {
		tmp = t_1;
	} else if (t <= -1.05e+186) {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	} else if ((t <= -3.2e+120) || !(t <= 1.35e+138)) {
		tmp = t_1;
	} else {
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -1.75e+258:
		tmp = t_1
	elif t <= -1.05e+186:
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	elif (t <= -3.2e+120) or not (t <= 1.35e+138):
		tmp = t_1
	else:
		tmp = x - ((z - t) / ((a - t) / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -1.75e+258)
		tmp = t_1;
	elseif (t <= -1.05e+186)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))));
	elseif ((t <= -3.2e+120) || !(t <= 1.35e+138))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -1.75e+258)
		tmp = t_1;
	elseif (t <= -1.05e+186)
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	elseif ((t <= -3.2e+120) || ~((t <= 1.35e+138)))
		tmp = t_1;
	else
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+258], t$95$1, If[LessEqual[t, -1.05e+186], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.2e+120], N[Not[LessEqual[t, 1.35e+138]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e258 or -1.05e186 < t < -3.19999999999999982e120 or 1.35000000000000004e138 < t

   1. Initial program 21.4%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. distribute-lft-out-- 66.0%

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

      3. div-sub 66.0%

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

      4. mul-1-neg 66.0%

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

      5. unsub-neg 66.0%

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

      6. div-sub 66.0%

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

      7. associate-/l* 73.3%

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

      8. associate-/l* 93.6%

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

      9. distribute-rgt-out-- 93.6%

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

   5. Simplified 93.6%

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

   if -1.75e258 < t < -1.05e186

   1. Initial program 44.9%

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

      1. div-inv 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*l* 80.5%

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

   4. Applied egg-rr 80.5%

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

   if -3.19999999999999982e120 < t < 1.35000000000000004e138

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. add-cube-cbrt 82.5%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 91.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 91.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 91.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{a - t}} \cdot \frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \]

      2. clear-num 91.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\sqrt[3]{a - t}}{y - x}}} \cdot \frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \]

      3. frac-times 89.4%

         \[\leadsto x + \color{blue}{\frac{1 \cdot \left(z - t\right)}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}} \]

      4. *-un-lft-identity 89.4%

         \[\leadsto x + \frac{\color{blue}{z - t}}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}} \]

   6. Applied egg-rr 89.4%

      \[\leadsto x + \color{blue}{\frac{z - t}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 89.4%

         \[\leadsto x + \frac{z - t}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}{y - x}}} \]

      2. unpow2 89.4%

         \[\leadsto x + \frac{z - t}{\frac{\sqrt[3]{a - t} \cdot \color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right)}}{y - x}} \]

      3. rem-3cbrt-rft 90.1%

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

   8. Simplified 90.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+258}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+186}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+120} \lor \neg \left(t \leq 1.35 \cdot 10^{+138}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ t_2 := \sqrt[3]{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{t\_2} \cdot \frac{t - z}{{t\_2}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))) (t_2 (cbrt (- a t))))
   (if (<= t_1 -2e-253)
     (fma (- y x) (/ (- z t) (- a t)) x)
     (if (<= t_1 0.0)
       (+ y (/ (* (- y x) (- a z)) t))
       (- x (* (/ (- y x) t_2) (/ (- t z) (pow t_2 2.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double t_2 = cbrt((a - t));
	double tmp;
	if (t_1 <= -2e-253) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x - (((y - x) / t_2) * ((t - z) / pow(t_2, 2.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	t_2 = cbrt(Float64(a - t))
	tmp = 0.0
	if (t_1 <= -2e-253)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / t_2) * Float64(Float64(t - z) / (t_2 ^ 2.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(a - t), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[t$95$1, -2e-253], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - x), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[Power[t$95$2, 2.0], $MachinePrecision]), $MachinePrecision]), $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-253

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-/l* 89.0%

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

      3. fma-define 89.0%

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

   3. Simplified 89.0%

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

   if -2.0000000000000001e-253 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. *-commutative 4.7%

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

      2. add-cube-cbrt 5.4%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 5.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 5.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 5.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

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

   1. Initial program 72.3%

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

      1. *-commutative 72.3%

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

      2. add-cube-cbrt 71.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 87.6%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 87.6%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 87.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{\sqrt[3]{a - t}} \cdot \frac{t - z}{{\left(\sqrt[3]{a - t}\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+258} \lor \neg \left(t \leq 2.45 \cdot 10^{+131}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+258) (not (<= t 2.45e+131)))
   (+ y (* (- z a) (/ (- x y) t)))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+258) || !(t <= 2.45e+131)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+258) || !(t <= 2.45e+131))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+258], N[Not[LessEqual[t, 2.45e+131]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e258 or 2.45000000000000016e131 < t

   1. Initial program 16.3%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. distribute-lft-out-- 62.9%

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

      3. div-sub 62.9%

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

      4. mul-1-neg 62.9%

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

      5. unsub-neg 62.9%

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

      6. div-sub 62.9%

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

      7. associate-/l* 70.4%

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

      8. associate-/l* 94.3%

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

      9. distribute-rgt-out-- 94.3%

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

   5. Simplified 94.3%

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

   if -2.4e258 < t < 2.45000000000000016e131

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 88.9%

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

      3. fma-define 88.9%

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

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+258} \lor \neg \left(t \leq 2.45 \cdot 10^{+131}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-200}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-253)
       t_2
       (if (<= t_2 1e-200)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 5e+306) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-253) {
		tmp = t_2;
	} else if (t_2 <= 1e-200) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+306) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-253) {
		tmp = t_2;
	} else if (t_2 <= 1e-200) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+306) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-253:
		tmp = t_2
	elif t_2 <= 1e-200:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 5e+306:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-253)
		tmp = t_2;
	elseif (t_2 <= 1e-200)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+306)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-253)
		tmp = t_2;
	elseif (t_2 <= 1e-200)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 5e+306)
		tmp = t_2;
	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 - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-253], t$95$2, If[LessEqual[t$95$2, 1e-200], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 4.99999999999999993e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 39.0%

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

   3. Taylor expanded in t around inf 50.3%

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

      1. associate--l+ 50.3%

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

      2. distribute-lft-out-- 50.3%

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

      3. div-sub 52.1%

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

      4. mul-1-neg 52.1%

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

      5. unsub-neg 52.1%

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

      6. div-sub 50.3%

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

      7. associate-/l* 59.5%

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

      8. associate-/l* 69.1%

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

      9. distribute-rgt-out-- 74.6%

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

   5. Simplified 74.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.0000000000000001e-253 or 9.9999999999999998e-201 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.99999999999999993e306

   1. Initial program 98.4%

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

   if -2.0000000000000001e-253 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999998e-201

   1. Initial program 4.8%

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

      1. *-commutative 4.8%

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

      2. add-cube-cbrt 5.4%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 10.0%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 10.0%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 10.0%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in t around inf 95.8%

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

      1. associate--l+ 95.8%

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

      2. associate-*r/ 95.8%

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

      3. associate-*r/ 95.8%

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

      4. mul-1-neg 95.8%

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

      5. div-sub 95.8%

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

      6. mul-1-neg 95.8%

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

      7. distribute-lft-out-- 95.8%

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

      8. associate-*r/ 95.8%

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

      9. mul-1-neg 95.8%

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

      10. unsub-neg 95.8%

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

      11. distribute-rgt-out-- 95.8%

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

   7. Simplified 95.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{-200}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 160 \lor \neg \left(t \leq 1.1 \cdot 10^{+134}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t)))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -1.9e+258)
     t_2
     (if (<= t -1.7e+186)
       t_1
       (if (<= t -3.5e+77)
         t_2
         (if (<= t 6.8e-84)
           (- x (* z (/ (- y x) (- t a))))
           (if (or (<= t 160.0) (not (<= t 1.1e+134))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.9e+258) {
		tmp = t_2;
	} else if (t <= -1.7e+186) {
		tmp = t_1;
	} else if (t <= -3.5e+77) {
		tmp = t_2;
	} else if (t <= 6.8e-84) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if ((t <= 160.0) || !(t <= 1.1e+134)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-1.9d+258)) then
        tmp = t_2
    else if (t <= (-1.7d+186)) then
        tmp = t_1
    else if (t <= (-3.5d+77)) then
        tmp = t_2
    else if (t <= 6.8d-84) then
        tmp = x - (z * ((y - x) / (t - a)))
    else if ((t <= 160.0d0) .or. (.not. (t <= 1.1d+134))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -1.9e+258) {
		tmp = t_2;
	} else if (t <= -1.7e+186) {
		tmp = t_1;
	} else if (t <= -3.5e+77) {
		tmp = t_2;
	} else if (t <= 6.8e-84) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if ((t <= 160.0) || !(t <= 1.1e+134)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -1.9e+258:
		tmp = t_2
	elif t <= -1.7e+186:
		tmp = t_1
	elif t <= -3.5e+77:
		tmp = t_2
	elif t <= 6.8e-84:
		tmp = x - (z * ((y - x) / (t - a)))
	elif (t <= 160.0) or not (t <= 1.1e+134):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -1.9e+258)
		tmp = t_2;
	elseif (t <= -1.7e+186)
		tmp = t_1;
	elseif (t <= -3.5e+77)
		tmp = t_2;
	elseif (t <= 6.8e-84)
		tmp = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))));
	elseif ((t <= 160.0) || !(t <= 1.1e+134))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -1.9e+258)
		tmp = t_2;
	elseif (t <= -1.7e+186)
		tmp = t_1;
	elseif (t <= -3.5e+77)
		tmp = t_2;
	elseif (t <= 6.8e-84)
		tmp = x - (z * ((y - x) / (t - a)));
	elseif ((t <= 160.0) || ~((t <= 1.1e+134)))
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+258], t$95$2, If[LessEqual[t, -1.7e+186], t$95$1, If[LessEqual[t, -3.5e+77], t$95$2, If[LessEqual[t, 6.8e-84], N[(x - N[(z * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 160.0], N[Not[LessEqual[t, 1.1e+134]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000004e258 or -1.70000000000000003e186 < t < -3.5000000000000001e77 or 6.80000000000000042e-84 < t < 160 or 1.1e134 < t

   1. Initial program 34.9%

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

   3. Taylor expanded in t around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. distribute-lft-out-- 70.4%

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

      3. div-sub 70.4%

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

      4. mul-1-neg 70.4%

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

      5. unsub-neg 70.4%

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

      6. div-sub 70.4%

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

      7. associate-/l* 77.0%

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

      8. associate-/l* 91.4%

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

      9. distribute-rgt-out-- 91.4%

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

   5. Simplified 91.4%

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

   if -1.90000000000000004e258 < t < -1.70000000000000003e186 or 160 < t < 1.1e134

   1. Initial program 56.8%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -3.5000000000000001e77 < t < 6.80000000000000042e-84

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 82.0%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+258}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+77}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 160 \lor \neg \left(t \leq 1.1 \cdot 10^{+134}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t)))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -4e+258)
     t_2
     (if (<= t -7e+183)
       t_1
       (if (<= t -7.4e+77)
         t_2
         (if (<= t 6.8e-84)
           (- x (* z (/ (- y x) (- t a))))
           (if (<= t 7e+66)
             (+ y (/ (* (- y x) (- a z)) t))
             (if (<= t 1.1e+137) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -4e+258) {
		tmp = t_2;
	} else if (t <= -7e+183) {
		tmp = t_1;
	} else if (t <= -7.4e+77) {
		tmp = t_2;
	} else if (t <= 6.8e-84) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if (t <= 7e+66) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.1e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-4d+258)) then
        tmp = t_2
    else if (t <= (-7d+183)) then
        tmp = t_1
    else if (t <= (-7.4d+77)) then
        tmp = t_2
    else if (t <= 6.8d-84) then
        tmp = x - (z * ((y - x) / (t - a)))
    else if (t <= 7d+66) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t <= 1.1d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -4e+258) {
		tmp = t_2;
	} else if (t <= -7e+183) {
		tmp = t_1;
	} else if (t <= -7.4e+77) {
		tmp = t_2;
	} else if (t <= 6.8e-84) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if (t <= 7e+66) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.1e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -4e+258:
		tmp = t_2
	elif t <= -7e+183:
		tmp = t_1
	elif t <= -7.4e+77:
		tmp = t_2
	elif t <= 6.8e-84:
		tmp = x - (z * ((y - x) / (t - a)))
	elif t <= 7e+66:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t <= 1.1e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -4e+258)
		tmp = t_2;
	elseif (t <= -7e+183)
		tmp = t_1;
	elseif (t <= -7.4e+77)
		tmp = t_2;
	elseif (t <= 6.8e-84)
		tmp = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))));
	elseif (t <= 7e+66)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t <= 1.1e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -4e+258)
		tmp = t_2;
	elseif (t <= -7e+183)
		tmp = t_1;
	elseif (t <= -7.4e+77)
		tmp = t_2;
	elseif (t <= 6.8e-84)
		tmp = x - (z * ((y - x) / (t - a)));
	elseif (t <= 7e+66)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t <= 1.1e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+258], t$95$2, If[LessEqual[t, -7e+183], t$95$1, If[LessEqual[t, -7.4e+77], t$95$2, If[LessEqual[t, 6.8e-84], N[(x - N[(z * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+66], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+137], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.00000000000000023e258 or -6.99999999999999974e183 < t < -7.3999999999999999e77 or 1.10000000000000008e137 < t

   1. Initial program 23.9%

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

   3. Taylor expanded in t around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. distribute-lft-out-- 67.1%

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

      3. div-sub 67.1%

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

      4. mul-1-neg 67.1%

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

      5. unsub-neg 67.1%

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

      6. div-sub 67.1%

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

      7. associate-/l* 75.6%

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

      8. associate-/l* 93.8%

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

      9. distribute-rgt-out-- 93.8%

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

   5. Simplified 93.8%

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

   if -4.00000000000000023e258 < t < -6.99999999999999974e183 or 6.9999999999999994e66 < t < 1.10000000000000008e137

   1. Initial program 50.1%

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

   3. Taylor expanded in y around inf 58.6%

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

      1. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   if -7.3999999999999999e77 < t < 6.80000000000000042e-84

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 82.0%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

   if 6.80000000000000042e-84 < t < 6.9999999999999994e66

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

      2. add-cube-cbrt 78.1%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 75.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 75.9%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 75.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in t around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. associate-*r/ 78.9%

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

      3. associate-*r/ 78.9%

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

      4. mul-1-neg 78.9%

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

      5. div-sub 78.9%

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

      6. mul-1-neg 78.9%

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

      7. distribute-lft-out-- 78.9%

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

      8. associate-*r/ 78.9%

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

      9. mul-1-neg 78.9%

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

      10. unsub-neg 78.9%

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

      11. distribute-rgt-out-- 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+258}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+183}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+77}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -3e+77)
     y
     (if (<= t -6.4e-291)
       t_1
       (if (<= t 1.95e-205)
         (* z (/ (- y x) a))
         (if (<= t 1.75e-45)
           t_1
           (if (<= t 2.6e+59)
             (* y (/ z (- a t)))
             (if (<= t 5.8e+125) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -3e+77) {
		tmp = y;
	} else if (t <= -6.4e-291) {
		tmp = t_1;
	} else if (t <= 1.95e-205) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.75e-45) {
		tmp = t_1;
	} else if (t <= 2.6e+59) {
		tmp = y * (z / (a - t));
	} else if (t <= 5.8e+125) {
		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 + (y * (z / a))
    if (t <= (-3d+77)) then
        tmp = y
    else if (t <= (-6.4d-291)) then
        tmp = t_1
    else if (t <= 1.95d-205) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.75d-45) then
        tmp = t_1
    else if (t <= 2.6d+59) then
        tmp = y * (z / (a - t))
    else if (t <= 5.8d+125) 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 + (y * (z / a));
	double tmp;
	if (t <= -3e+77) {
		tmp = y;
	} else if (t <= -6.4e-291) {
		tmp = t_1;
	} else if (t <= 1.95e-205) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.75e-45) {
		tmp = t_1;
	} else if (t <= 2.6e+59) {
		tmp = y * (z / (a - t));
	} else if (t <= 5.8e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -3e+77:
		tmp = y
	elif t <= -6.4e-291:
		tmp = t_1
	elif t <= 1.95e-205:
		tmp = z * ((y - x) / a)
	elif t <= 1.75e-45:
		tmp = t_1
	elif t <= 2.6e+59:
		tmp = y * (z / (a - t))
	elif t <= 5.8e+125:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -3e+77)
		tmp = y;
	elseif (t <= -6.4e-291)
		tmp = t_1;
	elseif (t <= 1.95e-205)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.75e-45)
		tmp = t_1;
	elseif (t <= 2.6e+59)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 5.8e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -3e+77)
		tmp = y;
	elseif (t <= -6.4e-291)
		tmp = t_1;
	elseif (t <= 1.95e-205)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.75e-45)
		tmp = t_1;
	elseif (t <= 2.6e+59)
		tmp = y * (z / (a - t));
	elseif (t <= 5.8e+125)
		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[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+77], y, If[LessEqual[t, -6.4e-291], t$95$1, If[LessEqual[t, 1.95e-205], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-45], t$95$1, If[LessEqual[t, 2.6e+59], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+125], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9999999999999998e77 or 5.79999999999999986e125 < t

   1. Initial program 28.9%

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

   3. Taylor expanded in t around inf 53.0%

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

   if -2.9999999999999998e77 < t < -6.4000000000000003e-291 or 1.95000000000000009e-205 < t < 1.75e-45 or 2.59999999999999999e59 < t < 5.79999999999999986e125

   1. Initial program 82.4%

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

   3. Taylor expanded in t around 0 59.3%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. associate-/l* 56.0%

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

   6. Simplified 56.0%

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

   if -6.4000000000000003e-291 < t < 1.95000000000000009e-205

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. add-cube-cbrt 88.8%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 99.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 99.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 75.8%

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

      1. div-sub 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in a around inf 70.8%

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

   if 1.75e-45 < t < 2.59999999999999999e59

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. add-cube-cbrt 81.0%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 78.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 78.4%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 78.4%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 40.4%

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

      1. associate-/l* 40.1%

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

   10. Simplified 40.1%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-291}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -8.5e+77)
     y
     (if (<= t -1.15e-290)
       t_1
       (if (<= t 4.3e-206)
         (* z (/ (- y x) a))
         (if (<= t 2.65e-45)
           t_1
           (if (<= t 1.8e+62)
             (* y (/ z (- a t)))
             (if (<= t 4e+126) (+ x (/ (* y z) a)) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -8.5e+77) {
		tmp = y;
	} else if (t <= -1.15e-290) {
		tmp = t_1;
	} else if (t <= 4.3e-206) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.65e-45) {
		tmp = t_1;
	} else if (t <= 1.8e+62) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+126) {
		tmp = x + ((y * 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-8.5d+77)) then
        tmp = y
    else if (t <= (-1.15d-290)) then
        tmp = t_1
    else if (t <= 4.3d-206) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.65d-45) then
        tmp = t_1
    else if (t <= 1.8d+62) then
        tmp = y * (z / (a - t))
    else if (t <= 4d+126) then
        tmp = x + ((y * 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 t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -8.5e+77) {
		tmp = y;
	} else if (t <= -1.15e-290) {
		tmp = t_1;
	} else if (t <= 4.3e-206) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.65e-45) {
		tmp = t_1;
	} else if (t <= 1.8e+62) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+126) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -8.5e+77:
		tmp = y
	elif t <= -1.15e-290:
		tmp = t_1
	elif t <= 4.3e-206:
		tmp = z * ((y - x) / a)
	elif t <= 2.65e-45:
		tmp = t_1
	elif t <= 1.8e+62:
		tmp = y * (z / (a - t))
	elif t <= 4e+126:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -8.5e+77)
		tmp = y;
	elseif (t <= -1.15e-290)
		tmp = t_1;
	elseif (t <= 4.3e-206)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.65e-45)
		tmp = t_1;
	elseif (t <= 1.8e+62)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4e+126)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -8.5e+77)
		tmp = y;
	elseif (t <= -1.15e-290)
		tmp = t_1;
	elseif (t <= 4.3e-206)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.65e-45)
		tmp = t_1;
	elseif (t <= 1.8e+62)
		tmp = y * (z / (a - t));
	elseif (t <= 4e+126)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+77], y, If[LessEqual[t, -1.15e-290], t$95$1, If[LessEqual[t, 4.3e-206], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e-45], t$95$1, If[LessEqual[t, 1.8e+62], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+126], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.50000000000000018e77 or 3.9999999999999997e126 < t

   1. Initial program 28.9%

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

   3. Taylor expanded in t around inf 53.0%

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

   if -8.50000000000000018e77 < t < -1.15e-290 or 4.30000000000000025e-206 < t < 2.6499999999999999e-45

   1. Initial program 88.6%

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

   3. Taylor expanded in t around 0 63.5%

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

   4. Taylor expanded in y around inf 56.4%

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

      1. associate-/l* 59.4%

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

   6. Simplified 59.4%

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

   if -1.15e-290 < t < 4.30000000000000025e-206

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. add-cube-cbrt 88.8%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 99.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 99.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 75.8%

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

      1. div-sub 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in a around inf 70.8%

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

   if 2.6499999999999999e-45 < t < 1.8e62

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. add-cube-cbrt 81.0%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 78.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 78.4%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 78.4%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 40.4%

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

      1. associate-/l* 40.1%

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

   10. Simplified 40.1%

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

   if 1.8e62 < t < 3.9999999999999997e126

   1. Initial program 56.8%

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

   3. Taylor expanded in t around 0 41.6%

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

   4. Taylor expanded in y around inf 41.7%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-290}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+221)
   y
   (if (<= t -8.2e+192)
     (- x (* x (/ z a)))
     (if (<= t -1.3e+78)
       y
       (if (<= t 8.6e-49)
         (+ x (* y (/ z a)))
         (if (<= t 5.8e+60)
           (* y (/ z (- a t)))
           (if (<= t 6.4e+125) (+ x (/ (* y z) a)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+221) {
		tmp = y;
	} else if (t <= -8.2e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -1.3e+78) {
		tmp = y;
	} else if (t <= 8.6e-49) {
		tmp = x + (y * (z / a));
	} else if (t <= 5.8e+60) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.4e+125) {
		tmp = x + ((y * 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 <= (-2.7d+221)) then
        tmp = y
    else if (t <= (-8.2d+192)) then
        tmp = x - (x * (z / a))
    else if (t <= (-1.3d+78)) then
        tmp = y
    else if (t <= 8.6d-49) then
        tmp = x + (y * (z / a))
    else if (t <= 5.8d+60) then
        tmp = y * (z / (a - t))
    else if (t <= 6.4d+125) then
        tmp = x + ((y * 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 <= -2.7e+221) {
		tmp = y;
	} else if (t <= -8.2e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -1.3e+78) {
		tmp = y;
	} else if (t <= 8.6e-49) {
		tmp = x + (y * (z / a));
	} else if (t <= 5.8e+60) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.4e+125) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+221:
		tmp = y
	elif t <= -8.2e+192:
		tmp = x - (x * (z / a))
	elif t <= -1.3e+78:
		tmp = y
	elif t <= 8.6e-49:
		tmp = x + (y * (z / a))
	elif t <= 5.8e+60:
		tmp = y * (z / (a - t))
	elif t <= 6.4e+125:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -8.2e+192)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= -1.3e+78)
		tmp = y;
	elseif (t <= 8.6e-49)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 5.8e+60)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 6.4e+125)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -8.2e+192)
		tmp = x - (x * (z / a));
	elseif (t <= -1.3e+78)
		tmp = y;
	elseif (t <= 8.6e-49)
		tmp = x + (y * (z / a));
	elseif (t <= 5.8e+60)
		tmp = y * (z / (a - t));
	elseif (t <= 6.4e+125)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+221], y, If[LessEqual[t, -8.2e+192], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e+78], y, If[LessEqual[t, 8.6e-49], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+60], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+125], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.7e221 or -8.20000000000000006e192 < t < -1.3e78 or 6.39999999999999967e125 < t

   1. Initial program 26.3%

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

   3. Taylor expanded in t around inf 57.5%

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

   if -2.7e221 < t < -8.20000000000000006e192

   1. Initial program 58.6%

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

   3. Taylor expanded in t around 0 44.4%

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

   4. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. associate-/l* 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. mul-1-neg 70.3%

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

      5. associate-*r/ 70.3%

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

      6. mul-1-neg 70.3%

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

   6. Simplified 70.3%

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

      1. *-commutative 70.3%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 43.9%

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

      4. sqr-neg 43.9%

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

      5. sqrt-unprod 55.4%

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

      6. add-sqr-sqrt 55.4%

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

      7. cancel-sign-sub 55.4%

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

      8. distribute-frac-neg 55.4%

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

      9. *-commutative 55.4%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 44.4%

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

      12. sqr-neg 44.4%

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

      13. sqrt-unprod 70.3%

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

      14. add-sqr-sqrt 70.3%

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

   8. Applied egg-rr 70.3%

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

   if -1.3e78 < t < 8.60000000000000033e-49

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 68.6%

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

   4. Taylor expanded in y around inf 57.2%

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

      1. associate-/l* 59.4%

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

   6. Simplified 59.4%

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

   if 8.60000000000000033e-49 < t < 5.79999999999999999e60

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. add-cube-cbrt 81.0%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 78.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 78.4%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 78.4%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 40.4%

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

      1. associate-/l* 40.1%

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

   10. Simplified 40.1%

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

   if 5.79999999999999999e60 < t < 6.39999999999999967e125

   1. Initial program 56.8%

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

   3. Taylor expanded in t around 0 41.6%

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

   4. Taylor expanded in y around inf 41.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+59}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+221)
   y
   (if (<= t -8.2e+192)
     (- x (* x (/ z a)))
     (if (<= t -2.3e+77)
       y
       (if (<= t 1.1e-46)
         (+ x (* y (/ z a)))
         (if (<= t 4e+59)
           (/ (* y z) (- a t))
           (if (<= t 6.5e+125) (+ x (/ (* y z) a)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+221) {
		tmp = y;
	} else if (t <= -8.2e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -2.3e+77) {
		tmp = y;
	} else if (t <= 1.1e-46) {
		tmp = x + (y * (z / a));
	} else if (t <= 4e+59) {
		tmp = (y * z) / (a - t);
	} else if (t <= 6.5e+125) {
		tmp = x + ((y * 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 <= (-2.7d+221)) then
        tmp = y
    else if (t <= (-8.2d+192)) then
        tmp = x - (x * (z / a))
    else if (t <= (-2.3d+77)) then
        tmp = y
    else if (t <= 1.1d-46) then
        tmp = x + (y * (z / a))
    else if (t <= 4d+59) then
        tmp = (y * z) / (a - t)
    else if (t <= 6.5d+125) then
        tmp = x + ((y * 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 <= -2.7e+221) {
		tmp = y;
	} else if (t <= -8.2e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -2.3e+77) {
		tmp = y;
	} else if (t <= 1.1e-46) {
		tmp = x + (y * (z / a));
	} else if (t <= 4e+59) {
		tmp = (y * z) / (a - t);
	} else if (t <= 6.5e+125) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+221:
		tmp = y
	elif t <= -8.2e+192:
		tmp = x - (x * (z / a))
	elif t <= -2.3e+77:
		tmp = y
	elif t <= 1.1e-46:
		tmp = x + (y * (z / a))
	elif t <= 4e+59:
		tmp = (y * z) / (a - t)
	elif t <= 6.5e+125:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -8.2e+192)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= -2.3e+77)
		tmp = y;
	elseif (t <= 1.1e-46)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 4e+59)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= 6.5e+125)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -8.2e+192)
		tmp = x - (x * (z / a));
	elseif (t <= -2.3e+77)
		tmp = y;
	elseif (t <= 1.1e-46)
		tmp = x + (y * (z / a));
	elseif (t <= 4e+59)
		tmp = (y * z) / (a - t);
	elseif (t <= 6.5e+125)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+221], y, If[LessEqual[t, -8.2e+192], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+77], y, If[LessEqual[t, 1.1e-46], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+59], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+125], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.7e221 or -8.20000000000000006e192 < t < -2.29999999999999995e77 or 6.4999999999999999e125 < t

   1. Initial program 26.3%

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

   3. Taylor expanded in t around inf 57.5%

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

   if -2.7e221 < t < -8.20000000000000006e192

   1. Initial program 58.6%

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

   3. Taylor expanded in t around 0 44.4%

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

   4. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. associate-/l* 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. mul-1-neg 70.3%

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

      5. associate-*r/ 70.3%

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

      6. mul-1-neg 70.3%

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

   6. Simplified 70.3%

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

      1. *-commutative 70.3%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 43.9%

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

      4. sqr-neg 43.9%

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

      5. sqrt-unprod 55.4%

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

      6. add-sqr-sqrt 55.4%

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

      7. cancel-sign-sub 55.4%

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

      8. distribute-frac-neg 55.4%

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

      9. *-commutative 55.4%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 44.4%

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

      12. sqr-neg 44.4%

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

      13. sqrt-unprod 70.3%

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

      14. add-sqr-sqrt 70.3%

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

   8. Applied egg-rr 70.3%

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

   if -2.29999999999999995e77 < t < 1.1e-46

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 68.6%

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

   4. Taylor expanded in y around inf 57.2%

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

      1. associate-/l* 59.4%

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

   6. Simplified 59.4%

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

   if 1.1e-46 < t < 3.99999999999999989e59

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. add-cube-cbrt 81.0%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 78.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 78.4%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 78.4%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 40.4%

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

   if 3.99999999999999989e59 < t < 6.4999999999999999e125

   1. Initial program 56.8%

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

   3. Taylor expanded in t around 0 41.6%

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

   4. Taylor expanded in y around inf 41.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+59}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+237} \lor \neg \left(t \leq -1.55 \cdot 10^{+186} \lor \neg \left(t \leq -5.6 \cdot 10^{+116}\right) \land t \leq 9.2 \cdot 10^{+136}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+237)
         (not
          (or (<= t -1.55e+186) (and (not (<= t -5.6e+116)) (<= t 9.2e+136)))))
   (+ y (* (- z a) (/ (- x y) t)))
   (- x (/ (- z t) (/ (- a t) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+237) || !((t <= -1.55e+186) || (!(t <= -5.6e+116) && (t <= 9.2e+136)))) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d+237)) .or. (.not. (t <= (-1.55d+186)) .or. (.not. (t <= (-5.6d+116))) .and. (t <= 9.2d+136))) then
        tmp = y + ((z - a) * ((x - y) / t))
    else
        tmp = x - ((z - t) / ((a - t) / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+237) || !((t <= -1.55e+186) || (!(t <= -5.6e+116) && (t <= 9.2e+136)))) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+237) or not ((t <= -1.55e+186) or (not (t <= -5.6e+116) and (t <= 9.2e+136))):
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x - ((z - t) / ((a - t) / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+237) || !((t <= -1.55e+186) || (!(t <= -5.6e+116) && (t <= 9.2e+136))))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x - Float64(Float64(z - t) / Float64(Float64(a - t) / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+237) || ~(((t <= -1.55e+186) || (~((t <= -5.6e+116)) && (t <= 9.2e+136)))))
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x - ((z - t) / ((a - t) / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+237], N[Not[Or[LessEqual[t, -1.55e+186], And[N[Not[LessEqual[t, -5.6e+116]], $MachinePrecision], LessEqual[t, 9.2e+136]]]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999952e237 or -1.5500000000000001e186 < t < -5.60000000000000009e116 or 9.2e136 < t

   1. Initial program 22.5%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. distribute-lft-out-- 62.6%

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

      3. div-sub 62.6%

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

      4. mul-1-neg 62.6%

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

      5. unsub-neg 62.6%

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

      6. div-sub 62.6%

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

      7. associate-/l* 70.5%

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

      8. associate-/l* 90.2%

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

      9. distribute-rgt-out-- 90.2%

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

   5. Simplified 90.2%

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

   if -7.99999999999999952e237 < t < -1.5500000000000001e186 or -5.60000000000000009e116 < t < 9.2e136

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

      2. add-cube-cbrt 80.5%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 91.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 91.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 91.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{a - t}} \cdot \frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \]

      2. clear-num 91.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\sqrt[3]{a - t}}{y - x}}} \cdot \frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \]

      3. frac-times 89.5%

         \[\leadsto x + \color{blue}{\frac{1 \cdot \left(z - t\right)}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}} \]

      4. *-un-lft-identity 89.5%

         \[\leadsto x + \frac{\color{blue}{z - t}}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}} \]

   6. Applied egg-rr 89.5%

      \[\leadsto x + \color{blue}{\frac{z - t}{\frac{\sqrt[3]{a - t}}{y - x} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 89.5%

         \[\leadsto x + \frac{z - t}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot {\left(\sqrt[3]{a - t}\right)}^{2}}{y - x}}} \]

      2. unpow2 89.5%

         \[\leadsto x + \frac{z - t}{\frac{\sqrt[3]{a - t} \cdot \color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right)}}{y - x}} \]

      3. rem-3cbrt-rft 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+237} \lor \neg \left(t \leq -1.55 \cdot 10^{+186} \lor \neg \left(t \leq -5.6 \cdot 10^{+116}\right) \land t \leq 9.2 \cdot 10^{+136}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+221)
   y
   (if (<= t -7.5e+192)
     (- x (* x (/ z a)))
     (if (<= t -5.3e+77)
       y
       (if (<= t 6.8e-84)
         (+ x (* y (/ z a)))
         (if (<= t 7.5e+78) (* x (/ z (- t a))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+221) {
		tmp = y;
	} else if (t <= -7.5e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -5.3e+77) {
		tmp = y;
	} else if (t <= 6.8e-84) {
		tmp = x + (y * (z / a));
	} else if (t <= 7.5e+78) {
		tmp = x * (z / (t - a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d+221)) then
        tmp = y
    else if (t <= (-7.5d+192)) then
        tmp = x - (x * (z / a))
    else if (t <= (-5.3d+77)) then
        tmp = y
    else if (t <= 6.8d-84) then
        tmp = x + (y * (z / a))
    else if (t <= 7.5d+78) then
        tmp = x * (z / (t - a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+221) {
		tmp = y;
	} else if (t <= -7.5e+192) {
		tmp = x - (x * (z / a));
	} else if (t <= -5.3e+77) {
		tmp = y;
	} else if (t <= 6.8e-84) {
		tmp = x + (y * (z / a));
	} else if (t <= 7.5e+78) {
		tmp = x * (z / (t - a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+221:
		tmp = y
	elif t <= -7.5e+192:
		tmp = x - (x * (z / a))
	elif t <= -5.3e+77:
		tmp = y
	elif t <= 6.8e-84:
		tmp = x + (y * (z / a))
	elif t <= 7.5e+78:
		tmp = x * (z / (t - a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -7.5e+192)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= -5.3e+77)
		tmp = y;
	elseif (t <= 6.8e-84)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 7.5e+78)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+221)
		tmp = y;
	elseif (t <= -7.5e+192)
		tmp = x - (x * (z / a));
	elseif (t <= -5.3e+77)
		tmp = y;
	elseif (t <= 6.8e-84)
		tmp = x + (y * (z / a));
	elseif (t <= 7.5e+78)
		tmp = x * (z / (t - a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+221], y, If[LessEqual[t, -7.5e+192], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.3e+77], y, If[LessEqual[t, 6.8e-84], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+78], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7e221 or -7.5e192 < t < -5.3e77 or 7.49999999999999934e78 < t

   1. Initial program 29.0%

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

   3. Taylor expanded in t around inf 53.2%

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

   if -2.7e221 < t < -7.5e192

   1. Initial program 58.6%

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

   3. Taylor expanded in t around 0 44.4%

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

   4. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. associate-/l* 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. mul-1-neg 70.3%

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

      5. associate-*r/ 70.3%

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

      6. mul-1-neg 70.3%

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

   6. Simplified 70.3%

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

      1. *-commutative 70.3%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 43.9%

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

      4. sqr-neg 43.9%

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

      5. sqrt-unprod 55.4%

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

      6. add-sqr-sqrt 55.4%

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

      7. cancel-sign-sub 55.4%

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

      8. distribute-frac-neg 55.4%

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

      9. *-commutative 55.4%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 44.4%

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

      12. sqr-neg 44.4%

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

      13. sqrt-unprod 70.3%

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

      14. add-sqr-sqrt 70.3%

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

   8. Applied egg-rr 70.3%

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

   if -5.3e77 < t < 6.80000000000000042e-84

   1. Initial program 89.3%

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

   3. Taylor expanded in t around 0 69.7%

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

   4. Taylor expanded in y around inf 58.7%

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

      1. associate-/l* 60.9%

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

   6. Simplified 60.9%

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

   if 6.80000000000000042e-84 < t < 7.49999999999999934e78

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. add-cube-cbrt 81.2%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 79.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 79.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 79.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 61.9%

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

      1. div-sub 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in y around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-/l* 44.0%

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

      3. distribute-rgt-neg-in 44.0%

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

      4. distribute-neg-frac 44.0%

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

   10. Simplified 44.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+192}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-84}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -3.4e+77)
     y
     (if (<= t -5.9e-114)
       t_1
       (if (<= t -5.3e-114)
         y
         (if (<= t -1.4e-227)
           x
           (if (<= t 7.8e-210) t_1 (if (<= t 4.4e+129) 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 <= -3.4e+77) {
		tmp = y;
	} else if (t <= -5.9e-114) {
		tmp = t_1;
	} else if (t <= -5.3e-114) {
		tmp = y;
	} else if (t <= -1.4e-227) {
		tmp = x;
	} else if (t <= 7.8e-210) {
		tmp = t_1;
	} else if (t <= 4.4e+129) {
		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 <= (-3.4d+77)) then
        tmp = y
    else if (t <= (-5.9d-114)) then
        tmp = t_1
    else if (t <= (-5.3d-114)) then
        tmp = y
    else if (t <= (-1.4d-227)) then
        tmp = x
    else if (t <= 7.8d-210) then
        tmp = t_1
    else if (t <= 4.4d+129) 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 <= -3.4e+77) {
		tmp = y;
	} else if (t <= -5.9e-114) {
		tmp = t_1;
	} else if (t <= -5.3e-114) {
		tmp = y;
	} else if (t <= -1.4e-227) {
		tmp = x;
	} else if (t <= 7.8e-210) {
		tmp = t_1;
	} else if (t <= 4.4e+129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -3.4e+77:
		tmp = y
	elif t <= -5.9e-114:
		tmp = t_1
	elif t <= -5.3e-114:
		tmp = y
	elif t <= -1.4e-227:
		tmp = x
	elif t <= 7.8e-210:
		tmp = t_1
	elif t <= 4.4e+129:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -3.4e+77)
		tmp = y;
	elseif (t <= -5.9e-114)
		tmp = t_1;
	elseif (t <= -5.3e-114)
		tmp = y;
	elseif (t <= -1.4e-227)
		tmp = x;
	elseif (t <= 7.8e-210)
		tmp = t_1;
	elseif (t <= 4.4e+129)
		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 <= -3.4e+77)
		tmp = y;
	elseif (t <= -5.9e-114)
		tmp = t_1;
	elseif (t <= -5.3e-114)
		tmp = y;
	elseif (t <= -1.4e-227)
		tmp = x;
	elseif (t <= 7.8e-210)
		tmp = t_1;
	elseif (t <= 4.4e+129)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+77], y, If[LessEqual[t, -5.9e-114], t$95$1, If[LessEqual[t, -5.3e-114], y, If[LessEqual[t, -1.4e-227], x, If[LessEqual[t, 7.8e-210], t$95$1, If[LessEqual[t, 4.4e+129], x, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999997e77 or -5.9000000000000001e-114 < t < -5.29999999999999973e-114 or 4.3999999999999999e129 < t

   1. Initial program 29.3%

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

   3. Taylor expanded in t around inf 53.6%

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

   if -3.39999999999999997e77 < t < -5.9000000000000001e-114 or -1.3999999999999999e-227 < t < 7.7999999999999995e-210

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

      2. add-cube-cbrt 89.1%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 95.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 95.9%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 95.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 52.5%

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

      1. associate-/l* 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in t around 0 41.8%

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

   if -5.29999999999999973e-114 < t < -1.3999999999999999e-227 or 7.7999999999999995e-210 < t < 4.3999999999999999e129

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 33.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -7.2e+76)
     y
     (if (<= t -1.65e-98)
       t_1
       (if (<= t -2e-122)
         (* x (/ z (- a)))
         (if (<= t -3.3e-226)
           x
           (if (<= t 8.6e-210) t_1 (if (<= t 1.08e+130) 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 <= -7.2e+76) {
		tmp = y;
	} else if (t <= -1.65e-98) {
		tmp = t_1;
	} else if (t <= -2e-122) {
		tmp = x * (z / -a);
	} else if (t <= -3.3e-226) {
		tmp = x;
	} else if (t <= 8.6e-210) {
		tmp = t_1;
	} else if (t <= 1.08e+130) {
		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 <= (-7.2d+76)) then
        tmp = y
    else if (t <= (-1.65d-98)) then
        tmp = t_1
    else if (t <= (-2d-122)) then
        tmp = x * (z / -a)
    else if (t <= (-3.3d-226)) then
        tmp = x
    else if (t <= 8.6d-210) then
        tmp = t_1
    else if (t <= 1.08d+130) 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 <= -7.2e+76) {
		tmp = y;
	} else if (t <= -1.65e-98) {
		tmp = t_1;
	} else if (t <= -2e-122) {
		tmp = x * (z / -a);
	} else if (t <= -3.3e-226) {
		tmp = x;
	} else if (t <= 8.6e-210) {
		tmp = t_1;
	} else if (t <= 1.08e+130) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -7.2e+76:
		tmp = y
	elif t <= -1.65e-98:
		tmp = t_1
	elif t <= -2e-122:
		tmp = x * (z / -a)
	elif t <= -3.3e-226:
		tmp = x
	elif t <= 8.6e-210:
		tmp = t_1
	elif t <= 1.08e+130:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -7.2e+76)
		tmp = y;
	elseif (t <= -1.65e-98)
		tmp = t_1;
	elseif (t <= -2e-122)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (t <= -3.3e-226)
		tmp = x;
	elseif (t <= 8.6e-210)
		tmp = t_1;
	elseif (t <= 1.08e+130)
		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 <= -7.2e+76)
		tmp = y;
	elseif (t <= -1.65e-98)
		tmp = t_1;
	elseif (t <= -2e-122)
		tmp = x * (z / -a);
	elseif (t <= -3.3e-226)
		tmp = x;
	elseif (t <= 8.6e-210)
		tmp = t_1;
	elseif (t <= 1.08e+130)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+76], y, If[LessEqual[t, -1.65e-98], t$95$1, If[LessEqual[t, -2e-122], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-226], x, If[LessEqual[t, 8.6e-210], t$95$1, If[LessEqual[t, 1.08e+130], x, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2000000000000006e76 or 1.08e130 < t

   1. Initial program 28.4%

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

   3. Taylor expanded in t around inf 53.1%

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

   if -7.2000000000000006e76 < t < -1.6500000000000001e-98 or -3.3e-226 < t < 8.6000000000000001e-210

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. add-cube-cbrt 88.9%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 95.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 95.9%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 95.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 53.1%

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

      1. associate-/l* 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around 0 42.3%

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

   if -1.6500000000000001e-98 < t < -2.00000000000000012e-122

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 50.7%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/l* 52.4%

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

      3. distribute-rgt-neg-in 52.4%

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

      4. mul-1-neg 52.4%

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

      5. associate-*r/ 52.4%

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

      6. mul-1-neg 52.4%

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

   6. Simplified 52.4%

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

      1. *-commutative 52.4%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 2.2%

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

      4. sqr-neg 2.2%

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

      5. sqrt-unprod 1.0%

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

      6. add-sqr-sqrt 1.0%

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

      7. cancel-sign-sub 1.0%

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

      8. distribute-frac-neg 1.0%

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

      9. *-commutative 1.0%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 52.2%

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

      12. sqr-neg 52.2%

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

      13. sqrt-unprod 52.4%

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

      14. add-sqr-sqrt 52.4%

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

   8. Applied egg-rr 52.4%

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

   9. Taylor expanded in z around inf 51.5%

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

       1. mul-1-neg 51.5%

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

       2. associate-*r/ 52.4%

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

       3. *-commutative 52.4%

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

       4. distribute-rgt-neg-out 52.4%

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

   11. Simplified 52.4%

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

   if -2.00000000000000012e-122 < t < -3.3e-226 or 8.6000000000000001e-210 < t < 1.08e130

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 33.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-70} \lor \neg \left(t \leq 2.6 \cdot 10^{-45}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.7e+221)
     t_1
     (if (<= t -8.2e+192)
       (* x (+ (/ z (- t a)) 1.0))
       (if (or (<= t -1.42e-70) (not (<= t 2.6e-45)))
         t_1
         (- x (* z (/ (- x y) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+221) {
		tmp = t_1;
	} else if (t <= -8.2e+192) {
		tmp = x * ((z / (t - a)) + 1.0);
	} else if ((t <= -1.42e-70) || !(t <= 2.6e-45)) {
		tmp = t_1;
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.7d+221)) then
        tmp = t_1
    else if (t <= (-8.2d+192)) then
        tmp = x * ((z / (t - a)) + 1.0d0)
    else if ((t <= (-1.42d-70)) .or. (.not. (t <= 2.6d-45))) then
        tmp = t_1
    else
        tmp = x - (z * ((x - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+221) {
		tmp = t_1;
	} else if (t <= -8.2e+192) {
		tmp = x * ((z / (t - a)) + 1.0);
	} else if ((t <= -1.42e-70) || !(t <= 2.6e-45)) {
		tmp = t_1;
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.7e+221:
		tmp = t_1
	elif t <= -8.2e+192:
		tmp = x * ((z / (t - a)) + 1.0)
	elif (t <= -1.42e-70) or not (t <= 2.6e-45):
		tmp = t_1
	else:
		tmp = x - (z * ((x - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.7e+221)
		tmp = t_1;
	elseif (t <= -8.2e+192)
		tmp = Float64(x * Float64(Float64(z / Float64(t - a)) + 1.0));
	elseif ((t <= -1.42e-70) || !(t <= 2.6e-45))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.7e+221)
		tmp = t_1;
	elseif (t <= -8.2e+192)
		tmp = x * ((z / (t - a)) + 1.0);
	elseif ((t <= -1.42e-70) || ~((t <= 2.6e-45)))
		tmp = t_1;
	else
		tmp = x - (z * ((x - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+221], t$95$1, If[LessEqual[t, -8.2e+192], N[(x * N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.42e-70], N[Not[LessEqual[t, 2.6e-45]], $MachinePrecision]], t$95$1, N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e221 or -8.20000000000000006e192 < t < -1.42000000000000002e-70 or 2.59999999999999987e-45 < t

   1. Initial program 50.3%

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

      1. *-commutative 50.3%

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

      2. add-cube-cbrt 49.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 71.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 71.8%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 71.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 43.4%

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

      1. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   if -2.7e221 < t < -8.20000000000000006e192

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 58.6%

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

   4. Taylor expanded in x around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

   6. Simplified 85.5%

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

   if -1.42000000000000002e-70 < t < 2.59999999999999987e-45

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0 73.9%

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

      1. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-70} \lor \neg \left(t \leq 2.6 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-70} \lor \neg \left(t \leq 2.3 \cdot 10^{-45}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.7e+221)
     t_1
     (if (<= t -8.2e+192)
       (* x (+ (/ (- z t) (- t a)) 1.0))
       (if (or (<= t -2.3e-70) (not (<= t 2.3e-45)))
         t_1
         (- x (* z (/ (- x y) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+221) {
		tmp = t_1;
	} else if (t <= -8.2e+192) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if ((t <= -2.3e-70) || !(t <= 2.3e-45)) {
		tmp = t_1;
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.7d+221)) then
        tmp = t_1
    else if (t <= (-8.2d+192)) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else if ((t <= (-2.3d-70)) .or. (.not. (t <= 2.3d-45))) then
        tmp = t_1
    else
        tmp = x - (z * ((x - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+221) {
		tmp = t_1;
	} else if (t <= -8.2e+192) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if ((t <= -2.3e-70) || !(t <= 2.3e-45)) {
		tmp = t_1;
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.7e+221:
		tmp = t_1
	elif t <= -8.2e+192:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	elif (t <= -2.3e-70) or not (t <= 2.3e-45):
		tmp = t_1
	else:
		tmp = x - (z * ((x - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.7e+221)
		tmp = t_1;
	elseif (t <= -8.2e+192)
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif ((t <= -2.3e-70) || !(t <= 2.3e-45))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.7e+221)
		tmp = t_1;
	elseif (t <= -8.2e+192)
		tmp = x * (((z - t) / (t - a)) + 1.0);
	elseif ((t <= -2.3e-70) || ~((t <= 2.3e-45)))
		tmp = t_1;
	else
		tmp = x - (z * ((x - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+221], t$95$1, If[LessEqual[t, -8.2e+192], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.3e-70], N[Not[LessEqual[t, 2.3e-45]], $MachinePrecision]], t$95$1, N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e221 or -8.20000000000000006e192 < t < -2.30000000000000001e-70 or 2.29999999999999992e-45 < t

   1. Initial program 50.3%

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

      1. *-commutative 50.3%

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

      2. add-cube-cbrt 49.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 71.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 71.8%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 71.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 43.4%

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

      1. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   if -2.7e221 < t < -8.20000000000000006e192

   1. Initial program 58.6%

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

   3. Taylor expanded in x around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. unsub-neg 85.8%

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

   5. Simplified 85.8%

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

   if -2.30000000000000001e-70 < t < 2.29999999999999992e-45

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0 73.9%

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

      1. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-70} \lor \neg \left(t \leq 2.3 \cdot 10^{-45}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -1.55e+77)
     y
     (if (<= t 3.2e-207)
       t_1
       (if (<= t 1.76e-127) x (if (<= t 2.6e+87) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -1.55e+77) {
		tmp = y;
	} else if (t <= 3.2e-207) {
		tmp = t_1;
	} else if (t <= 1.76e-127) {
		tmp = x;
	} else if (t <= 2.6e+87) {
		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 = y * (z / (a - t))
    if (t <= (-1.55d+77)) then
        tmp = y
    else if (t <= 3.2d-207) then
        tmp = t_1
    else if (t <= 1.76d-127) then
        tmp = x
    else if (t <= 2.6d+87) 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 = y * (z / (a - t));
	double tmp;
	if (t <= -1.55e+77) {
		tmp = y;
	} else if (t <= 3.2e-207) {
		tmp = t_1;
	} else if (t <= 1.76e-127) {
		tmp = x;
	} else if (t <= 2.6e+87) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -1.55e+77:
		tmp = y
	elif t <= 3.2e-207:
		tmp = t_1
	elif t <= 1.76e-127:
		tmp = x
	elif t <= 2.6e+87:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.55e+77)
		tmp = y;
	elseif (t <= 3.2e-207)
		tmp = t_1;
	elseif (t <= 1.76e-127)
		tmp = x;
	elseif (t <= 2.6e+87)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -1.55e+77)
		tmp = y;
	elseif (t <= 3.2e-207)
		tmp = t_1;
	elseif (t <= 1.76e-127)
		tmp = x;
	elseif (t <= 2.6e+87)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+77], y, If[LessEqual[t, 3.2e-207], t$95$1, If[LessEqual[t, 1.76e-127], x, If[LessEqual[t, 2.6e+87], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999999e77 or 2.59999999999999998e87 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 50.2%

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

   if -1.54999999999999999e77 < t < 3.2000000000000003e-207 or 1.76000000000000007e-127 < t < 2.59999999999999998e87

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. add-cube-cbrt 84.8%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 90.5%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 90.5%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 90.5%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 64.5%

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

      1. div-sub 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in y around inf 38.6%

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

      1. associate-/l* 41.3%

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

   10. Simplified 41.3%

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

   if 3.2000000000000003e-207 < t < 1.76000000000000007e-127

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 59.8%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e+76)
   y
   (if (<= t 1.72e-208)
     (* y (/ (- z t) a))
     (if (<= t 2.4e-125) x (if (<= t 3.5e+84) (* y (/ z (- a t))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+76) {
		tmp = y;
	} else if (t <= 1.72e-208) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.4e-125) {
		tmp = x;
	} else if (t <= 3.5e+84) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.8d+76)) then
        tmp = y
    else if (t <= 1.72d-208) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.4d-125) then
        tmp = x
    else if (t <= 3.5d+84) then
        tmp = y * (z / (a - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+76) {
		tmp = y;
	} else if (t <= 1.72e-208) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.4e-125) {
		tmp = x;
	} else if (t <= 3.5e+84) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e+76:
		tmp = y
	elif t <= 1.72e-208:
		tmp = y * ((z - t) / a)
	elif t <= 2.4e-125:
		tmp = x
	elif t <= 3.5e+84:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e+76)
		tmp = y;
	elseif (t <= 1.72e-208)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.4e-125)
		tmp = x;
	elseif (t <= 3.5e+84)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e+76)
		tmp = y;
	elseif (t <= 1.72e-208)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.4e-125)
		tmp = x;
	elseif (t <= 3.5e+84)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e+76], y, If[LessEqual[t, 1.72e-208], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-125], x, If[LessEqual[t, 3.5e+84], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.79999999999999979e76 or 3.4999999999999999e84 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 50.2%

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

   if -7.79999999999999979e76 < t < 1.72000000000000002e-208

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

      2. add-cube-cbrt 89.0%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 96.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 96.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 50.8%

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

      1. associate-/l* 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in a around inf 43.2%

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

   if 1.72000000000000002e-208 < t < 2.4000000000000001e-125

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 59.8%

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

   if 2.4000000000000001e-125 < t < 3.4999999999999999e84

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. add-cube-cbrt 76.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 79.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 79.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 79.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 64.9%

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

      1. div-sub 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around inf 34.9%

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

      1. associate-/l* 38.7%

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

   10. Simplified 38.7%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+76)
   y
   (if (<= t 6.2e-206)
     (* z (/ (- y x) a))
     (if (<= t 6.2e-127) x (if (<= t 3e+85) (* y (/ z (- a t))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+76) {
		tmp = y;
	} else if (t <= 6.2e-206) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.2e-127) {
		tmp = x;
	} else if (t <= 3e+85) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+76)) then
        tmp = y
    else if (t <= 6.2d-206) then
        tmp = z * ((y - x) / a)
    else if (t <= 6.2d-127) then
        tmp = x
    else if (t <= 3d+85) then
        tmp = y * (z / (a - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+76) {
		tmp = y;
	} else if (t <= 6.2e-206) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.2e-127) {
		tmp = x;
	} else if (t <= 3e+85) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+76:
		tmp = y
	elif t <= 6.2e-206:
		tmp = z * ((y - x) / a)
	elif t <= 6.2e-127:
		tmp = x
	elif t <= 3e+85:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+76)
		tmp = y;
	elseif (t <= 6.2e-206)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 6.2e-127)
		tmp = x;
	elseif (t <= 3e+85)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+76)
		tmp = y;
	elseif (t <= 6.2e-206)
		tmp = z * ((y - x) / a);
	elseif (t <= 6.2e-127)
		tmp = x;
	elseif (t <= 3e+85)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+76], y, If[LessEqual[t, 6.2e-206], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-127], x, If[LessEqual[t, 3e+85], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2000000000000006e76 or 3e85 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 50.2%

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

   if -7.2000000000000006e76 < t < 6.2000000000000005e-206

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. add-cube-cbrt 88.3%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 96.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 96.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.9%

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

      1. div-sub 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in a around inf 54.8%

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

   if 6.2000000000000005e-206 < t < 6.2e-127

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 61.0%

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

   if 6.2e-127 < t < 3e85

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. add-cube-cbrt 76.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 79.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 79.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 79.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 64.9%

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

      1. div-sub 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around inf 34.9%

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

      1. associate-/l* 38.7%

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

   10. Simplified 38.7%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+76)
   y
   (if (<= t 1.62e-205)
     (* z (/ (- y x) a))
     (if (<= t 2.1e-125)
       (* x (+ (/ z a) 1.0))
       (if (<= t 7e+85) (* y (/ z (- a t))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+76) {
		tmp = y;
	} else if (t <= 1.62e-205) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.1e-125) {
		tmp = x * ((z / a) + 1.0);
	} else if (t <= 7e+85) {
		tmp = y * (z / (a - t));
	} 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 <= (-9d+76)) then
        tmp = y
    else if (t <= 1.62d-205) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.1d-125) then
        tmp = x * ((z / a) + 1.0d0)
    else if (t <= 7d+85) then
        tmp = y * (z / (a - t))
    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 <= -9e+76) {
		tmp = y;
	} else if (t <= 1.62e-205) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.1e-125) {
		tmp = x * ((z / a) + 1.0);
	} else if (t <= 7e+85) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+76:
		tmp = y
	elif t <= 1.62e-205:
		tmp = z * ((y - x) / a)
	elif t <= 2.1e-125:
		tmp = x * ((z / a) + 1.0)
	elif t <= 7e+85:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+76)
		tmp = y;
	elseif (t <= 1.62e-205)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.1e-125)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	elseif (t <= 7e+85)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+76)
		tmp = y;
	elseif (t <= 1.62e-205)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.1e-125)
		tmp = x * ((z / a) + 1.0);
	elseif (t <= 7e+85)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+76], y, If[LessEqual[t, 1.62e-205], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-125], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+85], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.9999999999999995e76 or 7.0000000000000001e85 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 50.2%

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

   if -8.9999999999999995e76 < t < 1.6200000000000001e-205

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. add-cube-cbrt 88.3%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 96.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 96.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 63.9%

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

      1. div-sub 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in a around inf 54.8%

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

   if 1.6200000000000001e-205 < t < 2.1e-125

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 79.3%

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

   4. Taylor expanded in y around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. mul-1-neg 65.2%

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

      5. associate-*r/ 65.2%

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

      6. mul-1-neg 65.2%

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

   6. Simplified 65.2%

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

      1. *-commutative 65.2%

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

      2. distribute-rgt1-in 65.2%

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

      3. add-sqr-sqrt 35.3%

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

      4. sqrt-unprod 54.9%

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

      5. sqr-neg 54.9%

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

      6. sqrt-unprod 25.3%

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

      7. add-sqr-sqrt 67.2%

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

   8. Applied egg-rr 67.2%

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

   if 2.1e-125 < t < 7.0000000000000001e85

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. add-cube-cbrt 76.7%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 79.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 79.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 79.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 64.9%

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

      1. div-sub 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around inf 34.9%

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

      1. associate-/l* 38.7%

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

   10. Simplified 38.7%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5.3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 38:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= t -5.3e-22)
     t_1
     (if (<= t 38.0)
       (- x (* z (/ (- y x) (- t a))))
       (if (<= t 1.72e+161) t_1 (* y (/ (- t z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -5.3e-22) {
		tmp = t_1;
	} else if (t <= 38.0) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if (t <= 1.72e+161) {
		tmp = t_1;
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (t <= (-5.3d-22)) then
        tmp = t_1
    else if (t <= 38.0d0) then
        tmp = x - (z * ((y - x) / (t - a)))
    else if (t <= 1.72d+161) then
        tmp = t_1
    else
        tmp = y * ((t - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -5.3e-22) {
		tmp = t_1;
	} else if (t <= 38.0) {
		tmp = x - (z * ((y - x) / (t - a)));
	} else if (t <= 1.72e+161) {
		tmp = t_1;
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if t <= -5.3e-22:
		tmp = t_1
	elif t <= 38.0:
		tmp = x - (z * ((y - x) / (t - a)))
	elif t <= 1.72e+161:
		tmp = t_1
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (t <= -5.3e-22)
		tmp = t_1;
	elseif (t <= 38.0)
		tmp = Float64(x - Float64(z * Float64(Float64(y - x) / Float64(t - a))));
	elseif (t <= 1.72e+161)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (t <= -5.3e-22)
		tmp = t_1;
	elseif (t <= 38.0)
		tmp = x - (z * ((y - x) / (t - a)));
	elseif (t <= 1.72e+161)
		tmp = t_1;
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.3e-22], t$95$1, If[LessEqual[t, 38.0], N[(x - N[(z * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e+161], t$95$1, N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.29999999999999972e-22 or 38 < t < 1.71999999999999996e161

   1. Initial program 56.1%

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

   3. Taylor expanded in y around inf 53.2%

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

      1. associate-/l* 68.7%

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

   5. Simplified 68.7%

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

   if -5.29999999999999972e-22 < t < 38

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

   if 1.71999999999999996e161 < t

   1. Initial program 17.5%

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

      1. *-commutative 17.5%

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

      2. add-cube-cbrt 17.2%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 47.6%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 47.6%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 47.6%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 34.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in a around 0 67.0%

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

      1. mul-1-neg 67.0%

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

   10. Simplified 67.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 38:\\ \;\;\;\;x - z \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+161}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+102} \lor \neg \left(z \leq 4 \cdot 10^{+112}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+102) (not (<= z 4e+112)))
   (* z (/ (- y x) (- a t)))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+102) || !(z <= 4e+112)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.8d+102)) .or. (.not. (z <= 4d+112))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+102) || !(z <= 4e+112)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+102) or not (z <= 4e+112):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+102) || !(z <= 4e+112))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+102) || ~((z <= 4e+112)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+102], N[Not[LessEqual[z, 4e+112]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000018e102 or 3.9999999999999997e112 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. add-cube-cbrt 71.2%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 90.3%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 90.3%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 90.3%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in z around inf 80.4%

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

      1. div-sub 80.4%

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

   7. Simplified 80.4%

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

   if -2.80000000000000018e102 < z < 3.9999999999999997e112

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 57.1%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+102} \lor \neg \left(z \leq 4 \cdot 10^{+112}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-57} \lor \neg \left(x \leq 10^{+163}\right):\\ \;\;\;\;x \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.6e-57) (not (<= x 1e+163)))
   (* x (+ (/ z (- t a)) 1.0))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.6e-57) || !(x <= 1e+163)) {
		tmp = x * ((z / (t - a)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.6d-57)) .or. (.not. (x <= 1d+163))) then
        tmp = x * ((z / (t - a)) + 1.0d0)
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.6e-57) || !(x <= 1e+163)) {
		tmp = x * ((z / (t - a)) + 1.0);
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.6e-57) or not (x <= 1e+163):
		tmp = x * ((z / (t - a)) + 1.0)
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.6e-57) || !(x <= 1e+163))
		tmp = Float64(x * Float64(Float64(z / Float64(t - a)) + 1.0));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.6e-57) || ~((x <= 1e+163)))
		tmp = x * ((z / (t - a)) + 1.0);
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.6e-57], N[Not[LessEqual[x, 1e+163]], $MachinePrecision]], N[(x * N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e-57 or 9.9999999999999994e162 < x

   1. Initial program 56.0%

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

   3. Taylor expanded in z around inf 56.2%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   6. Simplified 55.7%

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

   if -4.6e-57 < x < 9.9999999999999994e162

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

      2. add-cube-cbrt 71.2%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 88.2%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 88.2%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 88.2%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 56.9%

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

      1. associate-/l* 71.9%

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

   7. Simplified 71.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-57} \lor \neg \left(x \leq 10^{+163}\right):\\ \;\;\;\;x \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 55.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-31} \lor \neg \left(a \leq 1.15 \cdot 10^{+76}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e-31) (not (<= a 1.15e+76)))
   (+ x (* y (/ z a)))
   (* y (/ (- t z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-31) || !(a <= 1.15e+76)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.85d-31)) .or. (.not. (a <= 1.15d+76))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * ((t - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-31) || !(a <= 1.15e+76)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e-31) or not (a <= 1.15e+76):
		tmp = x + (y * (z / a))
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e-31) || !(a <= 1.15e+76))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.85e-31) || ~((a <= 1.15e+76)))
		tmp = x + (y * (z / a));
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e-31], N[Not[LessEqual[a, 1.15e+76]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8499999999999999e-31 or 1.15000000000000001e76 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in t around 0 56.1%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. associate-/l* 57.1%

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

   6. Simplified 57.1%

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

   if -1.8499999999999999e-31 < a < 1.15000000000000001e76

   1. Initial program 68.1%

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

      1. *-commutative 68.1%

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

      2. add-cube-cbrt 67.5%

         \[\leadsto x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}} \]

      3. times-frac 77.7%

         \[\leadsto x + \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

      4. pow2 77.7%

         \[\leadsto x + \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y - x}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 77.7%

      \[\leadsto x + \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y - x}{\sqrt[3]{a - t}}} \]

   5. Taylor expanded in x around 0 51.9%

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

      1. associate-/l* 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in a around 0 52.4%

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

      1. mul-1-neg 52.4%

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

   10. Simplified 52.4%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-31} \lor \neg \left(a \leq 1.15 \cdot 10^{+76}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-120}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.1e-120) y (if (<= t 4.4e+129) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e-120) {
		tmp = y;
	} else if (t <= 4.4e+129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.1d-120)) then
        tmp = y
    else if (t <= 4.4d+129) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e-120) {
		tmp = y;
	} else if (t <= 4.4e+129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.1e-120:
		tmp = y
	elif t <= 4.4e+129:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.1e-120)
		tmp = y;
	elseif (t <= 4.4e+129)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.1e-120)
		tmp = y;
	elseif (t <= 4.4e+129)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.1e-120], y, If[LessEqual[t, 4.4e+129], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.10000000000000034e-120 or 4.3999999999999999e129 < t

   1. Initial program 45.0%

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

   3. Taylor expanded in t around inf 42.4%

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

   if -4.10000000000000034e-120 < t < 4.3999999999999999e129

   1. Initial program 83.0%

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

   3. Taylor expanded in a around inf 29.0%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-120}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 25.0% 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 65.3%

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

3. Taylor expanded in a around inf 21.1%

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

4. Final simplification 21.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.3% 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 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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