Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.8% → 97.8%

Time: 7.1s

Alternatives: 12

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

2. Final simplification 97.8%

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

Alternative 2: 65.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -1e+248)
     (/ (* y z) t)
     (if (<= (/ z t) -4e+88)
       (/ (- z) (/ t x))
       (if (<= (/ z t) -2e-44)
         t_1
         (if (<= (/ z t) 4e-13)
           x
           (if (<= (/ z t) 2e+22)
             t_1
             (if (or (<= (/ z t) 2e+45) (not (<= (/ z t) 5e+62)))
               (* (/ z t) (- x))
               (/ y (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = -z / (t / x);
	} else if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = t_1;
	} else if (((z / t) <= 2e+45) || !((z / t) <= 5e+62)) {
		tmp = (z / t) * -x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-1d+248)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-4d+88)) then
        tmp = -z / (t / x)
    else if ((z / t) <= (-2d-44)) then
        tmp = t_1
    else if ((z / t) <= 4d-13) then
        tmp = x
    else if ((z / t) <= 2d+22) then
        tmp = t_1
    else if (((z / t) <= 2d+45) .or. (.not. ((z / t) <= 5d+62))) then
        tmp = (z / t) * -x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = -z / (t / x);
	} else if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = t_1;
	} else if (((z / t) <= 2e+45) || !((z / t) <= 5e+62)) {
		tmp = (z / t) * -x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e+248:
		tmp = (y * z) / t
	elif (z / t) <= -4e+88:
		tmp = -z / (t / x)
	elif (z / t) <= -2e-44:
		tmp = t_1
	elif (z / t) <= 4e-13:
		tmp = x
	elif (z / t) <= 2e+22:
		tmp = t_1
	elif ((z / t) <= 2e+45) or not ((z / t) <= 5e+62):
		tmp = (z / t) * -x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+248)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -4e+88)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (Float64(z / t) <= -2e-44)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	elseif (Float64(z / t) <= 2e+22)
		tmp = t_1;
	elseif ((Float64(z / t) <= 2e+45) || !(Float64(z / t) <= 5e+62))
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+248)
		tmp = (y * z) / t;
	elseif ((z / t) <= -4e+88)
		tmp = -z / (t / x);
	elseif ((z / t) <= -2e-44)
		tmp = t_1;
	elseif ((z / t) <= 4e-13)
		tmp = x;
	elseif ((z / t) <= 2e+22)
		tmp = t_1;
	elseif (((z / t) <= 2e+45) || ~(((z / t) <= 5e+62)))
		tmp = (z / t) * -x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+248], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -4e+88], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+22], t$95$1, If[Or[LessEqual[N[(z / t), $MachinePrecision], 2e+45], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+62]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 z t) < -1.00000000000000005e248

   1. Initial program 87.8%

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

   2. Taylor expanded in z around -inf 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   6. Simplified 68.2%

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

   if -1.00000000000000005e248 < (/.f64 z t) < -3.99999999999999984e88

   1. Initial program 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 66.3%

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

      1. neg-mul-1 66.3%

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

      2. +-commutative 66.3%

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

      3. distribute-rgt1-in 66.3%

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

      4. distribute-lft-neg-out 66.3%

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

      5. associate-*l/ 62.5%

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

      6. associate-/l* 66.3%

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

      7. unsub-neg 66.3%

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

      8. associate-/l* 62.5%

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

      9. associate-*r/ 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in z around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 66.3%

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

   9. Simplified 66.3%

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

   if -3.99999999999999984e88 < (/.f64 z t) < -1.99999999999999991e-44 or 4.0000000000000001e-13 < (/.f64 z t) < 2e22

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 80.1%

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

   3. Taylor expanded in t around 0 64.7%

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

   4. Taylor expanded in y around inf 48.4%

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

      1. *-commutative 48.4%

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

   6. Simplified 48.4%

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

      1. associate-/l* 46.8%

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

      2. associate-/r/ 61.5%

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

   8. Applied egg-rr 61.5%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 2e22 < (/.f64 z t) < 1.9999999999999999e45 or 5.00000000000000029e62 < (/.f64 z t)

   1. Initial program 97.8%

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

   2. Taylor expanded in z around -inf 93.6%

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

   3. Taylor expanded in t around 0 93.7%

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

      1. associate-/l* 97.8%

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

      2. div-inv 97.7%

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

      3. clear-num 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around 0 62.1%

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

      1. associate-*l/ 68.3%

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

      2. neg-mul-1 68.3%

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

      3. distribute-rgt-neg-out 68.3%

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

   8. Simplified 68.3%

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

   if 1.9999999999999999e45 < (/.f64 z t) < 5.00000000000000029e62

   1. Initial program 99.4%

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

   2. Taylor expanded in z around -inf 80.6%

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

   3. Taylor expanded in t around 0 80.6%

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

   4. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in z around 0 80.6%

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

      1. associate-/l* 99.7%

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

   9. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 65.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -1e+248)
     (/ (* y z) t)
     (if (<= (/ z t) -4e+88)
       (/ (- z) (/ t x))
       (if (<= (/ z t) -2e-44)
         t_1
         (if (<= (/ z t) 4e-13)
           x
           (if (<= (/ z t) 2e+22)
             t_1
             (if (or (<= (/ z t) 2e+45) (not (<= (/ z t) 5e+62)))
               (/ (- x) (/ t z))
               (/ y (/ t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = -z / (t / x);
	} else if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = t_1;
	} else if (((z / t) <= 2e+45) || !((z / t) <= 5e+62)) {
		tmp = -x / (t / z);
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-1d+248)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-4d+88)) then
        tmp = -z / (t / x)
    else if ((z / t) <= (-2d-44)) then
        tmp = t_1
    else if ((z / t) <= 4d-13) then
        tmp = x
    else if ((z / t) <= 2d+22) then
        tmp = t_1
    else if (((z / t) <= 2d+45) .or. (.not. ((z / t) <= 5d+62))) then
        tmp = -x / (t / z)
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = -z / (t / x);
	} else if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = t_1;
	} else if (((z / t) <= 2e+45) || !((z / t) <= 5e+62)) {
		tmp = -x / (t / z);
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e+248:
		tmp = (y * z) / t
	elif (z / t) <= -4e+88:
		tmp = -z / (t / x)
	elif (z / t) <= -2e-44:
		tmp = t_1
	elif (z / t) <= 4e-13:
		tmp = x
	elif (z / t) <= 2e+22:
		tmp = t_1
	elif ((z / t) <= 2e+45) or not ((z / t) <= 5e+62):
		tmp = -x / (t / z)
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+248)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -4e+88)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (Float64(z / t) <= -2e-44)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	elseif (Float64(z / t) <= 2e+22)
		tmp = t_1;
	elseif ((Float64(z / t) <= 2e+45) || !(Float64(z / t) <= 5e+62))
		tmp = Float64(Float64(-x) / Float64(t / z));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+248)
		tmp = (y * z) / t;
	elseif ((z / t) <= -4e+88)
		tmp = -z / (t / x);
	elseif ((z / t) <= -2e-44)
		tmp = t_1;
	elseif ((z / t) <= 4e-13)
		tmp = x;
	elseif ((z / t) <= 2e+22)
		tmp = t_1;
	elseif (((z / t) <= 2e+45) || ~(((z / t) <= 5e+62)))
		tmp = -x / (t / z);
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+248], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -4e+88], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+22], t$95$1, If[Or[LessEqual[N[(z / t), $MachinePrecision], 2e+45], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+62]], $MachinePrecision]], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 z t) < -1.00000000000000005e248

   1. Initial program 87.8%

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

   2. Taylor expanded in z around -inf 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   6. Simplified 68.2%

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

   if -1.00000000000000005e248 < (/.f64 z t) < -3.99999999999999984e88

   1. Initial program 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 66.3%

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

      1. neg-mul-1 66.3%

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

      2. +-commutative 66.3%

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

      3. distribute-rgt1-in 66.3%

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

      4. distribute-lft-neg-out 66.3%

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

      5. associate-*l/ 62.5%

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

      6. associate-/l* 66.3%

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

      7. unsub-neg 66.3%

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

      8. associate-/l* 62.5%

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

      9. associate-*r/ 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in z around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 66.3%

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

   9. Simplified 66.3%

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

   if -3.99999999999999984e88 < (/.f64 z t) < -1.99999999999999991e-44 or 4.0000000000000001e-13 < (/.f64 z t) < 2e22

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 80.1%

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

   3. Taylor expanded in t around 0 64.7%

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

   4. Taylor expanded in y around inf 48.4%

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

      1. *-commutative 48.4%

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

   6. Simplified 48.4%

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

      1. associate-/l* 46.8%

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

      2. associate-/r/ 61.5%

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

   8. Applied egg-rr 61.5%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 2e22 < (/.f64 z t) < 1.9999999999999999e45 or 5.00000000000000029e62 < (/.f64 z t)

   1. Initial program 97.8%

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

      1. clear-num 97.7%

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

      2. un-div-inv 97.8%

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

   3. Applied egg-rr 97.8%

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

   4. Taylor expanded in x around inf 68.3%

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

      1. neg-mul-1 68.3%

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

      2. +-commutative 68.3%

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

      3. distribute-rgt1-in 68.3%

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

      4. distribute-lft-neg-out 68.3%

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

      5. associate-*l/ 62.0%

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

      6. associate-/l* 62.1%

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

      7. unsub-neg 62.1%

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

      8. associate-/l* 62.0%

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

      9. associate-*r/ 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in z around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-/l* 68.3%

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

      4. distribute-neg-frac 68.3%

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

   9. Simplified 68.3%

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

   if 1.9999999999999999e45 < (/.f64 z t) < 5.00000000000000029e62

   1. Initial program 99.4%

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

   2. Taylor expanded in z around -inf 80.6%

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

   3. Taylor expanded in t around 0 80.6%

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

   4. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in z around 0 80.6%

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

      1. associate-/l* 99.7%

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

   9. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{\frac{t}{x}}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+62} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- z) (/ t x))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -1e+248)
     (/ (* y z) t)
     (if (<= (/ z t) -4e+88)
       t_1
       (if (<= (/ z t) -2e-44)
         t_2
         (if (<= (/ z t) 4e-13)
           x
           (if (or (<= (/ z t) 5e+62) (not (<= (/ z t) 2e+231))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z / (t / x);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = t_1;
	} else if ((z / t) <= -2e-44) {
		tmp = t_2;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if (((z / t) <= 5e+62) || !((z / t) <= 2e+231)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -z / (t / x)
    t_2 = y * (z / t)
    if ((z / t) <= (-1d+248)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-4d+88)) then
        tmp = t_1
    else if ((z / t) <= (-2d-44)) then
        tmp = t_2
    else if ((z / t) <= 4d-13) then
        tmp = x
    else if (((z / t) <= 5d+62) .or. (.not. ((z / t) <= 2d+231))) 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 t_1 = -z / (t / x);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+248) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -4e+88) {
		tmp = t_1;
	} else if ((z / t) <= -2e-44) {
		tmp = t_2;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if (((z / t) <= 5e+62) || !((z / t) <= 2e+231)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z / (t / x)
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e+248:
		tmp = (y * z) / t
	elif (z / t) <= -4e+88:
		tmp = t_1
	elif (z / t) <= -2e-44:
		tmp = t_2
	elif (z / t) <= 4e-13:
		tmp = x
	elif ((z / t) <= 5e+62) or not ((z / t) <= 2e+231):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) / Float64(t / x))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+248)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -4e+88)
		tmp = t_1;
	elseif (Float64(z / t) <= -2e-44)
		tmp = t_2;
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	elseif ((Float64(z / t) <= 5e+62) || !(Float64(z / t) <= 2e+231))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z / (t / x);
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+248)
		tmp = (y * z) / t;
	elseif ((z / t) <= -4e+88)
		tmp = t_1;
	elseif ((z / t) <= -2e-44)
		tmp = t_2;
	elseif ((z / t) <= 4e-13)
		tmp = x;
	elseif (((z / t) <= 5e+62) || ~(((z / t) <= 2e+231)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+248], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -4e+88], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, If[Or[LessEqual[N[(z / t), $MachinePrecision], 5e+62], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e+231]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -1.00000000000000005e248

   1. Initial program 87.8%

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

   2. Taylor expanded in z around -inf 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   6. Simplified 68.2%

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

   if -1.00000000000000005e248 < (/.f64 z t) < -3.99999999999999984e88 or 5.00000000000000029e62 < (/.f64 z t) < 2.0000000000000001e231

   1. Initial program 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. neg-mul-1 67.8%

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

      2. +-commutative 67.8%

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

      3. distribute-rgt1-in 67.8%

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

      4. distribute-lft-neg-out 67.8%

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

      5. associate-*l/ 65.7%

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

      6. associate-/l* 67.8%

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

      7. unsub-neg 67.8%

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

      8. associate-/l* 65.7%

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

      9. associate-*r/ 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in z around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-/l* 67.8%

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

   9. Simplified 67.8%

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

   if -3.99999999999999984e88 < (/.f64 z t) < -1.99999999999999991e-44 or 4.0000000000000001e-13 < (/.f64 z t) < 5.00000000000000029e62 or 2.0000000000000001e231 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 84.9%

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

   3. Taylor expanded in t around 0 77.0%

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

   4. Taylor expanded in y around inf 55.1%

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

      1. *-commutative 55.1%

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

   6. Simplified 55.1%

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

      1. associate-/l* 55.4%

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

      2. associate-/r/ 63.5%

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

   8. Applied egg-rr 63.5%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+62} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 5: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= (/ z t) -2e-44)
     t_1
     (if (<= (/ z t) 4e-13)
       x
       (if (<= (/ z t) 2e+22)
         (* y (/ z t))
         (if (<= (/ z t) 2e+45) (/ (- x) (/ t z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e+45) {
		tmp = -x / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if ((z / t) <= (-2d-44)) then
        tmp = t_1
    else if ((z / t) <= 4d-13) then
        tmp = x
    else if ((z / t) <= 2d+22) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d+45) then
        tmp = -x / (t / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = t_1;
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else if ((z / t) <= 2e+22) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e+45) {
		tmp = -x / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if (z / t) <= -2e-44:
		tmp = t_1
	elif (z / t) <= 4e-13:
		tmp = x
	elif (z / t) <= 2e+22:
		tmp = y * (z / t)
	elif (z / t) <= 2e+45:
		tmp = -x / (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e-44)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	elseif (Float64(z / t) <= 2e+22)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e+45)
		tmp = Float64(Float64(-x) / Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if ((z / t) <= -2e-44)
		tmp = t_1;
	elseif ((z / t) <= 4e-13)
		tmp = x;
	elseif ((z / t) <= 2e+22)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e+45)
		tmp = -x / (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+22], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e+45], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -1.99999999999999991e-44 or 1.9999999999999999e45 < (/.f64 z t)

   1. Initial program 96.6%

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

   2. Taylor expanded in z around -inf 92.5%

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

   3. Taylor expanded in t around 0 89.4%

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

   4. Taylor expanded in y around 0 80.8%

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

      1. associate-*r/ 79.0%

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

      2. +-commutative 79.0%

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

      3. mul-1-neg 79.0%

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

      4. associate-/l* 79.0%

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

      5. sub-neg 79.0%

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

      6. associate-/r/ 78.0%

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

      7. *-commutative 78.0%

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

      8. distribute-rgt-out-- 92.7%

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

      9. associate-*l/ 89.4%

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

      10. associate-*r/ 93.5%

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

   6. Simplified 93.5%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 4.0000000000000001e-13 < (/.f64 z t) < 2e22

   1. Initial program 99.6%

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

   2. Taylor expanded in z around -inf 85.8%

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

   3. Taylor expanded in t around 0 74.1%

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

   4. Taylor expanded in y around inf 72.0%

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

      1. *-commutative 72.0%

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

   6. Simplified 72.0%

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

      1. associate-/l* 24.9%

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

      2. associate-/r/ 72.2%

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

   8. Applied egg-rr 72.2%

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

   if 2e22 < (/.f64 z t) < 1.9999999999999999e45

   1. Initial program 99.4%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 94.9%

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

      1. neg-mul-1 94.9%

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

      2. +-commutative 94.9%

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

      3. distribute-rgt1-in 94.9%

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

      4. distribute-lft-neg-out 94.9%

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

      5. associate-*l/ 57.7%

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

      6. associate-/l* 57.5%

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

      7. unsub-neg 57.5%

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

      8. associate-/l* 57.7%

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

      9. associate-*r/ 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in z around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-/l* 95.2%

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

      4. distribute-neg-frac 95.2%

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

   9. Simplified 95.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-44)
   (* z (/ (- y x) t))
   (if (<= (/ z t) 4e-13) x (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-44)) then
        tmp = z * ((y - x) / t)
    else if ((z / t) <= 4d-13) then
        tmp = x
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-44:
		tmp = z * ((y - x) / t)
	elif (z / t) <= 4e-13:
		tmp = x
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-44)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-44)
		tmp = z * ((y - x) / t);
	elseif ((z / t) <= 4e-13)
		tmp = x;
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.99999999999999991e-44

   1. Initial program 95.9%

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

   2. Taylor expanded in z around -inf 90.5%

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

   3. Taylor expanded in t around 0 85.4%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. associate-*r/ 74.1%

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

      2. +-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. associate-/l* 74.1%

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

      5. sub-neg 74.1%

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

      6. associate-/r/ 74.0%

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

      7. *-commutative 74.0%

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

      8. distribute-rgt-out-- 89.5%

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

      9. associate-*l/ 85.4%

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

      10. associate-*r/ 90.8%

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

   6. Simplified 90.8%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 4.0000000000000001e-13 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 91.5%

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

   3. Taylor expanded in t around 0 90.1%

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

      1. associate-/l* 95.6%

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

      2. div-inv 95.5%

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

      3. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+33)
   (* z (/ (- y x) t))
   (if (<= (/ z t) 4e-13) (+ x (* y (/ z t))) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+33) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d+33)) then
        tmp = z * ((y - x) / t)
    else if ((z / t) <= 4d-13) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+33) {
		tmp = z * ((y - x) / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+33:
		tmp = z * ((y - x) / t)
	elif (z / t) <= 4e-13:
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+33)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (Float64(z / t) <= 4e-13)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+33)
		tmp = z * ((y - x) / t);
	elseif ((z / t) <= 4e-13)
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+33], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.9999999999999999e33

   1. Initial program 94.8%

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

   2. Taylor expanded in z around -inf 94.8%

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

   3. Taylor expanded in t around 0 94.8%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 75.3%

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

      2. +-commutative 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 75.3%

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

      5. sub-neg 75.3%

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

      6. associate-/r/ 75.1%

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

      7. *-commutative 75.1%

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

      8. distribute-rgt-out-- 94.8%

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

      9. associate-*l/ 94.8%

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

      10. associate-*r/ 98.2%

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

   6. Simplified 98.2%

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

   if -1.9999999999999999e33 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.9%

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

   2. Taylor expanded in y around inf 92.8%

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

      1. associate-*r/ 97.8%

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

   4. Simplified 97.8%

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

   if 4.0000000000000001e-13 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 91.5%

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

   3. Taylor expanded in t around 0 90.1%

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

      1. associate-/l* 95.6%

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

      2. div-inv 95.5%

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

      3. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e+33)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 4e-13) (+ x (* y (/ z t))) (* (- y x) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+33) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 4e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d+33)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 4d-13) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - x) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e+33) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 4e-13) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e+33:
		tmp = z / (t / (y - x))
	elif (z / t) <= 4e-13:
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e+33)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 4e-13)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e+33)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 4e-13)
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e+33], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.9999999999999999e33

   1. Initial program 94.8%

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

   2. Taylor expanded in z around -inf 94.8%

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

   3. Taylor expanded in t around 0 94.8%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 75.3%

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

      2. +-commutative 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 75.3%

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

      5. sub-neg 75.3%

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

      6. associate-/r/ 75.1%

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

      7. *-commutative 75.1%

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

      8. distribute-rgt-out-- 94.8%

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

      9. associate-*l/ 94.8%

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

      10. associate-*r/ 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in z around 0 94.8%

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

      1. associate-/l* 98.2%

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

   9. Simplified 98.2%

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

   if -1.9999999999999999e33 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.9%

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

   2. Taylor expanded in y around inf 92.8%

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

      1. associate-*r/ 97.8%

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

   4. Simplified 97.8%

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

   if 4.0000000000000001e-13 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 91.5%

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

   3. Taylor expanded in t around 0 90.1%

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

      1. associate-/l* 95.6%

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

      2. div-inv 95.5%

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

      3. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-37} \lor \neg \left(t \leq 8.2 \cdot 10^{+47}\right) \land t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.2e+51)
   x
   (if (or (<= t 3.7e-37) (and (not (<= t 8.2e+47)) (<= t 3.1e+182)))
     (* z (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+51) {
		tmp = x;
	} else if ((t <= 3.7e-37) || (!(t <= 8.2e+47) && (t <= 3.1e+182))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.2d+51)) then
        tmp = x
    else if ((t <= 3.7d-37) .or. (.not. (t <= 8.2d+47)) .and. (t <= 3.1d+182)) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+51) {
		tmp = x;
	} else if ((t <= 3.7e-37) || (!(t <= 8.2e+47) && (t <= 3.1e+182))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e+51:
		tmp = x
	elif (t <= 3.7e-37) or (not (t <= 8.2e+47) and (t <= 3.1e+182)):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e+51)
		tmp = x;
	elseif ((t <= 3.7e-37) || (!(t <= 8.2e+47) && (t <= 3.1e+182)))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.2e+51)
		tmp = x;
	elseif ((t <= 3.7e-37) || (~((t <= 8.2e+47)) && (t <= 3.1e+182)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.2e+51], x, If[Or[LessEqual[t, 3.7e-37], And[N[Not[LessEqual[t, 8.2e+47]], $MachinePrecision], LessEqual[t, 3.1e+182]]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000002e51 or 3.7e-37 < t < 8.2000000000000002e47 or 3.09999999999999996e182 < t

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 74.4%

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

   if -5.2000000000000002e51 < t < 3.7e-37 or 8.2000000000000002e47 < t < 3.09999999999999996e182

   1. Initial program 96.9%

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

   2. Taylor expanded in z around -inf 96.5%

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

   3. Taylor expanded in t around 0 82.2%

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

   4. Taylor expanded in y around 0 75.1%

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

      1. associate-*r/ 71.3%

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

      2. +-commutative 71.3%

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

      3. mul-1-neg 71.3%

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

      4. associate-/l* 69.9%

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

      5. sub-neg 69.9%

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

      6. associate-/r/ 70.5%

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

      7. *-commutative 70.5%

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

      8. distribute-rgt-out-- 82.6%

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

      9. associate-*l/ 82.2%

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

      10. associate-*r/ 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in y around inf 48.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-37} \lor \neg \left(t \leq 8.2 \cdot 10^{+47}\right) \land t \leq 3.1 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-44)
   (* z (/ y t))
   (if (<= (/ z t) 4e-13) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * (y / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-44)) then
        tmp = z * (y / t)
    else if ((z / t) <= 4d-13) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * (y / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-44:
		tmp = z * (y / t)
	elif (z / t) <= 4e-13:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-44)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-44)
		tmp = z * (y / t);
	elseif ((z / t) <= 4e-13)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.99999999999999991e-44

   1. Initial program 95.9%

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

   2. Taylor expanded in z around -inf 90.5%

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

   3. Taylor expanded in t around 0 85.4%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. associate-*r/ 74.1%

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

      2. +-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. associate-/l* 74.1%

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

      5. sub-neg 74.1%

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

      6. associate-/r/ 74.0%

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

      7. *-commutative 74.0%

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

      8. distribute-rgt-out-- 89.5%

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

      9. associate-*l/ 85.4%

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

      10. associate-*r/ 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around inf 54.6%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 4.0000000000000001e-13 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 91.5%

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

   3. Taylor expanded in t around 0 90.1%

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

   4. Taylor expanded in y around inf 52.3%

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

      1. *-commutative 52.3%

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

   6. Simplified 52.3%

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

      1. associate-/l* 49.2%

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

      2. associate-/r/ 55.6%

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

   8. Applied egg-rr 55.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2e-44)
   (* z (/ y t))
   (if (<= (/ z t) 4e-13) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * (y / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-2d-44)) then
        tmp = z * (y / t)
    else if ((z / t) <= 4d-13) then
        tmp = x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2e-44) {
		tmp = z * (y / t);
	} else if ((z / t) <= 4e-13) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2e-44:
		tmp = z * (y / t)
	elif (z / t) <= 4e-13:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2e-44)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= 4e-13)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2e-44)
		tmp = z * (y / t);
	elseif ((z / t) <= 4e-13)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2e-44], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-13], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.99999999999999991e-44

   1. Initial program 95.9%

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

   2. Taylor expanded in z around -inf 90.5%

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

   3. Taylor expanded in t around 0 85.4%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. associate-*r/ 74.1%

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

      2. +-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. associate-/l* 74.1%

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

      5. sub-neg 74.1%

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

      6. associate-/r/ 74.0%

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

      7. *-commutative 74.0%

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

      8. distribute-rgt-out-- 89.5%

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

      9. associate-*l/ 85.4%

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

      10. associate-*r/ 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around inf 54.6%

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

   if -1.99999999999999991e-44 < (/.f64 z t) < 4.0000000000000001e-13

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.6%

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

   if 4.0000000000000001e-13 < (/.f64 z t)

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 91.5%

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

   3. Taylor expanded in t around 0 90.1%

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

   4. Taylor expanded in y around inf 52.3%

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

      1. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in z around 0 52.3%

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

      1. associate-/l* 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 12: 38.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 97.8%

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

2. Taylor expanded in z around 0 42.4%

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

3. Final simplification 42.4%

   \[\leadsto x \]

Developer target: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

  (+ x (* (- y x) (/ z t))))