Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.4% → 98.7%

Time: 13.2s

Alternatives: 13

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.4% accurate, 1.0× speedup

Math

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

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(Float64(y - x) * 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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+291)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+291)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+291)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+291):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(z * Float64(y - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+291))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((z * (y - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+291)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0 or 9.9999999999999996e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 78.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 9.9999999999999996e290

   1. Initial program 98.8%

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

4. Final simplification 99.2%

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

Alternative 2: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 4.5e-123) (+ x (/ (- y x) (/ t z))) (fma (/ (- y x) t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.5e-123) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = fma(((y - x) / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.5e-123)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = fma(Float64(Float64(y - x) / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 4.5e-123], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.49999999999999993e-123

   1. Initial program 91.9%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   if 4.49999999999999993e-123 < z

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \end{array} \]

Alternative 3: 71.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= x -5e+164)
     t_1
     (if (<= x -4.9e+109)
       (* z (/ (- x) t))
       (if (<= x 1.6e+122) t_1 (* x (/ (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (x <= -5e+164) {
		tmp = t_1;
	} else if (x <= -4.9e+109) {
		tmp = z * (-x / t);
	} else if (x <= 1.6e+122) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (x <= (-5d+164)) then
        tmp = t_1
    else if (x <= (-4.9d+109)) then
        tmp = z * (-x / t)
    else if (x <= 1.6d+122) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (x <= -5e+164) {
		tmp = t_1;
	} else if (x <= -4.9e+109) {
		tmp = z * (-x / t);
	} else if (x <= 1.6e+122) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if x <= -5e+164:
		tmp = t_1
	elif x <= -4.9e+109:
		tmp = z * (-x / t)
	elif x <= 1.6e+122:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (x <= -5e+164)
		tmp = t_1;
	elseif (x <= -4.9e+109)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (x <= 1.6e+122)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (x <= -5e+164)
		tmp = t_1;
	elseif (x <= -4.9e+109)
		tmp = z * (-x / t);
	elseif (x <= 1.6e+122)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+164], t$95$1, If[LessEqual[x, -4.9e+109], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+122], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9999999999999995e164 or -4.9000000000000003e109 < x < 1.60000000000000006e122

   1. Initial program 93.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. associate-*r/ 77.3%

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

   6. Simplified 77.3%

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

   if -4.9999999999999995e164 < x < -4.9000000000000003e109

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 90.8%

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

      1. distribute-rgt-in 90.8%

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

      2. *-lft-identity 90.8%

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

      3. mul-1-neg 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

      5. associate-*l/ 83.1%

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

      6. associate-*r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in z around inf 71.5%

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

       1. associate-*r/ 79.2%

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

       2. *-commutative 79.2%

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

       3. associate-*r* 79.2%

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

       4. neg-mul-1 79.2%

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

       5. distribute-neg-frac 79.2%

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

   11. Simplified 79.2%

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

   12. Taylor expanded in z around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 79.2%

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

       3. distribute-rgt-neg-in 79.2%

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

   14. Simplified 79.2%

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

   if 1.60000000000000006e122 < x

   1. Initial program 88.2%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. *-lft-identity 99.9%

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

      3. mul-1-neg 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. associate-*l/ 88.4%

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

      6. associate-*r/ 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in z around inf 63.9%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. associate-*r* 69.5%

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

       4. neg-mul-1 69.5%

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

       5. distribute-neg-frac 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+164}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 4: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= x -6.8e+164)
     t_1
     (if (<= x -3.55e+109)
       (* z (/ (- x) t))
       (if (<= x 5.6e+121) t_1 (* x (/ (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (x <= -6.8e+164) {
		tmp = t_1;
	} else if (x <= -3.55e+109) {
		tmp = z * (-x / t);
	} else if (x <= 5.6e+121) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (x <= (-6.8d+164)) then
        tmp = t_1
    else if (x <= (-3.55d+109)) then
        tmp = z * (-x / t)
    else if (x <= 5.6d+121) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (x <= -6.8e+164) {
		tmp = t_1;
	} else if (x <= -3.55e+109) {
		tmp = z * (-x / t);
	} else if (x <= 5.6e+121) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if x <= -6.8e+164:
		tmp = t_1
	elif x <= -3.55e+109:
		tmp = z * (-x / t)
	elif x <= 5.6e+121:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (x <= -6.8e+164)
		tmp = t_1;
	elseif (x <= -3.55e+109)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (x <= 5.6e+121)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (x <= -6.8e+164)
		tmp = t_1;
	elseif (x <= -3.55e+109)
		tmp = z * (-x / t);
	elseif (x <= 5.6e+121)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+164], t$95$1, If[LessEqual[x, -3.55e+109], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+121], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000002e164 or -3.5500000000000001e109 < x < 5.60000000000000012e121

   1. Initial program 93.3%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 77.7%

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

   if -6.8000000000000002e164 < x < -3.5500000000000001e109

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 90.8%

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

      1. distribute-rgt-in 90.8%

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

      2. *-lft-identity 90.8%

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

      3. mul-1-neg 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

      5. associate-*l/ 83.1%

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

      6. associate-*r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in z around inf 71.5%

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

       1. associate-*r/ 79.2%

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

       2. *-commutative 79.2%

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

       3. associate-*r* 79.2%

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

       4. neg-mul-1 79.2%

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

       5. distribute-neg-frac 79.2%

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

   11. Simplified 79.2%

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

   12. Taylor expanded in z around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 79.2%

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

       3. distribute-rgt-neg-in 79.2%

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

   14. Simplified 79.2%

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

   if 5.60000000000000012e121 < x

   1. Initial program 88.2%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. *-lft-identity 99.9%

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

      3. mul-1-neg 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. associate-*l/ 88.4%

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

      6. associate-*r/ 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in z around inf 63.9%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. associate-*r* 69.5%

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

       4. neg-mul-1 69.5%

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

       5. distribute-neg-frac 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 5: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.5e+164)
   (+ x (* z (/ y t)))
   (if (<= x -2.8e+110)
     (* z (/ (- x) t))
     (if (<= x 1.1e+122) (+ x (/ z (/ t y))) (* x (/ (- z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.5e+164) {
		tmp = x + (z * (y / t));
	} else if (x <= -2.8e+110) {
		tmp = z * (-x / t);
	} else if (x <= 1.1e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = 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 (x <= (-7.5d+164)) then
        tmp = x + (z * (y / t))
    else if (x <= (-2.8d+110)) then
        tmp = z * (-x / t)
    else if (x <= 1.1d+122) then
        tmp = x + (z / (t / y))
    else
        tmp = 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 (x <= -7.5e+164) {
		tmp = x + (z * (y / t));
	} else if (x <= -2.8e+110) {
		tmp = z * (-x / t);
	} else if (x <= 1.1e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.5e+164:
		tmp = x + (z * (y / t))
	elif x <= -2.8e+110:
		tmp = z * (-x / t)
	elif x <= 1.1e+122:
		tmp = x + (z / (t / y))
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.5e+164)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (x <= -2.8e+110)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (x <= 1.1e+122)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.5e+164)
		tmp = x + (z * (y / t));
	elseif (x <= -2.8e+110)
		tmp = z * (-x / t);
	elseif (x <= 1.1e+122)
		tmp = x + (z / (t / y));
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.5e+164], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e+110], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+122], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.49999999999999976e164

   1. Initial program 91.5%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -7.49999999999999976e164 < x < -2.79999999999999987e110

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 90.8%

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

      1. distribute-rgt-in 90.8%

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

      2. *-lft-identity 90.8%

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

      3. mul-1-neg 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

      5. associate-*l/ 83.1%

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

      6. associate-*r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in z around inf 71.5%

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

       1. associate-*r/ 79.2%

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

       2. *-commutative 79.2%

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

       3. associate-*r* 79.2%

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

       4. neg-mul-1 79.2%

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

       5. distribute-neg-frac 79.2%

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

   11. Simplified 79.2%

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

   12. Taylor expanded in z around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 79.2%

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

       3. distribute-rgt-neg-in 79.2%

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

   14. Simplified 79.2%

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

   if -2.79999999999999987e110 < x < 1.1e122

   1. Initial program 93.5%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if 1.1e122 < x

   1. Initial program 88.2%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. *-lft-identity 99.9%

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

      3. mul-1-neg 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. associate-*l/ 88.4%

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

      6. associate-*r/ 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in z around inf 63.9%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. associate-*r* 69.5%

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

       4. neg-mul-1 69.5%

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

       5. distribute-neg-frac 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 6: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.2e+164)
   (+ x (/ (* z y) t))
   (if (<= x -4.9e+109)
     (* z (/ (- x) t))
     (if (<= x 4.8e+122) (+ x (/ z (/ t y))) (* x (/ (- z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.2e+164) {
		tmp = x + ((z * y) / t);
	} else if (x <= -4.9e+109) {
		tmp = z * (-x / t);
	} else if (x <= 4.8e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = 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 (x <= (-7.2d+164)) then
        tmp = x + ((z * y) / t)
    else if (x <= (-4.9d+109)) then
        tmp = z * (-x / t)
    else if (x <= 4.8d+122) then
        tmp = x + (z / (t / y))
    else
        tmp = 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 (x <= -7.2e+164) {
		tmp = x + ((z * y) / t);
	} else if (x <= -4.9e+109) {
		tmp = z * (-x / t);
	} else if (x <= 4.8e+122) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.2e+164:
		tmp = x + ((z * y) / t)
	elif x <= -4.9e+109:
		tmp = z * (-x / t)
	elif x <= 4.8e+122:
		tmp = x + (z / (t / y))
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.2e+164)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	elseif (x <= -4.9e+109)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (x <= 4.8e+122)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.2e+164)
		tmp = x + ((z * y) / t);
	elseif (x <= -4.9e+109)
		tmp = z * (-x / t);
	elseif (x <= 4.8e+122)
		tmp = x + (z / (t / y));
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.2e+164], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.9e+109], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+122], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.19999999999999981e164

   1. Initial program 91.5%

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

   2. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   if -7.19999999999999981e164 < x < -4.9000000000000003e109

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 90.8%

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

      1. distribute-rgt-in 90.8%

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

      2. *-lft-identity 90.8%

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

      3. mul-1-neg 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

      5. associate-*l/ 83.1%

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

      6. associate-*r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in z around inf 71.5%

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

       1. associate-*r/ 79.2%

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

       2. *-commutative 79.2%

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

       3. associate-*r* 79.2%

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

       4. neg-mul-1 79.2%

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

       5. distribute-neg-frac 79.2%

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

   11. Simplified 79.2%

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

   12. Taylor expanded in z around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 79.2%

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

       3. distribute-rgt-neg-in 79.2%

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

   14. Simplified 79.2%

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

   if -4.9000000000000003e109 < x < 4.8000000000000004e122

   1. Initial program 93.5%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if 4.8000000000000004e122 < x

   1. Initial program 88.2%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. *-lft-identity 99.9%

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

      3. mul-1-neg 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. associate-*l/ 88.4%

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

      6. associate-*r/ 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in z around inf 63.9%

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

       1. associate-*r/ 69.5%

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

       2. *-commutative 69.5%

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

       3. associate-*r* 69.5%

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

       4. neg-mul-1 69.5%

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

       5. distribute-neg-frac 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 7: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-74}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-95}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e-74)
   (+ x (* z (/ y t)))
   (if (<= y 1.45e-95) (- x (* x (/ z t))) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-74) {
		tmp = x + (z * (y / t));
	} else if (y <= 1.45e-95) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (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 (y <= (-8.2d-74)) then
        tmp = x + (z * (y / t))
    else if (y <= 1.45d-95) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (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 (y <= -8.2e-74) {
		tmp = x + (z * (y / t));
	} else if (y <= 1.45e-95) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e-74:
		tmp = x + (z * (y / t))
	elif y <= 1.45e-95:
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-74)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (y <= 1.45e-95)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-74)
		tmp = x + (z * (y / t));
	elseif (y <= 1.45e-95)
		tmp = x - (x * (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e-74], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-95], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000063e-74

   1. Initial program 91.6%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 86.9%

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

   if -8.20000000000000063e-74 < y < 1.45000000000000001e-95

   1. Initial program 96.1%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around inf 84.9%

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

      1. distribute-lft-in 84.9%

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

      2. mul-1-neg 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. unsub-neg 84.9%

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

      5. *-rgt-identity 84.9%

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

   6. Simplified 84.9%

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

   if 1.45000000000000001e-95 < y

   1. Initial program 88.2%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around inf 77.7%

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

      1. associate-*r/ 83.7%

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

   6. Simplified 83.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-74}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-95}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.7e-122) (+ x (/ (- y x) (/ t z))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.7e-122) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + (z * ((y - x) / 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 <= 3.7d-122) then
        tmp = x + ((y - x) / (t / z))
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.7e-122) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.7e-122:
		tmp = x + ((y - x) / (t / z))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.7e-122)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3.7e-122)
		tmp = x + ((y - x) / (t / z));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.7e-122], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.6999999999999997e-122

   1. Initial program 91.9%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   if 3.6999999999999997e-122 < z

   1. Initial program 92.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 9: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-5} \lor \neg \left(z \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.28e-5) (not (<= z 6.6e-81))) (* z (/ (- x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.28e-5) || !(z <= 6.6e-81)) {
		tmp = z * (-x / 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 ((z <= (-1.28d-5)) .or. (.not. (z <= 6.6d-81))) then
        tmp = z * (-x / 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 ((z <= -1.28e-5) || !(z <= 6.6e-81)) {
		tmp = z * (-x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.28e-5) or not (z <= 6.6e-81):
		tmp = z * (-x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.28e-5) || !(z <= 6.6e-81))
		tmp = Float64(z * Float64(Float64(-x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.28e-5) || ~((z <= 6.6e-81)))
		tmp = z * (-x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.28e-5], N[Not[LessEqual[z, 6.6e-81]], $MachinePrecision]], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.2799999999999999e-5 or 6.59999999999999975e-81 < z

   1. Initial program 87.8%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

      1. associate-/r/ 95.5%

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

      2. clear-num 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in x around inf 61.2%

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

      1. distribute-rgt-in 61.2%

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

      2. *-lft-identity 61.2%

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

      3. mul-1-neg 61.2%

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

      4. cancel-sign-sub-inv 61.2%

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

      5. associate-*l/ 54.8%

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

      6. associate-*r/ 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around inf 45.6%

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

       1. associate-*r/ 49.5%

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

       2. *-commutative 49.5%

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

       3. associate-*r* 49.5%

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

       4. neg-mul-1 49.5%

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

       5. distribute-neg-frac 49.5%

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

   11. Simplified 49.5%

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

   12. Taylor expanded in z around 0 45.6%

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

       1. mul-1-neg 45.6%

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

       2. associate-*l/ 48.0%

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

       3. distribute-rgt-neg-in 48.0%

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

   14. Simplified 48.0%

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

   if -1.2799999999999999e-5 < z < 6.59999999999999975e-81

   1. Initial program 98.2%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-5} \lor \neg \left(z \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00062 \lor \neg \left(z \leq 6.2 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00062) (not (<= z 6.2e-81))) (* x (/ (- z) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00062) || !(z <= 6.2e-81)) {
		tmp = x * (-z / 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 ((z <= (-0.00062d0)) .or. (.not. (z <= 6.2d-81))) then
        tmp = x * (-z / 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 ((z <= -0.00062) || !(z <= 6.2e-81)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00062) or not (z <= 6.2e-81):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00062) || !(z <= 6.2e-81))
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00062) || ~((z <= 6.2e-81)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00062], N[Not[LessEqual[z, 6.2e-81]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e-4 or 6.19999999999999976e-81 < z

   1. Initial program 87.8%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

      1. associate-/r/ 95.5%

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

      2. clear-num 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in x around inf 61.2%

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

      1. distribute-rgt-in 61.2%

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

      2. *-lft-identity 61.2%

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

      3. mul-1-neg 61.2%

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

      4. cancel-sign-sub-inv 61.2%

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

      5. associate-*l/ 54.8%

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

      6. associate-*r/ 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around inf 45.6%

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

       1. associate-*r/ 49.5%

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

       2. *-commutative 49.5%

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

       3. associate-*r* 49.5%

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

       4. neg-mul-1 49.5%

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

       5. distribute-neg-frac 49.5%

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

   11. Simplified 49.5%

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

   if -6.2e-4 < z < 6.19999999999999976e-81

   1. Initial program 98.2%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00062 \lor \neg \left(z \leq 6.2 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.012:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.012) (* x (/ (- z) t)) (if (<= z 6.6e-81) x (/ (- x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.012) {
		tmp = x * (-z / t);
	} else if (z <= 6.6e-81) {
		tmp = x;
	} else {
		tmp = -x / (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 <= (-0.012d0)) then
        tmp = x * (-z / t)
    else if (z <= 6.6d-81) then
        tmp = x
    else
        tmp = -x / (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 <= -0.012) {
		tmp = x * (-z / t);
	} else if (z <= 6.6e-81) {
		tmp = x;
	} else {
		tmp = -x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.012:
		tmp = x * (-z / t)
	elif z <= 6.6e-81:
		tmp = x
	else:
		tmp = -x / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.012)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 6.6e-81)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.012)
		tmp = x * (-z / t);
	elseif (z <= 6.6e-81)
		tmp = x;
	else
		tmp = -x / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.012], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-81], x, N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.012

   1. Initial program 83.8%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

      1. associate-/r/ 97.4%

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

      2. clear-num 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. distribute-rgt-in 59.2%

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

      2. *-lft-identity 59.2%

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

      3. mul-1-neg 59.2%

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

      4. cancel-sign-sub-inv 59.2%

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

      5. associate-*l/ 54.2%

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

      6. associate-*r/ 58.9%

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

   8. Simplified 58.9%

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

   9. Taylor expanded in z around inf 46.2%

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

       1. associate-*r/ 48.7%

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

       2. *-commutative 48.7%

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

       3. associate-*r* 48.7%

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

       4. neg-mul-1 48.7%

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

       5. distribute-neg-frac 48.7%

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

   11. Simplified 48.7%

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

   if -0.012 < z < 6.59999999999999975e-81

   1. Initial program 98.2%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around inf 66.9%

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

   if 6.59999999999999975e-81 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 93.5%

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

      2. clear-num 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in x around inf 63.4%

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

      1. distribute-rgt-in 63.4%

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

      2. *-lft-identity 63.4%

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

      3. mul-1-neg 63.4%

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

      4. cancel-sign-sub-inv 63.4%

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

      5. associate-*l/ 55.5%

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

      6. associate-*r/ 60.6%

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

   8. Simplified 60.6%

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

   9. Taylor expanded in z around inf 44.9%

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

       1. mul-1-neg 44.9%

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

       2. associate-/l* 50.3%

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

       3. distribute-frac-neg 50.3%

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

   11. Simplified 50.3%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.012:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \end{array} \]

Alternative 12: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 13: 38.6% 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 92.2%

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

   1. associate-/l* 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in t around inf 36.5%

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

5. Final simplification 36.5%

   \[\leadsto x \]

Developer target: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (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 (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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