Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.7% → 98.8%

Time: 8.2s

Alternatives: 12

Speedup: 1.0×

• 24.7% 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: 92.7% 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+299}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+299)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+299)) {
		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 + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+299)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+299):
		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(Float64(y - x) * z) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+299))
		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 + (((y - x) * z) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+299)))
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+299]], $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 1.0000000000000001e299 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 85.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1.0000000000000001e299

   1. Initial program 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 10^{+299}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+223}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e+223)
   (* (/ z t) (- x))
   (if (<= z -9e+66) (* z (/ y t)) (if (<= z 8e-27) x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+223) {
		tmp = (z / t) * -x;
	} else if (z <= -9e+66) {
		tmp = z * (y / t);
	} else if (z <= 8e-27) {
		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 <= (-2d+223)) then
        tmp = (z / t) * -x
    else if (z <= (-9d+66)) then
        tmp = z * (y / t)
    else if (z <= 8d-27) 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 <= -2e+223) {
		tmp = (z / t) * -x;
	} else if (z <= -9e+66) {
		tmp = z * (y / t);
	} else if (z <= 8e-27) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e+223:
		tmp = (z / t) * -x
	elif z <= -9e+66:
		tmp = z * (y / t)
	elif z <= 8e-27:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e+223)
		tmp = Float64(Float64(z / t) * Float64(-x));
	elseif (z <= -9e+66)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 8e-27)
		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 <= -2e+223)
		tmp = (z / t) * -x;
	elseif (z <= -9e+66)
		tmp = z * (y / t);
	elseif (z <= 8e-27)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e+223], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, -9e+66], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-27], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.00000000000000009e223

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-lft-in 75.8%

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

   3. Applied egg-rr 75.8%

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

      1. distribute-rgt-neg-out 75.8%

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

      2. unsub-neg 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in x around inf 83.4%

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

   7. Taylor expanded in z around inf 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. *-commutative 67.7%

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

      4. distribute-rgt-neg-out 67.7%

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

      5. associate-*r/ 82.3%

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

   9. Simplified 82.3%

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

   if -2.00000000000000009e223 < z < -8.9999999999999997e66

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 86.1%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 60.8%

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

      1. associate-*l/ 67.1%

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

      2. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if -8.9999999999999997e66 < z < 8.0000000000000003e-27

   1. Initial program 99.2%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in t around inf 59.8%

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

   if 8.0000000000000003e-27 < z

   1. Initial program 91.1%

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

   2. Taylor expanded in t around 0 83.8%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   5. Simplified 58.7%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 61.9%

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

   7. Applied egg-rr 61.9%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+223}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+224}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+224)
   (* z (/ (- x) t))
   (if (<= z -1.75e+65) (* z (/ y t)) (if (<= z 2.02e-25) x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+224) {
		tmp = z * (-x / t);
	} else if (z <= -1.75e+65) {
		tmp = z * (y / t);
	} else if (z <= 2.02e-25) {
		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 <= (-5d+224)) then
        tmp = z * (-x / t)
    else if (z <= (-1.75d+65)) then
        tmp = z * (y / t)
    else if (z <= 2.02d-25) 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 <= -5e+224) {
		tmp = z * (-x / t);
	} else if (z <= -1.75e+65) {
		tmp = z * (y / t);
	} else if (z <= 2.02e-25) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+224:
		tmp = z * (-x / t)
	elif z <= -1.75e+65:
		tmp = z * (y / t)
	elif z <= 2.02e-25:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+224)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (z <= -1.75e+65)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 2.02e-25)
		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 <= -5e+224)
		tmp = z * (-x / t);
	elseif (z <= -1.75e+65)
		tmp = z * (y / t);
	elseif (z <= 2.02e-25)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+224], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e+65], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.02e-25], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999964e224

   1. Initial program 84.1%

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

   2. Taylor expanded in t around 0 84.1%

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

   3. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-rgt-neg-out 67.7%

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

   5. Simplified 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 82.2%

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

      3. distribute-neg-frac 82.2%

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

      4. associate-/r/ 82.4%

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

      5. distribute-rgt-neg-in 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -4.99999999999999964e224 < z < -1.75e65

   1. Initial program 90.7%

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

   2. Taylor expanded in t around 0 86.1%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 60.8%

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

      1. associate-*l/ 67.1%

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

      2. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if -1.75e65 < z < 2.02000000000000002e-25

   1. Initial program 99.2%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in t around inf 59.8%

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

   if 2.02000000000000002e-25 < z

   1. Initial program 91.1%

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

   2. Taylor expanded in t around 0 83.8%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   5. Simplified 58.7%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 61.9%

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

   7. Applied egg-rr 61.9%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+224}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-58} \lor \neg \left(x \leq 1.2 \cdot 10^{-204}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.06e-58) (not (<= x 1.2e-204)))
   (* x (- 1.0 (/ z t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.06e-58) || !(x <= 1.2e-204)) {
		tmp = x * (1.0 - (z / t));
	} 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 ((x <= (-1.06d-58)) .or. (.not. (x <= 1.2d-204))) then
        tmp = x * (1.0d0 - (z / t))
    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 ((x <= -1.06e-58) || !(x <= 1.2e-204)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.06e-58) or not (x <= 1.2e-204):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.06e-58) || !(x <= 1.2e-204))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.06e-58) || ~((x <= 1.2e-204)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.06e-58], N[Not[LessEqual[x, 1.2e-204]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0600000000000001e-58 or 1.2e-204 < x

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. sub-neg 94.7%

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

      3. distribute-lft-in 94.0%

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

   3. Applied egg-rr 94.0%

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

      1. distribute-rgt-neg-out 94.0%

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

      2. unsub-neg 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in x around inf 83.0%

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

   if -1.0600000000000001e-58 < x < 1.2e-204

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 78.4%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-58} \lor \neg \left(x \leq 1.2 \cdot 10^{-204}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-42} \lor \neg \left(x \leq 2.2 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e-42) (not (<= x 2.2e-55)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e-42) || !(x <= 2.2e-55)) {
		tmp = x * (1.0 - (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 ((x <= (-2.1d-42)) .or. (.not. (x <= 2.2d-55))) then
        tmp = x * (1.0d0 - (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 ((x <= -2.1e-42) || !(x <= 2.2e-55)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e-42) or not (x <= 2.2e-55):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e-42) || !(x <= 2.2e-55))
		tmp = Float64(x * Float64(1.0 - 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 ((x <= -2.1e-42) || ~((x <= 2.2e-55)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e-42], N[Not[LessEqual[x, 2.2e-55]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000006e-42 or 2.2e-55 < x

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. sub-neg 94.0%

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

      3. distribute-lft-in 93.2%

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

   3. Applied egg-rr 93.2%

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

      1. distribute-rgt-neg-out 93.2%

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

      2. unsub-neg 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in x around inf 87.5%

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

   if -2.10000000000000006e-42 < x < 2.2e-55

   1. Initial program 97.3%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 91.5%

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

      1. associate-*r/ 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-42} \lor \neg \left(x \leq 2.2 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.68 \cdot 10^{-43} \lor \neg \left(x \leq 1.95 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.68e-43) (not (<= x 1.95e-55)))
   (* x (- 1.0 (/ z t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.68e-43) || !(x <= 1.95e-55)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * (y / 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 <= (-1.68d-43)) .or. (.not. (x <= 1.95d-55))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.68e-43) || !(x <= 1.95e-55)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.68e-43) or not (x <= 1.95e-55):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.68e-43) || !(x <= 1.95e-55))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.68e-43) || ~((x <= 1.95e-55)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.68e-43], N[Not[LessEqual[x, 1.95e-55]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.68000000000000001e-43 or 1.95e-55 < x

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. sub-neg 94.0%

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

      3. distribute-lft-in 93.2%

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

   3. Applied egg-rr 93.2%

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

      1. distribute-rgt-neg-out 93.2%

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

      2. unsub-neg 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in x around inf 87.5%

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

   if -1.68000000000000001e-43 < x < 1.95e-55

   1. Initial program 97.3%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 90.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.68 \cdot 10^{-43} \lor \neg \left(x \leq 1.95 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{-39}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-56}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.85e-39)
   (- x (/ x (/ t z)))
   (if (<= x 1.1e-56) (+ x (* z (/ y t))) (* x (- 1.0 (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.85e-39) {
		tmp = x - (x / (t / z));
	} else if (x <= 1.1e-56) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (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 <= (-2.85d-39)) then
        tmp = x - (x / (t / z))
    else if (x <= 1.1d-56) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (1.0d0 - (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 <= -2.85e-39) {
		tmp = x - (x / (t / z));
	} else if (x <= 1.1e-56) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.85e-39:
		tmp = x - (x / (t / z))
	elif x <= 1.1e-56:
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.85e-39)
		tmp = Float64(x - Float64(x / Float64(t / z)));
	elseif (x <= 1.1e-56)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.85e-39)
		tmp = x - (x / (t / z));
	elseif (x <= 1.1e-56)
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.85e-39], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-56], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8499999999999998e-39

   1. Initial program 93.9%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 77.5%

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

      1. neg-mul-1 77.5%

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

      2. distribute-neg-frac 77.5%

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

   6. Simplified 77.5%

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

      1. *-commutative 77.5%

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

      2. add-sqr-sqrt 40.1%

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

      3. sqrt-unprod 62.8%

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

      4. sqr-neg 62.8%

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

      5. sqrt-unprod 23.8%

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

      6. add-sqr-sqrt 45.9%

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

      7. cancel-sign-sub-inv 45.9%

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

      8. add-sqr-sqrt 45.9%

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

      9. sqrt-unprod 27.7%

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

      10. sqr-neg 27.7%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 77.5%

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

   8. Applied egg-rr 77.5%

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

   9. Taylor expanded in z around 0 83.6%

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

       1. *-commutative 83.6%

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

       2. associate-/l* 85.9%

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

   11. Simplified 85.9%

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

   if -2.8499999999999998e-39 < x < 1.10000000000000002e-56

   1. Initial program 97.3%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 90.3%

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

   if 1.10000000000000002e-56 < x

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. sub-neg 94.1%

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

      3. distribute-lft-in 92.4%

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

   3. Applied egg-rr 92.4%

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

      1. distribute-rgt-neg-out 92.4%

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

      2. unsub-neg 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in x around inf 89.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{-39}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-56}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{+139}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.1e+139) (+ x (* z (/ (- y x) t))) (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.1e+139) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x * (1.0 - (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 <= 1.1d+139) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x * (1.0d0 - (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 <= 1.1e+139) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.1e+139:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.1e+139)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.1e+139)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.1e+139], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1e139

   1. Initial program 96.0%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   if 1.1e139 < x

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. sub-neg 91.6%

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

      3. distribute-lft-in 88.2%

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

   3. Applied egg-rr 88.2%

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

      1. distribute-rgt-neg-out 88.2%

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

      2. unsub-neg 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in x around inf 100.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{+139}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 9: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+65} \lor \neg \left(z \leq 1.9 \cdot 10^{-19}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+65) (not (<= z 1.9e-19))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+65) || !(z <= 1.9e-19)) {
		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 ((z <= (-1.8d+65)) .or. (.not. (z <= 1.9d-19))) 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 ((z <= -1.8e+65) || !(z <= 1.9e-19)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+65) or not (z <= 1.9e-19):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+65) || !(z <= 1.9e-19))
		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 ((z <= -1.8e+65) || ~((z <= 1.9e-19)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+65], N[Not[LessEqual[z, 1.9e-19]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999989e65 or 1.9e-19 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in t around 0 84.5%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in z around 0 54.9%

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

      1. associate-*l/ 57.5%

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

      2. *-commutative 57.5%

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

   8. Simplified 57.5%

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

   if -1.79999999999999989e65 < z < 1.9e-19

   1. Initial program 99.2%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in t around inf 59.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+65} \lor \neg \left(z \leq 1.9 \cdot 10^{-19}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 55.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+65) (* z (/ y t)) (if (<= z 2.7e-19) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+65) {
		tmp = z * (y / t);
	} else if (z <= 2.7e-19) {
		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 <= (-4.5d+65)) then
        tmp = z * (y / t)
    else if (z <= 2.7d-19) 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 <= -4.5e+65) {
		tmp = z * (y / t);
	} else if (z <= 2.7e-19) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+65:
		tmp = z * (y / t)
	elif z <= 2.7e-19:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+65)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 2.7e-19)
		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 <= -4.5e+65)
		tmp = z * (y / t);
	elseif (z <= 2.7e-19)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+65], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-19], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e65

   1. Initial program 88.9%

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

   2. Taylor expanded in t around 0 85.5%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in z around 0 49.3%

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

      1. associate-*l/ 53.8%

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

      2. *-commutative 53.8%

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

   8. Simplified 53.8%

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

   if -4.5e65 < z < 2.7000000000000001e-19

   1. Initial program 99.2%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in t around inf 59.8%

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

   if 2.7000000000000001e-19 < z

   1. Initial program 91.1%

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

   2. Taylor expanded in t around 0 83.8%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   5. Simplified 58.7%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 61.9%

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

   7. Applied egg-rr 61.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. associate-/l* 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 12: 38.2% 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 95.5%

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

   1. associate-*l/ 92.5%

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

3. Simplified 92.5%

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

4. Taylor expanded in t around inf 39.0%

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

5. Final simplification 39.0%

   \[\leadsto x \]

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 2023268 
(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)))