Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 95.9%

Time: 7.7s

Alternatives: 13

Speedup: 1.0×

• 24.2% 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: 92.9% 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: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 (- INFINITY)) (+ x (* (- y x) (/ z 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)) {
		tmp = x + ((y - x) * (z / 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) {
		tmp = x + ((y - x) * (z / 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:
		tmp = x + ((y - x) * (z / 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))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / 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)
		tmp = x + ((y - x) * (z / 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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / 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

   1. Initial program 83.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 96.7%

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

Alternative 2: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00016:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e-25)
   (* z (/ y t))
   (if (<= z 1.2e-14)
     x
     (if (<= z 0.00016)
       (* z (/ (- x) t))
       (if (<= z 4.9e+31) x (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-25) {
		tmp = z * (y / t);
	} else if (z <= 1.2e-14) {
		tmp = x;
	} else if (z <= 0.00016) {
		tmp = z * (-x / t);
	} else if (z <= 4.9e+31) {
		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 <= (-3.8d-25)) then
        tmp = z * (y / t)
    else if (z <= 1.2d-14) then
        tmp = x
    else if (z <= 0.00016d0) then
        tmp = z * (-x / t)
    else if (z <= 4.9d+31) 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 <= -3.8e-25) {
		tmp = z * (y / t);
	} else if (z <= 1.2e-14) {
		tmp = x;
	} else if (z <= 0.00016) {
		tmp = z * (-x / t);
	} else if (z <= 4.9e+31) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e-25:
		tmp = z * (y / t)
	elif z <= 1.2e-14:
		tmp = x
	elif z <= 0.00016:
		tmp = z * (-x / t)
	elif z <= 4.9e+31:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e-25)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.2e-14)
		tmp = x;
	elseif (z <= 0.00016)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (z <= 4.9e+31)
		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 <= -3.8e-25)
		tmp = z * (y / t);
	elseif (z <= 1.2e-14)
		tmp = x;
	elseif (z <= 0.00016)
		tmp = z * (-x / t);
	elseif (z <= 4.9e+31)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e-25], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-14], x, If[LessEqual[z, 0.00016], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+31], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999998e-25

   1. Initial program 94.0%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 77.4%

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

   6. Taylor expanded in y around inf 56.9%

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

   if -3.7999999999999998e-25 < z < 1.2e-14 or 1.60000000000000013e-4 < z < 4.89999999999999996e31

   1. Initial program 97.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 64.2%

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

   if 1.2e-14 < z < 1.60000000000000013e-4

   1. Initial program 99.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 95.3%

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

   6. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-frac-neg2 68.1%

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

   8. Simplified 68.1%

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

   if 4.89999999999999996e31 < z

   1. Initial program 88.8%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-div 87.1%

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

      3. associate-*l/ 84.2%

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

   7. Applied egg-rr 84.2%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

   9. Applied egg-rr 81.5%

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

   10. Taylor expanded in y around inf 45.7%

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

       1. associate-*r/ 55.1%

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

       2. *-commutative 55.1%

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

   12. Simplified 55.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00016:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0064:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e-25)
   (* z (/ y t))
   (if (<= z 8.2e-14)
     x
     (if (<= z 0.0064)
       (/ (- z) (/ t x))
       (if (<= z 7.2e+31) x (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-25) {
		tmp = z * (y / t);
	} else if (z <= 8.2e-14) {
		tmp = x;
	} else if (z <= 0.0064) {
		tmp = -z / (t / x);
	} else if (z <= 7.2e+31) {
		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 <= (-3.3d-25)) then
        tmp = z * (y / t)
    else if (z <= 8.2d-14) then
        tmp = x
    else if (z <= 0.0064d0) then
        tmp = -z / (t / x)
    else if (z <= 7.2d+31) 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 <= -3.3e-25) {
		tmp = z * (y / t);
	} else if (z <= 8.2e-14) {
		tmp = x;
	} else if (z <= 0.0064) {
		tmp = -z / (t / x);
	} else if (z <= 7.2e+31) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e-25:
		tmp = z * (y / t)
	elif z <= 8.2e-14:
		tmp = x
	elif z <= 0.0064:
		tmp = -z / (t / x)
	elif z <= 7.2e+31:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e-25)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 8.2e-14)
		tmp = x;
	elseif (z <= 0.0064)
		tmp = Float64(Float64(-z) / Float64(t / x));
	elseif (z <= 7.2e+31)
		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 <= -3.3e-25)
		tmp = z * (y / t);
	elseif (z <= 8.2e-14)
		tmp = x;
	elseif (z <= 0.0064)
		tmp = -z / (t / x);
	elseif (z <= 7.2e+31)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e-25], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-14], x, If[LessEqual[z, 0.0064], N[((-z) / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+31], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2999999999999998e-25

   1. Initial program 94.0%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 77.4%

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

   6. Taylor expanded in y around inf 56.9%

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

   if -3.2999999999999998e-25 < z < 8.2000000000000004e-14 or 0.00640000000000000031 < z < 7.19999999999999992e31

   1. Initial program 97.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 64.2%

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

   if 8.2000000000000004e-14 < z < 0.00640000000000000031

   1. Initial program 99.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 95.3%

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

   6. Taylor expanded in y around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-frac-neg2 68.1%

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

   8. Simplified 68.1%

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

      1. associate-*r/ 67.9%

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

      2. distribute-frac-neg2 67.9%

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

      3. add-sqr-sqrt 39.4%

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

      4. sqrt-unprod 39.7%

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

      5. sqr-neg 39.7%

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

      6. sqrt-unprod 0.4%

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

      7. add-sqr-sqrt 1.7%

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

      8. associate-*r/ 1.7%

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

      9. *-commutative 1.7%

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

      10. *-commutative 1.7%

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

      11. clear-num 1.7%

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

      12. un-div-inv 1.7%

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

      13. add-sqr-sqrt 0.4%

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

      14. sqrt-unprod 39.4%

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

      15. sqr-neg 39.4%

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

      16. sqrt-unprod 39.1%

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

      17. add-sqr-sqrt 67.9%

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

   10. Applied egg-rr 67.9%

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

   if 7.19999999999999992e31 < z

   1. Initial program 88.8%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-div 87.1%

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

      3. associate-*l/ 84.2%

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

   7. Applied egg-rr 84.2%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

   9. Applied egg-rr 81.5%

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

   10. Taylor expanded in y around inf 45.7%

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

       1. associate-*r/ 55.1%

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

       2. *-commutative 55.1%

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

   12. Simplified 55.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0064:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+243)
   (* x (/ (- z) t))
   (if (<= z -1.3e-24) (* z (/ y t)) (if (<= z 3.3e+31) x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+243) {
		tmp = x * (-z / t);
	} else if (z <= -1.3e-24) {
		tmp = z * (y / t);
	} else if (z <= 3.3e+31) {
		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 <= (-1.85d+243)) then
        tmp = x * (-z / t)
    else if (z <= (-1.3d-24)) then
        tmp = z * (y / t)
    else if (z <= 3.3d+31) 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 <= -1.85e+243) {
		tmp = x * (-z / t);
	} else if (z <= -1.3e-24) {
		tmp = z * (y / t);
	} else if (z <= 3.3e+31) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+243:
		tmp = x * (-z / t)
	elif z <= -1.3e-24:
		tmp = z * (y / t)
	elif z <= 3.3e+31:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+243)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -1.3e-24)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 3.3e+31)
		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 <= -1.85e+243)
		tmp = x * (-z / t);
	elseif (z <= -1.3e-24)
		tmp = z * (y / t);
	elseif (z <= 3.3e+31)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+243], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-24], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+31], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8500000000000001e243

   1. Initial program 90.8%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   7. Simplified 74.9%

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

      1. sub-neg 74.9%

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

      2. distribute-lft-in 74.9%

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

      3. *-commutative 74.9%

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

      4. *-un-lft-identity 74.9%

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

      5. distribute-neg-frac2 74.9%

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

      6. add-sqr-sqrt 44.3%

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

      7. sqrt-unprod 34.4%

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

      8. sqr-neg 34.4%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 1.5%

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

      11. div-inv 1.5%

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

      12. *-commutative 1.5%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 34.2%

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

      15. sqr-neg 34.2%

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

      16. sqrt-unprod 44.2%

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

      17. add-sqr-sqrt 74.7%

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

      18. associate-*l* 64.1%

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

   9. Applied egg-rr 61.3%

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

   10. Taylor expanded in z around inf 56.2%

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

       1. mul-1-neg 56.2%

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

       2. associate-*r/ 74.9%

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

       3. *-commutative 74.9%

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

       4. distribute-rgt-neg-in 74.9%

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

   12. Simplified 74.9%

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

   if -1.8500000000000001e243 < z < -1.3e-24

   1. Initial program 94.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 74.6%

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

   6. Taylor expanded in y around inf 61.2%

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

   if -1.3e-24 < z < 3.29999999999999992e31

   1. Initial program 97.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 60.9%

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

   if 3.29999999999999992e31 < z

   1. Initial program 88.8%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-div 87.1%

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

      3. associate-*l/ 84.2%

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

   7. Applied egg-rr 84.2%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

   9. Applied egg-rr 81.5%

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

   10. Taylor expanded in y around inf 45.7%

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

       1. associate-*r/ 55.1%

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

       2. *-commutative 55.1%

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

   12. Simplified 55.1%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-88} \lor \neg \left(t \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e-88) (not (<= t 4.4e-7)))
   (+ x (* y (/ z t)))
   (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-88) || !(t <= 4.4e-7)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.1d-88)) .or. (.not. (t <= 4.4d-7))) then
        tmp = x + (y * (z / t))
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-88) || !(t <= 4.4e-7)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e-88) or not (t <= 4.4e-7):
		tmp = x + (y * (z / t))
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e-88) || !(t <= 4.4e-7))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e-88) || ~((t <= 4.4e-7)))
		tmp = x + (y * (z / t));
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e-88], N[Not[LessEqual[t, 4.4e-7]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1000000000000001e-88 or 4.4000000000000002e-7 < t

   1. Initial program 92.0%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. associate-*r/ 86.5%

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

   7. Simplified 86.5%

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

   if -4.1000000000000001e-88 < t < 4.4000000000000002e-7

   1. Initial program 97.5%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. sub-div 81.6%

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

      3. associate-*l/ 87.0%

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

   7. Applied egg-rr 87.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-88} \lor \neg \left(t \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-139} \lor \neg \left(y \leq 2.85 \cdot 10^{-116}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.8e-139) (not (<= y 2.85e-116)))
   (+ x (* y (/ z t)))
   (- x (/ z (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-139) || !(y <= 2.85e-116)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z / (t / 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 ((y <= (-4.8d-139)) .or. (.not. (y <= 2.85d-116))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-139) || !(y <= 2.85e-116)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.8e-139) or not (y <= 2.85e-116):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (z / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.8e-139) || !(y <= 2.85e-116))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.8e-139) || ~((y <= 2.85e-116)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.8e-139], N[Not[LessEqual[y, 2.85e-116]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000029e-139 or 2.8499999999999998e-116 < y

   1. Initial program 93.9%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. associate-*r/ 86.5%

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

   7. Simplified 86.5%

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

   if -4.80000000000000029e-139 < y < 2.8499999999999998e-116

   1. Initial program 95.9%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

   7. Simplified 81.5%

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

      1. sub-neg 81.5%

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

      2. distribute-lft-in 81.5%

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

      3. *-commutative 81.5%

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

      4. *-un-lft-identity 81.5%

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

      5. distribute-neg-frac2 81.5%

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

      6. add-sqr-sqrt 41.9%

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

      7. sqrt-unprod 55.6%

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

      8. sqr-neg 55.6%

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

      9. sqrt-unprod 21.7%

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

      10. add-sqr-sqrt 41.6%

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

      11. div-inv 41.6%

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

      12. *-commutative 41.6%

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

      13. add-sqr-sqrt 21.7%

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

      14. sqrt-unprod 55.6%

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

      15. sqr-neg 55.6%

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

      16. sqrt-unprod 41.9%

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

      17. add-sqr-sqrt 81.6%

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

      18. associate-*l* 84.1%

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

   9. Applied egg-rr 84.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-139} \lor \neg \left(y \leq 2.85 \cdot 10^{-116}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-24} \lor \neg \left(z \leq 8.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e-24) (not (<= z 8.5e-14)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e-24) || !(z <= 8.5e-14)) {
		tmp = z * ((y - x) / 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 ((z <= (-1.15d-24)) .or. (.not. (z <= 8.5d-14))) then
        tmp = z * ((y - x) / 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 ((z <= -1.15e-24) || !(z <= 8.5e-14)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e-24) or not (z <= 8.5e-14):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e-24) || !(z <= 8.5e-14))
		tmp = Float64(z * Float64(Float64(y - x) / 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 ((z <= -1.15e-24) || ~((z <= 8.5e-14)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e-24], N[Not[LessEqual[z, 8.5e-14]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e-24 or 8.50000000000000038e-14 < z

   1. Initial program 92.4%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 79.1%

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

   6. Taylor expanded in t around 0 83.3%

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

   if -1.1500000000000001e-24 < z < 8.50000000000000038e-14

   1. Initial program 97.5%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 86.7%

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

      1. associate-*r/ 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-24} \lor \neg \left(z \leq 8.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-25} \lor \neg \left(z \leq 1.46 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.6e-25) (not (<= z 1.46e+16)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.6e-25) || !(z <= 1.46e+16)) {
		tmp = 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 ((z <= (-5.6d-25)) .or. (.not. (z <= 1.46d+16))) then
        tmp = 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 ((z <= -5.6e-25) || !(z <= 1.46e+16)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.6e-25) or not (z <= 1.46e+16):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.6e-25) || !(z <= 1.46e+16))
		tmp = 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 ((z <= -5.6e-25) || ~((z <= 1.46e+16)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.6e-25], N[Not[LessEqual[z, 1.46e+16]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999976e-25 or 1.46e16 < z

   1. Initial program 91.6%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around inf 80.8%

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

   6. Taylor expanded in t around 0 85.5%

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

   if -5.59999999999999976e-25 < z < 1.46e16

   1. Initial program 97.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-25} \lor \neg \left(z \leq 1.46 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-199} \lor \neg \left(x \leq 8.5 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.9e-199) (not (<= x 8.5e-164)))
   (* x (- 1.0 (/ z t)))
   (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e-199) || !(x <= 8.5e-164)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = 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 <= (-2.9d-199)) .or. (.not. (x <= 8.5d-164))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = 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 <= -2.9e-199) || !(x <= 8.5e-164)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.9e-199) or not (x <= 8.5e-164):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.9e-199) || !(x <= 8.5e-164))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.9e-199) || ~((x <= 8.5e-164)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.9e-199], N[Not[LessEqual[x, 8.5e-164]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e-199 or 8.50000000000000035e-164 < x

   1. Initial program 95.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   7. Simplified 75.0%

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

   if -2.9e-199 < x < 8.50000000000000035e-164

   1. Initial program 91.3%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 88.2%

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

   6. Taylor expanded in y around inf 76.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-199} \lor \neg \left(x \leq 8.5 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-25} \lor \neg \left(z \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e-25) (not (<= z 1.2e+32))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-25) || !(z <= 1.2e+32)) {
		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 <= (-7.8d-25)) .or. (.not. (z <= 1.2d+32))) 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 <= -7.8e-25) || !(z <= 1.2e+32)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e-25) or not (z <= 1.2e+32):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e-25) || !(z <= 1.2e+32))
		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 <= -7.8e-25) || ~((z <= 1.2e+32)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e-25], N[Not[LessEqual[z, 1.2e+32]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e-25 or 1.19999999999999996e32 < z

   1. Initial program 91.5%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 80.5%

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

   6. Taylor expanded in y around inf 53.0%

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

   if -7.8e-25 < z < 1.19999999999999996e32

   1. Initial program 97.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 60.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-25} \lor \neg \left(z \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e-24) (* z (/ y t)) (if (<= z 1.85e+31) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-24) {
		tmp = z * (y / t);
	} else if (z <= 1.85e+31) {
		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 <= (-1.25d-24)) then
        tmp = z * (y / t)
    else if (z <= 1.85d+31) 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 <= -1.25e-24) {
		tmp = z * (y / t);
	} else if (z <= 1.85e+31) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e-24:
		tmp = z * (y / t)
	elif z <= 1.85e+31:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-24)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.85e+31)
		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 <= -1.25e-24)
		tmp = z * (y / t);
	elseif (z <= 1.85e+31)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e-24], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+31], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e-24

   1. Initial program 94.0%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 77.4%

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

   6. Taylor expanded in y around inf 56.9%

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

   if -1.24999999999999995e-24 < z < 1.8499999999999999e31

   1. Initial program 97.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 60.9%

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

   if 1.8499999999999999e31 < z

   1. Initial program 88.8%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-div 87.1%

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

      3. associate-*l/ 84.2%

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

   7. Applied egg-rr 84.2%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

   9. Applied egg-rr 81.5%

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

   10. Taylor expanded in y around inf 45.7%

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

       1. associate-*r/ 55.1%

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

       2. *-commutative 55.1%

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

   12. Simplified 55.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

Alternative 13: 39.2% 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 94.6%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

5. Taylor expanded in z around 0 37.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 97.5% accurate, 0.5× 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 2024103 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (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)))