Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.6% → 97.7%

Time: 7.0s

Alternatives: 7

Speedup: 1.0×

• 25.2% 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: 92.6% 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: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. +-commutative 94.7%

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

   2. associate-/l* 97.8%

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

   3. fma-define 97.8%

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

3. Simplified 97.8%

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

5. Final simplification 97.8%

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

Alternative 2: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-178} \lor \neg \left(z \leq 1.8 \cdot 10^{-192}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.9e-178) (not (<= z 1.8e-192)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e-178) || !(z <= 1.8e-192)) {
		tmp = x + (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 <= (-4.9d-178)) .or. (.not. (z <= 1.8d-192))) then
        tmp = x + (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 <= -4.9e-178) || !(z <= 1.8e-192)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.9e-178) or not (z <= 1.8e-192):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.9e-178) || !(z <= 1.8e-192))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.9e-178) || ~((z <= 1.8e-192)))
		tmp = x + (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, -4.9e-178], N[Not[LessEqual[z, 1.8e-192]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000002e-178 or 1.7999999999999999e-192 < z

   1. Initial program 93.5%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-out 87.5%

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

      4. associate-*r/ 89.0%

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

      5. distribute-rgt-out 97.8%

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

      6. +-commutative 97.8%

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

      7. sub-neg 97.8%

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

      8. associate-*l/ 93.5%

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

      9. associate-*r/ 96.2%

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

   7. Simplified 96.2%

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

   if -4.9000000000000002e-178 < z < 1.7999999999999999e-192

   1. Initial program 99.9%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around inf 98.1%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-178} \lor \neg \left(z \leq 1.8 \cdot 10^{-192}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+64} \lor \neg \left(y \leq 3.4 \cdot 10^{-80}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e+64) (not (<= y 3.4e-80)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e+64) || !(y <= 3.4e-80)) {
		tmp = x + (y * (z / 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 ((y <= (-4.4d+64)) .or. (.not. (y <= 3.4d-80))) then
        tmp = x + (y * (z / 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 ((y <= -4.4e+64) || !(y <= 3.4e-80)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e+64) or not (y <= 3.4e-80):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e+64) || !(y <= 3.4e-80))
		tmp = Float64(x + Float64(y * Float64(z / 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 ((y <= -4.4e+64) || ~((y <= 3.4e-80)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e+64], N[Not[LessEqual[y, 3.4e-80]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000004e64 or 3.4000000000000001e-80 < y

   1. Initial program 92.4%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around inf 87.2%

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

      1. associate-*r/ 92.0%

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

   7. Simplified 92.0%

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

   if -4.40000000000000004e64 < y < 3.4000000000000001e-80

   1. Initial program 97.0%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

   7. Simplified 89.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+64} \lor \neg \left(y \leq 3.4 \cdot 10^{-80}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-56} \lor \neg \left(z \leq 17\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-56) (not (<= z 17.0))) (* x (/ z (- t))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-56) || !(z <= 17.0)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.2d-56)) .or. (.not. (z <= 17.0d0))) then
        tmp = x * (z / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-56) || !(z <= 17.0)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-56) or not (z <= 17.0):
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-56) || !(z <= 17.0))
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-56) || ~((z <= 17.0)))
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-56], N[Not[LessEqual[z, 17.0]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999994e-56 or 17 < z

   1. Initial program 90.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

   7. Simplified 63.8%

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

   8. Taylor expanded in z around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. associate-*r/ 53.7%

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

   10. Simplified 53.7%

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

   if -5.19999999999999994e-56 < z < 17

   1. Initial program 99.1%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 64.1%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-56} \lor \neg \left(z \leq 17\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% 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 94.7%

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

   1. associate-/l* 97.8%

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

3. Simplified 97.8%

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

5. Final simplification 97.8%

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

Alternative 6: 65.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. associate-/l* 97.8%

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

3. Simplified 97.8%

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

5. Taylor expanded in x around inf 68.7%

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

   1. mul-1-neg 68.7%

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

   2. unsub-neg 68.7%

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

7. Simplified 68.7%

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

8. Final simplification 68.7%

   \[\leadsto x \cdot \left(1 - \frac{z}{t}\right) \]
9. Add Preprocessing

Alternative 7: 38.7% 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 94.7%

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

   1. associate-/l* 97.8%

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

3. Simplified 97.8%

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

5. Taylor expanded in z around 0 37.5%

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

6. Final simplification 37.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.8% 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 2024059 
(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)))