Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.0% → 97.6%

Time: 7.3s

Alternatives: 7

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% 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: 97.6% 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 94.3%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-180} \lor \neg \left(z \leq 1.9 \cdot 10^{-125}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.45e-180) (not (<= z 1.9e-125)))
   (+ x (* z (/ (- y x) t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e-180) || !(z <= 1.9e-125)) {
		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 <= (-2.45d-180)) .or. (.not. (z <= 1.9d-125))) 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 <= -2.45e-180) || !(z <= 1.9e-125)) {
		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 <= -2.45e-180) or not (z <= 1.9e-125):
		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 <= -2.45e-180) || !(z <= 1.9e-125))
		tmp = Float64(x + 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 <= -2.45e-180) || ~((z <= 1.9e-125)))
		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, -2.45e-180], N[Not[LessEqual[z, 1.9e-125]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4500000000000001e-180 or 1.9000000000000001e-125 < z

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-/l* 96.9%

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

   4. Applied egg-rr 96.9%

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

   if -2.4500000000000001e-180 < z < 1.9000000000000001e-125

   1. Initial program 98.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 89.5%

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

      1. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-180} \lor \neg \left(z \leq 1.9 \cdot 10^{-125}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-89} \lor \neg \left(y \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e-89) (not (<= y 1.1e+37)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e-89) || !(y <= 1.1e+37)) {
		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 <= (-8.5d-89)) .or. (.not. (y <= 1.1d+37))) 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 <= -8.5e-89) || !(y <= 1.1e+37)) {
		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 <= -8.5e-89) or not (y <= 1.1e+37):
		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 <= -8.5e-89) || !(y <= 1.1e+37))
		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 <= -8.5e-89) || ~((y <= 1.1e+37)))
		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, -8.5e-89], N[Not[LessEqual[y, 1.1e+37]], $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 < -8.49999999999999937e-89 or 1.1e37 < y

   1. Initial program 93.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.9%

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

      1. associate-*r/ 91.4%

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

   7. Simplified 91.4%

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

   if -8.49999999999999937e-89 < y < 1.1e37

   1. Initial program 95.9%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 89.5%

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

      3. neg-mul-1 89.5%

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

      4. distribute-rgt-neg-out 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in x around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   10. Simplified 89.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-89} \lor \neg \left(y \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-89} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e-89) (not (<= y 1.2e+37)))
   (+ x (* y (/ z t)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-89) || !(y <= 1.2e+37)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (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 ((y <= (-1.1d-89)) .or. (.not. (y <= 1.2d+37))) then
        tmp = x + (y * (z / t))
    else
        tmp = x - (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 ((y <= -1.1e-89) || !(y <= 1.2e+37)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.1e-89) or not (y <= 1.2e+37):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e-89) || !(y <= 1.2e+37))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.1e-89) || ~((y <= 1.2e+37)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e-89], N[Not[LessEqual[y, 1.2e+37]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000006e-89 or 1.2e37 < y

   1. Initial program 93.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.9%

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

      1. associate-*r/ 91.4%

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

   7. Simplified 91.4%

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

   if -1.10000000000000006e-89 < y < 1.2e37

   1. Initial program 95.9%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 89.5%

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

      3. neg-mul-1 89.5%

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

      4. distribute-rgt-neg-out 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-89} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000000 \lor \neg \left(z \leq 1.95 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -350000000000.0) (not (<= z 1.95e-16))) (* x (/ (- z) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -350000000000.0) || !(z <= 1.95e-16)) {
		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 <= (-350000000000.0d0)) .or. (.not. (z <= 1.95d-16))) 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 <= -350000000000.0) || !(z <= 1.95e-16)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -350000000000.0) or not (z <= 1.95e-16):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -350000000000.0) || !(z <= 1.95e-16))
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -350000000000.0) || ~((z <= 1.95e-16)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -350000000000.0], N[Not[LessEqual[z, 1.95e-16]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e11 or 1.94999999999999989e-16 < z

   1. Initial program 87.5%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 44.8%

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

      1. *-commutative 44.8%

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

      2. associate-*l/ 52.0%

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

      3. neg-mul-1 52.0%

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

      4. distribute-rgt-neg-out 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in x around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

   10. Simplified 52.0%

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

   11. Taylor expanded in z around 0 44.8%

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

       1. mul-1-neg 44.8%

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

       2. *-commutative 44.8%

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

       3. associate-*r/ 48.4%

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

       4. sub-neg 48.4%

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

   13. Simplified 48.4%

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

   14. Taylor expanded in z around inf 38.1%

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

       1. mul-1-neg 38.1%

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

       2. associate-*l/ 39.0%

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

       3. distribute-rgt-neg-in 39.0%

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

       4. associate-*l/ 38.1%

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

       5. associate-*r/ 42.6%

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

   16. Simplified 42.6%

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

   if -3.5e11 < z < 1.94999999999999989e-16

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l/ 71.8%

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

      3. neg-mul-1 71.8%

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

      4. distribute-rgt-neg-out 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in z around 0 59.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000000 \lor \neg \left(z \leq 1.95 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% 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 94.3%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in y around 0 60.1%

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

   1. *-commutative 60.1%

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

   2. associate-*l/ 63.5%

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

   3. neg-mul-1 63.5%

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

   4. distribute-rgt-neg-out 63.5%

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

7. Simplified 63.5%

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

8. Taylor expanded in x around 0 63.5%

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

   1. mul-1-neg 63.5%

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

   2. unsub-neg 63.5%

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

10. Simplified 63.5%

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

11. Final simplification 63.5%

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

Alternative 7: 39.1% 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 94.3%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in y around 0 60.1%

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

   1. *-commutative 60.1%

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

   2. associate-*l/ 63.5%

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

   3. neg-mul-1 63.5%

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

   4. distribute-rgt-neg-out 63.5%

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

7. Simplified 63.5%

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

8. Taylor expanded in z around 0 39.4%

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

9. Final simplification 39.4%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 97.9% 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 2024071 
(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)))