Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 99.2%

Time: 12.6s

Alternatives: 14

Speedup: 1.0×

• 25.4% 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: 92.8% 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: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+306)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+306)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+306)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+306):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+306))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - x) * z) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+306)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+306]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0 or 2.00000000000000003e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 78.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.00000000000000003e306

   1. Initial program 97.1%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-40} \lor \neg \left(z \leq 5.2 \cdot 10^{-113}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-40) (not (<= z 5.2e-113))) (* (- y x) (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-40) || !(z <= 5.2e-113)) {
		tmp = (y - 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 <= (-1.7d-40)) .or. (.not. (z <= 5.2d-113))) then
        tmp = (y - 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 <= -1.7e-40) || !(z <= 5.2e-113)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-40) or not (z <= 5.2e-113):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-40) || !(z <= 5.2e-113))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-40) || ~((z <= 5.2e-113)))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-40], N[Not[LessEqual[z, 5.2e-113]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999992e-40 or 5.1999999999999998e-113 < z

   1. Initial program 87.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

      1. associate-*l/ 87.8%

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

      2. associate-/l* 97.8%

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

      3. div-sub 85.6%

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

      4. associate-+r- 85.6%

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

      5. div-inv 84.7%

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

      6. clear-num 84.8%

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

      7. div-inv 84.1%

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

      8. clear-num 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in t around 0 70.8%

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

      1. distribute-rgt-out-- 74.6%

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

      2. associate-*l/ 79.4%

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

   8. Simplified 79.4%

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

   if -1.69999999999999992e-40 < z < 5.1999999999999998e-113

   1. Initial program 95.2%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in t around inf 73.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-40} \lor \neg \left(z \leq 5.2 \cdot 10^{-113}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+77} \lor \neg \left(z \leq 3 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+77) (not (<= z 3e-73)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+77) || !(z <= 3e-73)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d+77)) .or. (.not. (z <= 3d-73))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+77) || !(z <= 3e-73)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+77) or not (z <= 3e-73):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+77) || !(z <= 3e-73))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+77) || ~((z <= 3e-73)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+77], N[Not[LessEqual[z, 3e-73]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000036e77 or 3e-73 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 85.5%

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

      2. associate-/l* 97.2%

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

      3. div-sub 82.8%

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

      4. associate-+r- 82.8%

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

      5. div-inv 81.6%

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

      6. clear-num 81.7%

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

      7. div-inv 80.8%

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

      8. clear-num 80.9%

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

   5. Applied egg-rr 80.9%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. distribute-rgt-out-- 78.5%

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

      2. associate-*l/ 84.6%

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

   8. Simplified 84.6%

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

   if -5.50000000000000036e77 < z < 3e-73

   1. Initial program 95.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-*r/ 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+77} \lor \neg \left(z \leq 3 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+77} \lor \neg \left(z \leq 4.8 \cdot 10^{-74}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e+77) (not (<= z 4.8e-74)))
   (* (- y x) (/ z t))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+77) || !(z <= 4.8e-74)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d+77)) .or. (.not. (z <= 4.8d-74))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+77) || !(z <= 4.8e-74)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e+77) or not (z <= 4.8e-74):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e+77) || !(z <= 4.8e-74))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e+77) || ~((z <= 4.8e-74)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e+77], N[Not[LessEqual[z, 4.8e-74]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e77 or 4.7999999999999998e-74 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 85.5%

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

      2. associate-/l* 97.2%

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

      3. div-sub 82.8%

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

      4. associate-+r- 82.8%

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

      5. div-inv 81.6%

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

      6. clear-num 81.7%

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

      7. div-inv 80.8%

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

      8. clear-num 80.9%

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

   5. Applied egg-rr 80.9%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. distribute-rgt-out-- 78.5%

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

      2. associate-*l/ 84.6%

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

   8. Simplified 84.6%

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

   if -1.6499999999999999e77 < z < 4.7999999999999998e-74

   1. Initial program 95.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-*r/ 87.1%

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

   6. Simplified 87.1%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.1%

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

   8. Applied egg-rr 87.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+77} \lor \neg \left(z \leq 4.8 \cdot 10^{-74}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+78} \lor \neg \left(z \leq 3 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.25e+78) (not (<= z 3e-73)))
   (* (- y x) (/ z t))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.25e+78) || !(z <= 3e-73)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.25d+78)) .or. (.not. (z <= 3d-73))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.25e+78) || !(z <= 3e-73)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.25e+78) or not (z <= 3e-73):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.25e+78) || !(z <= 3e-73))
		tmp = Float64(Float64(y - x) * Float64(z / 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 <= -3.25e+78) || ~((z <= 3e-73)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.25e+78], N[Not[LessEqual[z, 3e-73]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.25000000000000018e78 or 3e-73 < z

   1. Initial program 85.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 85.5%

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

      2. associate-/l* 97.2%

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

      3. div-sub 82.8%

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

      4. associate-+r- 82.8%

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

      5. div-inv 81.6%

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

      6. clear-num 81.7%

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

      7. div-inv 80.8%

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

      8. clear-num 80.9%

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

   5. Applied egg-rr 80.9%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. distribute-rgt-out-- 78.5%

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

      2. associate-*l/ 84.6%

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

   8. Simplified 84.6%

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

   if -3.25000000000000018e78 < z < 3e-73

   1. Initial program 95.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. *-commutative 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+78} \lor \neg \left(z \leq 3 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 6: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-68} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.06e-68) (not (<= y 1.05e+66)))
   (+ x (/ y (/ t z)))
   (- x (* z (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-68) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.06d-68)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (z * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-68) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.06e-68) or not (y <= 1.05e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (z * (x / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.06e-68) || !(y <= 1.05e+66))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.06e-68) || ~((y <= 1.05e+66)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.06e-68], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e-68 or 1.05000000000000003e66 < y

   1. Initial program 88.4%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 92.1%

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

   6. Simplified 92.1%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   8. Applied egg-rr 92.2%

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

   if -1.06e-68 < y < 1.05000000000000003e66

   1. Initial program 92.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

      1. associate-/r/ 97.4%

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

      2. clear-num 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in y around 0 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-/l* 87.7%

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

      3. neg-mul-1 87.7%

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

      4. sub-neg 87.7%

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

      5. associate-/l* 86.3%

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

      6. associate-*r/ 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-68} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 7: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-73) (not (<= y 1.05e+66)))
   (+ x (/ y (/ t z)))
   (- x (/ z (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-73) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} 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 <= (-3d-73)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (y / (t / z))
    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 <= -3e-73) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e-73) or not (y <= 1.05e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (z / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e-73) || !(y <= 1.05e+66))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	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 <= -3e-73) || ~((y <= 1.05e+66)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e-73], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-73 or 1.05000000000000003e66 < y

   1. Initial program 88.4%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 92.1%

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

   6. Simplified 92.1%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   8. Applied egg-rr 92.2%

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

   if -3e-73 < y < 1.05000000000000003e66

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-lft-neg-out 86.3%

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

      3. *-commutative 86.3%

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

   4. Simplified 86.3%

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

      1. div-inv 86.2%

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

      2. add-sqr-sqrt 40.4%

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

      3. sqrt-unprod 52.7%

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

      4. sqr-neg 52.7%

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

      5. sqrt-unprod 24.9%

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

      6. add-sqr-sqrt 48.8%

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

      7. distribute-rgt-neg-in 48.8%

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

      8. cancel-sign-sub-inv 48.8%

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

      9. div-inv 48.8%

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

      10. associate-/l* 51.7%

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

      11. add-sqr-sqrt 24.9%

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

      12. sqrt-unprod 52.7%

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

      13. sqr-neg 52.7%

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

      14. sqrt-unprod 43.4%

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

      15. add-sqr-sqrt 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 8: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.9e-69) (not (<= y 1.05e+66)))
   (+ x (/ y (/ t z)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.9e-69) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} 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 <= (-6.9d-69)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (y / (t / z))
    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 <= -6.9e-69) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.9e-69) or not (y <= 1.05e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.9e-69) || !(y <= 1.05e+66))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	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 <= -6.9e-69) || ~((y <= 1.05e+66)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.9e-69], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8999999999999997e-69 or 1.05000000000000003e66 < y

   1. Initial program 88.4%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 92.1%

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

   6. Simplified 92.1%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   8. Applied egg-rr 92.2%

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

   if -6.8999999999999997e-69 < y < 1.05000000000000003e66

   1. Initial program 92.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 86.3%

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

      1. associate-*r/ 89.2%

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

      2. mul-1-neg 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+38} \lor \neg \left(z \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3e+38) (not (<= z 3e-22))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+38) || !(z <= 3e-22)) {
		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 <= (-3.3d+38)) .or. (.not. (z <= 3d-22))) 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 <= -3.3e+38) || !(z <= 3e-22)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e+38) or not (z <= 3e-22):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e+38) || !(z <= 3e-22))
		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 <= -3.3e+38) || ~((z <= 3e-22)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3e+38], N[Not[LessEqual[z, 3e-22]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e38 or 2.9999999999999999e-22 < z

   1. Initial program 85.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

      1. associate-*l/ 85.0%

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

      2. associate-/l* 97.3%

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

      3. div-sub 83.2%

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

      4. associate-+r- 83.2%

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

      5. div-inv 82.1%

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

      6. clear-num 82.2%

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

      7. div-inv 81.3%

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

      8. clear-num 81.3%

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

   5. Applied egg-rr 81.3%

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

   6. Taylor expanded in x around 0 49.2%

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

      1. associate-*l/ 57.3%

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

      2. *-commutative 57.3%

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

   8. Simplified 57.3%

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

   if -3.2999999999999999e38 < z < 2.9999999999999999e-22

   1. Initial program 96.3%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 67.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+38} \lor \neg \left(z \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 54.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.05e+38) (* z (/ y t)) (if (<= z 3.65e-22) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e+38) {
		tmp = z * (y / t);
	} else if (z <= 3.65e-22) {
		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 <= (-2.05d+38)) then
        tmp = z * (y / t)
    else if (z <= 3.65d-22) 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 <= -2.05e+38) {
		tmp = z * (y / t);
	} else if (z <= 3.65e-22) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.05e+38:
		tmp = z * (y / t)
	elif z <= 3.65e-22:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.05e+38)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 3.65e-22)
		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 <= -2.05e+38)
		tmp = z * (y / t);
	elseif (z <= 3.65e-22)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.05e+38], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.65e-22], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0500000000000002e38

   1. Initial program 86.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 86.7%

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

      2. associate-/l* 98.0%

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

      3. div-sub 80.0%

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

      4. associate-+r- 80.0%

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

      5. div-inv 78.1%

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

      6. clear-num 78.1%

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

      7. div-inv 77.9%

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

      8. clear-num 78.0%

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

   5. Applied egg-rr 78.0%

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

   6. Taylor expanded in x around 0 49.7%

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

      1. associate-*l/ 55.4%

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

      2. *-commutative 55.4%

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

   8. Simplified 55.4%

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

   if -2.0500000000000002e38 < z < 3.65000000000000014e-22

   1. Initial program 96.3%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 67.1%

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

   if 3.65000000000000014e-22 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

      1. associate-*l/ 83.9%

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

      2. associate-/l* 96.8%

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

      3. div-sub 85.2%

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

      4. associate-+r- 85.2%

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

      5. div-inv 84.6%

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

      6. clear-num 84.8%

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

      7. div-inv 83.4%

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

      8. clear-num 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in x around 0 48.8%

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

      1. *-commutative 48.8%

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

   8. Simplified 48.8%

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

      1. associate-*l/ 60.7%

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

   10. Applied egg-rr 60.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+38) (/ y (/ t z)) (if (<= z 1.55e-20) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+38) {
		tmp = y / (t / z);
	} else if (z <= 1.55e-20) {
		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 <= (-2.5d+38)) then
        tmp = y / (t / z)
    else if (z <= 1.55d-20) 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 <= -2.5e+38) {
		tmp = y / (t / z);
	} else if (z <= 1.55e-20) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+38:
		tmp = y / (t / z)
	elif z <= 1.55e-20:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+38)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 1.55e-20)
		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 <= -2.5e+38)
		tmp = y / (t / z);
	elseif (z <= 1.55e-20)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+38], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-20], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999985e38

   1. Initial program 86.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 86.7%

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

      2. associate-/l* 98.0%

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

      3. div-sub 80.0%

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

      4. associate-+r- 80.0%

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

      5. div-inv 78.1%

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

      6. clear-num 78.1%

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

      7. div-inv 77.9%

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

      8. clear-num 78.0%

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

   5. Applied egg-rr 78.0%

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

   6. Taylor expanded in x around 0 49.7%

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

      1. associate-*l/ 55.4%

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

      2. *-commutative 55.4%

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

   8. Simplified 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-/r/ 55.4%

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

   10. Applied egg-rr 55.4%

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

   if -2.49999999999999985e38 < z < 1.55e-20

   1. Initial program 96.3%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 67.1%

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

   if 1.55e-20 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

      1. associate-*l/ 83.9%

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

      2. associate-/l* 96.8%

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

      3. div-sub 85.2%

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

      4. associate-+r- 85.2%

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

      5. div-inv 84.6%

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

      6. clear-num 84.8%

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

      7. div-inv 83.4%

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

      8. clear-num 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in x around 0 48.8%

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

      1. *-commutative 48.8%

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

   8. Simplified 48.8%

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

      1. associate-*l/ 60.7%

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

   10. Applied egg-rr 60.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 12: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. associate-*l/ 94.4%

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

3. Simplified 94.4%

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

4. Final simplification 94.4%

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

Alternative 13: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. associate-/l* 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 14: 38.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 90.6%

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

   1. associate-*l/ 94.4%

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

3. Simplified 94.4%

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

4. Taylor expanded in t around inf 40.8%

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

5. Final simplification 40.8%

   \[\leadsto x \]

Developer target: 97.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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)))