Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.3% → 95.5%

Time: 8.0s

Alternatives: 10

Speedup: 1.0×

• 25.1% 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: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t_1 \leq 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (<= t_1 1e+289) t_1 (+ x (/ z (/ t (- y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((z * (y - x)) / t)
    if (t_1 <= 1d+289) then
        tmp = t_1
    else
        tmp = x + (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if t_1 <= 1e+289:
		tmp = t_1
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(z * Float64(y - x)) / t))
	tmp = 0.0
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((z * (y - x)) / t);
	tmp = 0.0;
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+289], t$95$1, N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1.0000000000000001e289

   1. Initial program 97.0%

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

   if 1.0000000000000001e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 83.5%

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

      1. associate-*l/ 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 72.7%

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

      1. associate-*r/ 74.1%

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

      2. +-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. sub-neg 74.1%

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

      5. associate-*r/ 72.7%

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

      6. associate-/l* 74.1%

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

      7. associate-/l* 80.3%

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

      8. div-sub 97.9%

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

      9. associate-/l* 83.5%

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

      10. *-commutative 83.5%

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

      11. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq 10^{+289}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. *-commutative 94.6%

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

   3. associate-*l/ 97.1%

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

   4. fma-def 97.1%

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

3. Simplified 97.1%

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

5. Final simplification 97.1%

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

Alternative 3: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-75} \lor \neg \left(x \leq 1050\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5e-75) (not (<= x 1050.0)))
   (* x (- 1.0 (/ z t)))
   (+ x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5e-75) || !(x <= 1050.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d-75)) .or. (.not. (x <= 1050.0d0))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5e-75) || !(x <= 1050.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5e-75) or not (x <= 1050.0):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5e-75) || !(x <= 1050.0))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5e-75) || ~((x <= 1050.0)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5e-75], N[Not[LessEqual[x, 1050.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999989e-75 or 1050 < x

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*l/ 99.9%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. mul-1-neg 88.4%

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

      6. distribute-lft-in 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

   7. Simplified 88.4%

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

   if -2.49999999999999989e-75 < x < 1050

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. associate-*r/ 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-75} \lor \neg \left(x \leq 1050\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-75} \lor \neg \left(x \leq 620\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-75) (not (<= x 620.0)))
   (* x (- 1.0 (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-75) || !(x <= 620.0)) {
		tmp = x * (1.0 - (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 ((x <= (-3.2d-75)) .or. (.not. (x <= 620.0d0))) then
        tmp = x * (1.0d0 - (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 ((x <= -3.2e-75) || !(x <= 620.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-75) or not (x <= 620.0):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-75) || !(x <= 620.0))
		tmp = Float64(x * Float64(1.0 - 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 ((x <= -3.2e-75) || ~((x <= 620.0)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.2e-75], N[Not[LessEqual[x, 620.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999977e-75 or 620 < x

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*l/ 99.9%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-*r/ 88.4%

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

      2. neg-mul-1 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. mul-1-neg 88.4%

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

      6. distribute-lft-in 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

   7. Simplified 88.4%

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

   if -3.19999999999999977e-75 < x < 620

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l/ 93.4%

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

      4. fma-def 93.4%

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

   3. Simplified 93.4%

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

      1. fma-udef 93.4%

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

      2. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in y around inf 84.6%

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

      1. associate-/l* 87.7%

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

   9. Simplified 87.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-75} \lor \neg \left(x \leq 620\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+183}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5.8e+183) (+ x (* z (/ (- y x) t))) (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+183) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 5.8d+183) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+183) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5.8e+183:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5.8e+183)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 5.8e+183)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5.8e+183], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.8000000000000001e183

   1. Initial program 94.1%

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

      1. associate-*l/ 93.0%

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

   4. Applied egg-rr 93.0%

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

   if 5.8000000000000001e183 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+183}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.15e+185) (+ x (/ z (/ t (- y x)))) (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.15e+185) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 1.15d+185) then
        tmp = x + (z / (t / (y - x)))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.15e+185) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.15e+185:
		tmp = x + (z / (t / (y - x)))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.15e+185)
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.15e+185)
		tmp = x + (z / (t / (y - x)));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.15e+185], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1500000000000001e185

   1. Initial program 94.1%

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

      1. associate-*l/ 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 88.4%

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

      2. +-commutative 88.4%

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

      3. mul-1-neg 88.4%

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

      4. sub-neg 88.4%

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

      5. associate-*r/ 89.4%

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

      6. associate-/l* 88.4%

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

      7. associate-/l* 89.5%

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

      8. div-sub 96.8%

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

      9. associate-/l* 94.1%

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

      10. *-commutative 94.1%

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

      11. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

   if 1.1500000000000001e185 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% 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 94.6%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{t}{z}}} \]
4. Add Preprocessing

5. Final simplification 97.1%

   \[\leadsto x + \frac{y - x}{\frac{t}{z}} \]
6. Add Preprocessing

Alternative 8: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. *-commutative 94.6%

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

   3. associate-*l/ 97.1%

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

   4. fma-def 97.1%

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

3. Simplified 97.1%

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

   1. fma-udef 97.1%

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

   2. *-commutative 97.1%

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

6. Applied egg-rr 97.1%

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

7. Final simplification 97.1%

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

Alternative 9: 65.1% 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 94.6%

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

   1. +-commutative 94.6%

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

   2. *-commutative 94.6%

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

   3. associate-*l/ 97.1%

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

   4. fma-def 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in y around 0 66.0%

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

   1. associate-*r/ 67.5%

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

   2. neg-mul-1 67.5%

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

   3. *-rgt-identity 67.5%

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

   4. distribute-rgt-neg-in 67.5%

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

   5. mul-1-neg 67.5%

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

   6. distribute-lft-in 67.5%

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

   7. mul-1-neg 67.5%

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

   8. unsub-neg 67.5%

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

7. Simplified 67.5%

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

8. Final simplification 67.5%

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

Alternative 10: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. *-commutative 94.6%

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

   3. associate-*l/ 97.1%

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

   4. fma-def 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in z around 0 38.6%

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

6. Final simplification 38.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.7% 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 2024024 
(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)))