Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.8% → 98.7%

Time: 8.4s

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: 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: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+292)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+292)) {
		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 + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+292)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+292):
		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(z * Float64(y - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+292))
		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 + ((z * (y - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+292)))
		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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+292]], $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 4.9999999999999996e292 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 67.7%

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

      1. associate-*l/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4.9999999999999996e292

   1. Initial program 99.2%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{z \cdot \left(y - x\right)}{t} \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]

Alternative 2: 97.7% 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 89.1%

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

   1. +-commutative 89.1%

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

   2. *-commutative 89.1%

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

   3. associate-*l/ 98.9%

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

   4. fma-def 98.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 3: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+31} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -2.55e-48)
     t_1
     (if (<= x 3.2e-162)
       (* (/ z t) y)
       (if (or (<= x 5.1e+31) (not (<= x 7.8e+43))) t_1 (* z (/ y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -2.55e-48) {
		tmp = t_1;
	} else if (x <= 3.2e-162) {
		tmp = (z / t) * y;
	} else if ((x <= 5.1e+31) || !(x <= 7.8e+43)) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / t))
    if (x <= (-2.55d-48)) then
        tmp = t_1
    else if (x <= 3.2d-162) then
        tmp = (z / t) * y
    else if ((x <= 5.1d+31) .or. (.not. (x <= 7.8d+43))) then
        tmp = t_1
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -2.55e-48) {
		tmp = t_1;
	} else if (x <= 3.2e-162) {
		tmp = (z / t) * y;
	} else if ((x <= 5.1e+31) || !(x <= 7.8e+43)) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -2.55e-48:
		tmp = t_1
	elif x <= 3.2e-162:
		tmp = (z / t) * y
	elif (x <= 5.1e+31) or not (x <= 7.8e+43):
		tmp = t_1
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -2.55e-48)
		tmp = t_1;
	elseif (x <= 3.2e-162)
		tmp = Float64(Float64(z / t) * y);
	elseif ((x <= 5.1e+31) || !(x <= 7.8e+43))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -2.55e-48)
		tmp = t_1;
	elseif (x <= 3.2e-162)
		tmp = (z / t) * y;
	elseif ((x <= 5.1e+31) || ~((x <= 7.8e+43)))
		tmp = t_1;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e-48], t$95$1, If[LessEqual[x, 3.2e-162], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[x, 5.1e+31], N[Not[LessEqual[x, 7.8e+43]], $MachinePrecision]], t$95$1, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.55000000000000006e-48 or 3.19999999999999975e-162 < x < 5.0999999999999997e31 or 7.8000000000000001e43 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 81.9%

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

      1. *-commutative 81.9%

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

      2. distribute-lft-in 81.9%

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

      3. *-rgt-identity 81.9%

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

      4. mul-1-neg 81.9%

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

      5. distribute-rgt-neg-in 81.9%

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

      6. unsub-neg 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in x around 0 81.9%

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

   if -2.55000000000000006e-48 < x < 3.19999999999999975e-162

   1. Initial program 92.4%

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

   2. Taylor expanded in t around 0 79.2%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 80.3%

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

   5. Simplified 80.3%

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

   if 5.0999999999999997e31 < x < 7.8000000000000001e43

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+31} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 55.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-95} \lor \neg \left(t \leq -3.45 \cdot 10^{-121}\right) \land t \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.25e+89)
   x
   (if (or (<= t -4.6e-95) (and (not (<= t -3.45e-121)) (<= t 1.55e+65)))
     (* (/ z t) y)
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.25e+89) {
		tmp = x;
	} else if ((t <= -4.6e-95) || (!(t <= -3.45e-121) && (t <= 1.55e+65))) {
		tmp = (z / t) * y;
	} 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 (t <= (-2.25d+89)) then
        tmp = x
    else if ((t <= (-4.6d-95)) .or. (.not. (t <= (-3.45d-121))) .and. (t <= 1.55d+65)) then
        tmp = (z / t) * y
    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 (t <= -2.25e+89) {
		tmp = x;
	} else if ((t <= -4.6e-95) || (!(t <= -3.45e-121) && (t <= 1.55e+65))) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.25e+89:
		tmp = x
	elif (t <= -4.6e-95) or (not (t <= -3.45e-121) and (t <= 1.55e+65)):
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.25e+89)
		tmp = x;
	elseif ((t <= -4.6e-95) || (!(t <= -3.45e-121) && (t <= 1.55e+65)))
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.25e+89)
		tmp = x;
	elseif ((t <= -4.6e-95) || (~((t <= -3.45e-121)) && (t <= 1.55e+65)))
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.25e+89], x, If[Or[LessEqual[t, -4.6e-95], And[N[Not[LessEqual[t, -3.45e-121]], $MachinePrecision], LessEqual[t, 1.55e+65]]], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e89 or -4.59999999999999998e-95 < t < -3.45e-121 or 1.54999999999999995e65 < t

   1. Initial program 76.7%

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

   2. Taylor expanded in z around 0 68.2%

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

   if -2.25e89 < t < -4.59999999999999998e-95 or -3.45e-121 < t < 1.54999999999999995e65

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 81.5%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. associate-*r/ 61.4%

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

   5. Simplified 61.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-95} \lor \neg \left(t \leq -3.45 \cdot 10^{-121}\right) \land t \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+200}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e+200)
   (* (/ x t) (- z))
   (if (<= z -1.9e-69) (* z (/ y t)) (if (<= z 7.8e-137) x (* (/ z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+200) {
		tmp = (x / t) * -z;
	} else if (z <= -1.9e-69) {
		tmp = z * (y / t);
	} else if (z <= 7.8e-137) {
		tmp = x;
	} else {
		tmp = (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 (z <= (-7d+200)) then
        tmp = (x / t) * -z
    else if (z <= (-1.9d-69)) then
        tmp = z * (y / t)
    else if (z <= 7.8d-137) then
        tmp = x
    else
        tmp = (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 (z <= -7e+200) {
		tmp = (x / t) * -z;
	} else if (z <= -1.9e-69) {
		tmp = z * (y / t);
	} else if (z <= 7.8e-137) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e+200:
		tmp = (x / t) * -z
	elif z <= -1.9e-69:
		tmp = z * (y / t)
	elif z <= 7.8e-137:
		tmp = x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e+200)
		tmp = Float64(Float64(x / t) * Float64(-z));
	elseif (z <= -1.9e-69)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 7.8e-137)
		tmp = x;
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7e+200)
		tmp = (x / t) * -z;
	elseif (z <= -1.9e-69)
		tmp = z * (y / t);
	elseif (z <= 7.8e-137)
		tmp = x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e+200], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, -1.9e-69], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-137], x, N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.00000000000000013e200

   1. Initial program 73.2%

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

   2. Taylor expanded in x around inf 92.0%

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

      1. *-commutative 92.0%

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

      2. distribute-lft-in 92.0%

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

      3. *-rgt-identity 92.0%

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

      4. mul-1-neg 92.0%

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

      5. distribute-rgt-neg-in 92.0%

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

      6. unsub-neg 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in x around 0 92.0%

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

   6. Taylor expanded in z around inf 53.9%

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

      1. associate-*r/ 61.2%

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

      2. neg-mul-1 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

   8. Simplified 61.2%

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

   if -7.00000000000000013e200 < z < -1.8999999999999999e-69

   1. Initial program 81.8%

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

   2. Taylor expanded in t around 0 67.1%

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

   3. Taylor expanded in y around inf 48.0%

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

      1. associate-*l/ 55.2%

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

      2. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if -1.8999999999999999e-69 < z < 7.7999999999999999e-137

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 66.2%

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

   if 7.7999999999999999e-137 < z

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 73.9%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. associate-*r/ 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+200}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]

Alternative 6: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+189}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+189)
   (* (/ z t) (- x))
   (if (<= z -1.2e-67) (* z (/ y t)) (if (<= z 6.5e-137) x (* (/ z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+189) {
		tmp = (z / t) * -x;
	} else if (z <= -1.2e-67) {
		tmp = z * (y / t);
	} else if (z <= 6.5e-137) {
		tmp = x;
	} else {
		tmp = (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 (z <= (-9.5d+189)) then
        tmp = (z / t) * -x
    else if (z <= (-1.2d-67)) then
        tmp = z * (y / t)
    else if (z <= 6.5d-137) then
        tmp = x
    else
        tmp = (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 (z <= -9.5e+189) {
		tmp = (z / t) * -x;
	} else if (z <= -1.2e-67) {
		tmp = z * (y / t);
	} else if (z <= 6.5e-137) {
		tmp = x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+189:
		tmp = (z / t) * -x
	elif z <= -1.2e-67:
		tmp = z * (y / t)
	elif z <= 6.5e-137:
		tmp = x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+189)
		tmp = Float64(Float64(z / t) * Float64(-x));
	elseif (z <= -1.2e-67)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 6.5e-137)
		tmp = x;
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+189)
		tmp = (z / t) * -x;
	elseif (z <= -1.2e-67)
		tmp = z * (y / t);
	elseif (z <= 6.5e-137)
		tmp = x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+189], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, -1.2e-67], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-137], x, N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.49999999999999911e189

   1. Initial program 65.8%

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

   2. Taylor expanded in t around 0 65.8%

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

   3. Taylor expanded in y around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. mul-1-neg 48.6%

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

      3. distribute-rgt-neg-out 48.6%

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

      4. associate-*l/ 75.3%

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

   5. Simplified 75.3%

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

   if -9.49999999999999911e189 < z < -1.2e-67

   1. Initial program 86.5%

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

   2. Taylor expanded in t around 0 70.9%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. associate-*l/ 56.4%

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

      2. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if -1.2e-67 < z < 6.49999999999999991e-137

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 66.2%

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

   if 6.49999999999999991e-137 < z

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 73.9%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. associate-*r/ 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+189}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \]

Alternative 7: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-19} \lor \neg \left(y \leq 7.4 \cdot 10^{-152}\right):\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-19) (not (<= y 7.4e-152)))
   (+ x (* (/ z t) y))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-19) || !(y <= 7.4e-152)) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.2d-19)) .or. (.not. (y <= 7.4d-152))) then
        tmp = x + ((z / t) * y)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-19) || !(y <= 7.4e-152)) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-19) or not (y <= 7.4e-152):
		tmp = x + ((z / t) * y)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-19) || !(y <= 7.4e-152))
		tmp = Float64(x + Float64(Float64(z / t) * y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e-19) || ~((y <= 7.4e-152)))
		tmp = x + ((z / t) * y);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-19], N[Not[LessEqual[y, 7.4e-152]], $MachinePrecision]], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999998e-19 or 7.3999999999999997e-152 < y

   1. Initial program 88.5%

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

   2. Taylor expanded in y around inf 85.5%

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

      1. associate-*r/ 60.5%

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

   4. Simplified 92.7%

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

   if -6.1999999999999998e-19 < y < 7.3999999999999997e-152

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf 91.6%

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

      1. *-commutative 91.6%

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

      2. distribute-lft-in 91.6%

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

      3. *-rgt-identity 91.6%

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

      4. mul-1-neg 91.6%

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

      5. distribute-rgt-neg-in 91.6%

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

      6. unsub-neg 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in x around 0 91.6%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-19} \lor \neg \left(y \leq 7.4 \cdot 10^{-152}\right):\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+82) (+ x (* (/ z t) y)) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+82) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = x + (z * ((y - 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 <= (-8.8d+82)) then
        tmp = x + ((z / t) * y)
    else
        tmp = x + (z * ((y - 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 <= -8.8e+82) {
		tmp = x + ((z / t) * y);
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.8e+82:
		tmp = x + ((z / t) * y)
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.8e+82)
		tmp = Float64(x + Float64(Float64(z / t) * y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.8e+82)
		tmp = x + ((z / t) * y);
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.8e+82], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000005e82

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf 80.9%

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

      1. associate-*r/ 66.4%

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

   4. Simplified 97.7%

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

   if -8.8000000000000005e82 < y

   1. Initial program 93.2%

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

      1. associate-*l/ 92.6%

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

   3. Applied egg-rr 92.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 9: 97.8% 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 89.1%

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

   1. associate-/l* 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 10: 37.4% 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 89.1%

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

2. Taylor expanded in z around 0 36.9%

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

3. Final simplification 36.9%

   \[\leadsto x \]

Developer target: 97.8% 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 2023238 
(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)))