Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 95.8%

Time: 9.0s

Alternatives: 11

Speedup: 1.0×

• 24.9% 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: 92.9% 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: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+282}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 5e+282) t_1 (fma (- y x) (/ z t) x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= 5e+282) {
		tmp = t_1;
	} else {
		tmp = fma((y - x), (z / t), x);
	}
	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 <= 5e+282)
		tmp = t_1;
	else
		tmp = fma(Float64(y - x), Float64(z / t), x);
	end
	return 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[LessEqual[t$95$1, 5e+282], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4.99999999999999978e282

   1. Initial program 98.7%

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

   if 4.99999999999999978e282 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+282}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 5e+282) t_1 (+ x (* (- y x) (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= 5e+282) {
		tmp = t_1;
	} else {
		tmp = x + ((y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * z) / t)
    if (t_1 <= 5d+282) then
        tmp = t_1
    else
        tmp = x + ((y - x) * (z / t))
    end if
    code = tmp
end function

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 <= 5e+282) {
		tmp = t_1;
	} else {
		tmp = x + ((y - x) * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if t_1 <= 5e+282:
		tmp = t_1
	else:
		tmp = x + ((y - x) * (z / t))
	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 <= 5e+282)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	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 <= 5e+282)
		tmp = t_1;
	else
		tmp = x + ((y - x) * (z / t));
	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[LessEqual[t$95$1, 5e+282], t$95$1, N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4.99999999999999978e282

   1. Initial program 98.7%

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

   if 4.99999999999999978e282 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 76.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

Alternative 3: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e+48)
   (/ x (/ t (- t z)))
   (if (<= x 0.65) (+ x (/ (* y z) t)) (- x (/ x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+48) {
		tmp = x / (t / (t - z));
	} else if (x <= 0.65) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x - (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 <= (-5.5d+48)) then
        tmp = x / (t / (t - z))
    else if (x <= 0.65d0) then
        tmp = x + ((y * z) / t)
    else
        tmp = x - (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 <= -5.5e+48) {
		tmp = x / (t / (t - z));
	} else if (x <= 0.65) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e+48:
		tmp = x / (t / (t - z))
	elif x <= 0.65:
		tmp = x + ((y * z) / t)
	else:
		tmp = x - (x / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e+48)
		tmp = Float64(x / Float64(t / Float64(t - z)));
	elseif (x <= 0.65)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x - Float64(x / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e+48)
		tmp = x / (t / (t - z));
	elseif (x <= 0.65)
		tmp = x + ((y * z) / t);
	else
		tmp = x - (x / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e+48], N[(x / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000002e48

   1. Initial program 94.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in t around 0 91.5%

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

      1. clear-num 91.6%

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

      2. un-div-inv 91.6%

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

   10. Applied egg-rr 91.6%

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

   if -5.5000000000000002e48 < x < 0.650000000000000022

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 0.650000000000000022 < x

   1. Initial program 90.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 90.3%

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

      1. neg-mul-1 90.3%

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

   9. Simplified 90.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{elif}\;x \leq 6.8:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.85e+48)
   (/ x (/ t (- t z)))
   (if (<= x 6.8) (+ x (/ (* y z) t)) (* x (/ (- t z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.85e+48) {
		tmp = x / (t / (t - z));
	} else if (x <= 6.8) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * ((t - 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 <= (-1.85d+48)) then
        tmp = x / (t / (t - z))
    else if (x <= 6.8d0) then
        tmp = x + ((y * z) / t)
    else
        tmp = x * ((t - 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 <= -1.85e+48) {
		tmp = x / (t / (t - z));
	} else if (x <= 6.8) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.85e+48:
		tmp = x / (t / (t - z))
	elif x <= 6.8:
		tmp = x + ((y * z) / t)
	else:
		tmp = x * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.85e+48)
		tmp = Float64(x / Float64(t / Float64(t - z)));
	elseif (x <= 6.8)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.85e+48)
		tmp = x / (t / (t - z));
	elseif (x <= 6.8)
		tmp = x + ((y * z) / t);
	else
		tmp = x * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.85e+48], N[(x / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e48

   1. Initial program 94.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in t around 0 91.5%

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

      1. clear-num 91.6%

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

      2. un-div-inv 91.6%

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

   10. Applied egg-rr 91.6%

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

   if -1.85e48 < x < 6.79999999999999982

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 6.79999999999999982 < x

   1. Initial program 90.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 90.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{elif}\;x \leq 6.8:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.5e+47)
   (* x (- 1.0 (/ z t)))
   (if (<= x 0.68) (+ x (/ (* y z) t)) (* x (/ (- t z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+47) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 0.68) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * ((t - 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 <= (-1.5d+47)) then
        tmp = x * (1.0d0 - (z / t))
    else if (x <= 0.68d0) then
        tmp = x + ((y * z) / t)
    else
        tmp = x * ((t - 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 <= -1.5e+47) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 0.68) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.5e+47:
		tmp = x * (1.0 - (z / t))
	elif x <= 0.68:
		tmp = x + ((y * z) / t)
	else:
		tmp = x * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.5e+47)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	elseif (x <= 0.68)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.5e+47)
		tmp = x * (1.0 - (z / t));
	elseif (x <= 0.68)
		tmp = x + ((y * z) / t);
	else
		tmp = x * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.5e+47], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.68], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5000000000000001e47

   1. Initial program 94.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

   7. Simplified 91.5%

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

   if -1.5000000000000001e47 < x < 0.680000000000000049

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 0.680000000000000049 < x

   1. Initial program 90.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 90.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e+48)
   (* x (- 1.0 (/ z t)))
   (if (<= x 3e+113) (+ x (* y (/ z t))) (* x (/ (- t z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+48) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 3e+113) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - 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 <= (-2.1d+48)) then
        tmp = x * (1.0d0 - (z / t))
    else if (x <= 3d+113) then
        tmp = x + (y * (z / t))
    else
        tmp = x * ((t - 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 <= -2.1e+48) {
		tmp = x * (1.0 - (z / t));
	} else if (x <= 3e+113) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e+48:
		tmp = x * (1.0 - (z / t))
	elif x <= 3e+113:
		tmp = x + (y * (z / t))
	else:
		tmp = x * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e+48)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	elseif (x <= 3e+113)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.1e+48)
		tmp = x * (1.0 - (z / t));
	elseif (x <= 3e+113)
		tmp = x + (y * (z / t));
	else
		tmp = x * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e+48], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+113], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999998e48

   1. Initial program 94.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

   7. Simplified 91.5%

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

   if -2.0999999999999998e48 < x < 3e113

   1. Initial program 96.5%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 83.9%

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

      1. associate-*r/ 83.3%

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

   7. Simplified 83.3%

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

   if 3e113 < x

   1. Initial program 88.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in t around 0 97.7%

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

Alternative 7: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 360000000:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.6e-70) x (if (<= t 360000000.0) (* x (/ z (- t))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e-70) {
		tmp = x;
	} else if (t <= 360000000.0) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.6d-70)) then
        tmp = x
    else if (t <= 360000000.0d0) then
        tmp = x * (z / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e-70) {
		tmp = x;
	} else if (t <= 360000000.0) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.6e-70:
		tmp = x
	elif t <= 360000000.0:
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.6e-70)
		tmp = x;
	elseif (t <= 360000000.0)
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.6e-70)
		tmp = x;
	elseif (t <= 360000000.0)
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.6e-70], x, If[LessEqual[t, 360000000.0], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999998e-70 or 3.6e8 < t

   1. Initial program 90.6%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 53.4%

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

   if -5.5999999999999998e-70 < t < 3.6e8

   1. Initial program 98.8%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in z around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-frac-neg2 49.4%

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

   10. Simplified 49.4%

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

Alternative 8: 38.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -6e+143) (* t (/ x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+143) {
		tmp = t * (x / 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 (x <= (-6d+143)) then
        tmp = t * (x / 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 (x <= -6e+143) {
		tmp = t * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e+143:
		tmp = t * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e+143)
		tmp = Float64(t * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e+143)
		tmp = t * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e+143], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000001e143

   1. Initial program 93.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 68.1%

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

   6. Taylor expanded in t around inf 19.3%

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

      1. *-commutative 19.3%

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

   8. Simplified 19.3%

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

      1. *-commutative 19.3%

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

      2. associate-/l* 63.4%

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

   10. Applied egg-rr 63.4%

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

   if -6.0000000000000001e143 < x

   1. Initial program 95.2%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 29.1%

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

Alternative 9: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

Alternative 10: 65.0% 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 94.9%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in x around inf 62.2%

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

   1. mul-1-neg 62.2%

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

   2. unsub-neg 62.2%

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

7. Simplified 62.2%

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

Alternative 11: 38.0% 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 94.9%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in z around 0 32.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

  (+ x (/ (* (- y x) z) t)))