Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 99.1%

Time: 7.4s

Alternatives: 9

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: 92.9% 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: 99.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.7%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 98.4%

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

4. Final simplification 98.9%

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

Alternative 2: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-80} \lor \neg \left(y \leq 8.4 \cdot 10^{-101}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e-80) (not (<= y 8.4e-101)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-80) || !(y <= 8.4e-101)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1d-80)) .or. (.not. (y <= 8.4d-101))) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-80) || !(y <= 8.4e-101)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e-80) or not (y <= 8.4e-101):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e-80) || !(y <= 8.4e-101))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e-80) || ~((y <= 8.4e-101)))
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e-80], N[Not[LessEqual[y, 8.4e-101]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999961e-81 or 8.40000000000000062e-101 < y

   1. Initial program 94.4%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around inf 86.0%

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

   if -9.99999999999999961e-81 < y < 8.40000000000000062e-101

   1. Initial program 94.6%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   6. Simplified 90.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-80} \lor \neg \left(y \leq 8.4 \cdot 10^{-101}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 3: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-77} \lor \neg \left(y \leq 4.9 \cdot 10^{-101}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-77) (not (<= y 4.9e-101)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-77) || !(y <= 4.9e-101)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.4d-77)) .or. (.not. (y <= 4.9d-101))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-77) || !(y <= 4.9e-101)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e-77) or not (y <= 4.9e-101):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e-77) || !(y <= 4.9e-101))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.4e-77) || ~((y <= 4.9e-101)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e-77], N[Not[LessEqual[y, 4.9e-101]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999983e-77 or 4.9e-101 < y

   1. Initial program 94.4%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around inf 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

      1. associate-/r/ 89.5%

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

   8. Applied egg-rr 89.5%

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

   if -3.39999999999999983e-77 < y < 4.9e-101

   1. Initial program 94.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-77} \lor \neg \left(y \leq 4.9 \cdot 10^{-101}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-79)
   (+ x (* y (/ z t)))
   (if (<= y 4.1e-101) (* x (- 1.0 (/ z t))) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-79) {
		tmp = x + (y * (z / t));
	} else if (y <= 4.1e-101) {
		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 (y <= (-5.5d-79)) then
        tmp = x + (y * (z / t))
    else if (y <= 4.1d-101) 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 (y <= -5.5e-79) {
		tmp = x + (y * (z / t));
	} else if (y <= 4.1e-101) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-79:
		tmp = x + (y * (z / t))
	elif y <= 4.1e-101:
		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 (y <= -5.5e-79)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (y <= 4.1e-101)
		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 (y <= -5.5e-79)
		tmp = x + (y * (z / t));
	elseif (y <= 4.1e-101)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-79], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-101], 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 3 regimes

2. if y < -5.4999999999999997e-79

   1. Initial program 93.4%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

      1. associate-/r/ 87.5%

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

   8. Applied egg-rr 87.5%

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

   if -5.4999999999999997e-79 < y < 4.10000000000000026e-101

   1. Initial program 94.6%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   6. Simplified 90.0%

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

   if 4.10000000000000026e-101 < y

   1. Initial program 95.3%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

      1. associate-/r/ 91.2%

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

   8. Applied egg-rr 91.2%

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

      1. *-commutative 91.2%

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

      2. clear-num 91.2%

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

      3. un-div-inv 92.3%

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

   10. Applied egg-rr 92.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.85e+121) (+ 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 <= 1.85e+121) {
		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 <= 1.85d+121) 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 <= 1.85e+121) {
		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 <= 1.85e+121:
		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 <= 1.85e+121)
		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 <= 1.85e+121)
		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, 1.85e+121], 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 < 1.85000000000000006e121

   1. Initial program 94.1%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   if 1.85000000000000006e121 < x

   1. Initial program 97.0%

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

      1. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

   6. Simplified 97.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 6: 49.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.35e+80) x (if (<= t 2.4e-47) (* (/ z t) (- x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e+80) {
		tmp = x;
	} else if (t <= 2.4e-47) {
		tmp = (z / t) * -x;
	} 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 <= (-1.35d+80)) then
        tmp = x
    else if (t <= 2.4d-47) then
        tmp = (z / t) * -x
    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 <= -1.35e+80) {
		tmp = x;
	} else if (t <= 2.4e-47) {
		tmp = (z / t) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.35e+80:
		tmp = x
	elif t <= 2.4e-47:
		tmp = (z / t) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.35e+80)
		tmp = x;
	elseif (t <= 2.4e-47)
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e+80)
		tmp = x;
	elseif (t <= 2.4e-47)
		tmp = (z / t) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.35e+80], x, If[LessEqual[t, 2.4e-47], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.34999999999999991e80 or 2.3999999999999999e-47 < t

   1. Initial program 90.3%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around inf 58.5%

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

   if -1.34999999999999991e80 < t < 2.3999999999999999e-47

   1. Initial program 98.0%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in y around 0 49.8%

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

      1. neg-mul-1 49.8%

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

      2. distribute-neg-frac 49.8%

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

   6. Simplified 49.8%

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

      1. div-inv 49.8%

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

      2. div-inv 49.8%

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

      3. add-sqr-sqrt 22.3%

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

      4. sqrt-unprod 26.1%

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

      5. sqr-neg 26.1%

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

      6. sqrt-unprod 9.4%

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

      7. add-sqr-sqrt 17.1%

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

      8. cancel-sign-sub 17.1%

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

      9. distribute-frac-neg 17.1%

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

      10. *-commutative 17.1%

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

      11. clear-num 17.1%

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

      12. un-div-inv 18.5%

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

      13. add-sqr-sqrt 8.4%

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

      14. sqrt-unprod 31.2%

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

      15. sqr-neg 31.2%

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

      16. sqrt-unprod 28.8%

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

      17. add-sqr-sqrt 51.8%

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

   8. Applied egg-rr 51.8%

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

   9. Taylor expanded in z around inf 39.9%

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

       1. mul-1-neg 39.9%

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

       2. associate-*l/ 37.4%

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

       3. distribute-lft-neg-in 37.4%

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

       4. *-commutative 37.4%

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

       5. distribute-neg-frac 37.4%

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

   11. Simplified 37.4%

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

   12. Taylor expanded in z around 0 39.9%

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

       1. mul-1-neg 39.9%

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

       2. associate-*r/ 43.1%

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

   14. Simplified 43.1%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 94.5%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
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 8: 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 94.5%

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

   1. associate-*l/ 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in x around inf 63.6%

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

   1. mul-1-neg 63.6%

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

   2. unsub-neg 63.6%

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

6. Simplified 63.6%

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

7. Final simplification 63.6%

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

Alternative 9: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in t around inf 36.3%

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

5. Final simplification 36.3%

   \[\leadsto x \]

Developer target: 97.7% 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 2023310 
(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)))