Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 86.2% → 98.2%

Time: 7.3s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

   1. associate-/l* 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 2: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+105} \lor \neg \left(t \leq 3.15 \cdot 10^{+119}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.08e+105) (not (<= t 3.15e+119)))
   (+ x y)
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.08e+105) || !(t <= 3.15e+119)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.08d+105)) .or. (.not. (t <= 3.15d+119))) then
        tmp = x + y
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.08e+105) || !(t <= 3.15e+119)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.08e+105) or not (t <= 3.15e+119):
		tmp = x + y
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.08e+105) || !(t <= 3.15e+119))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.08e+105) || ~((t <= 3.15e+119)))
		tmp = x + y;
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.08e+105], N[Not[LessEqual[t, 3.15e+119]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.07999999999999994e105 or 3.1499999999999999e119 < t

   1. Initial program 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-*l/ 95.7%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -1.07999999999999994e105 < t < 3.1499999999999999e119

   1. Initial program 89.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 78.3%

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

      1. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+105} \lor \neg \left(t \leq 3.15 \cdot 10^{+119}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+75} \lor \neg \left(t \leq 72000000000000\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+75) (not (<= t 72000000000000.0)))
   (- x (/ y (+ (/ a t) -1.0)))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+75) || !(t <= 72000000000000.0)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.2d+75)) .or. (.not. (t <= 72000000000000.0d0))) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+75) || !(t <= 72000000000000.0)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+75) or not (t <= 72000000000000.0):
		tmp = x - (y / ((a / t) + -1.0))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+75) || !(t <= 72000000000000.0))
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e+75) || ~((t <= 72000000000000.0)))
		tmp = x - (y / ((a / t) + -1.0));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+75], N[Not[LessEqual[t, 72000000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.19999999999999997e75 or 7.2e13 < t

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*l/ 96.6%

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

      3. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-/l* 90.0%

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

      5. div-sub 90.0%

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

      6. sub-neg 90.0%

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

      7. *-inverses 90.0%

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

      8. metadata-eval 90.0%

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

   6. Simplified 90.0%

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

   if -4.19999999999999997e75 < t < 7.2e13

   1. Initial program 89.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+75} \lor \neg \left(t \leq 72000000000000\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+106)
   (+ x y)
   (if (<= t 1.45e+114) (+ x (/ y (/ (- a t) z))) (+ x (* (/ y t) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = x + y;
	} else if (t <= 1.45e+114) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + ((y / t) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.9d+106)) then
        tmp = x + y
    else if (t <= 1.45d+114) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x + ((y / t) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = x + y;
	} else if (t <= 1.45e+114) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + ((y / t) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e+106:
		tmp = x + y
	elif t <= 1.45e+114:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x + ((y / t) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+106)
		tmp = Float64(x + y);
	elseif (t <= 1.45e+114)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e+106)
		tmp = x + y;
	elseif (t <= 1.45e+114)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x + ((y / t) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+106], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.45e+114], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e106

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-*l/ 95.6%

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

      3. fma-def 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around inf 95.9%

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

      1. +-commutative 95.9%

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

   6. Simplified 95.9%

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

   if -2.9000000000000002e106 < t < 1.45e114

   1. Initial program 89.0%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 86.5%

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

   6. Simplified 86.5%

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

   if 1.45e114 < t

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-*l/ 95.8%

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

      3. fma-def 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in a around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

      3. associate-/l* 95.9%

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

      4. associate-/r/ 91.9%

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

   6. Simplified 91.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-34} \lor \neg \left(t \leq 2.4 \cdot 10^{+115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e-34) (not (<= t 2.4e+115))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e-34) || !(t <= 2.4e+115)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.5d-34)) .or. (.not. (t <= 2.4d+115))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e-34) || !(t <= 2.4e+115)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e-34) or not (t <= 2.4e+115):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e-34) || !(t <= 2.4e+115))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.5e-34) || ~((t <= 2.4e+115)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e-34], N[Not[LessEqual[t, 2.4e+115]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999985e-34 or 2.4e115 < t

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-*l/ 96.7%

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

      3. fma-def 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   6. Simplified 85.5%

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

   if -6.49999999999999985e-34 < t < 2.4e115

   1. Initial program 91.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around 0 73.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-34} \lor \neg \left(t \leq 2.4 \cdot 10^{+115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 6: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-51} \lor \neg \left(t \leq 4.5 \cdot 10^{+115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e-51) (not (<= t 4.5e+115))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e-51) || !(t <= 4.5e+115)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9d-51)) .or. (.not. (t <= 4.5d+115))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e-51) || !(t <= 4.5e+115)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e-51) or not (t <= 4.5e+115):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e-51) || !(t <= 4.5e+115))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e-51) || ~((t <= 4.5e+115)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e-51], N[Not[LessEqual[t, 4.5e+115]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999948e-51 or 4.49999999999999963e115 < t

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around inf 86.0%

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

      1. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -8.99999999999999948e-51 < t < 4.49999999999999963e115

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. associate-*l/ 96.3%

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

      3. fma-def 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 78.8%

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

      3. associate-/r/ 79.6%

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

   6. Simplified 79.6%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-51} \lor \neg \left(t \leq 4.5 \cdot 10^{+115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 60.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 81.6%

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

   1. +-commutative 81.6%

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

   2. associate-*l/ 96.6%

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

   3. fma-def 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in t around inf 63.4%

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

   1. +-commutative 63.4%

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

6. Simplified 63.4%

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

7. Final simplification 63.4%

   \[\leadsto x + y \]

Alternative 8: 51.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

   1. +-commutative 81.6%

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

   2. associate-*l/ 96.6%

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

   3. fma-def 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in y around 0 51.2%

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

5. Final simplification 51.2%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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