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

Percentage Accurate: 84.9% → 99.7%

Time: 13.6s

Alternatives: 12

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: 84.9% 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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- z t) (/ (- a t) y)))
     (if (<= t_1 4e+307) (+ x t_1) (+ x (* (- z t) (/ y (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else if (t_1 <= 4e+307) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else if (t_1 <= 4e+307) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) / ((a - t) / y))
	elif t_1 <= 4e+307:
		tmp = x + t_1
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 4e+307)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - t) / ((a - t) / y));
	elseif (t_1 <= 4e+307)
		tmp = x + t_1;
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0

   1. Initial program 46.0%

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

      1. *-commutative 46.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 3.99999999999999994e307

   1. Initial program 99.2%

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

   if 3.99999999999999994e307 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 41.7%

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

      1. associate-*l/ 99.8%

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

   3. Applied egg-rr 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. +-commutative 84.8%

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

   2. *-commutative 84.8%

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

   3. associate-*l/ 98.0%

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

   4. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+307)))
     (+ x (* (- z t) (/ y (- a t))))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+307)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+307)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+307):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+307))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+307)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+307]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 3.99999999999999994e307 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 43.2%

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

      1. associate-*l/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 3.99999999999999994e307

   1. Initial program 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty \lor \neg \left(\frac{\left(z - t\right) \cdot y}{a - t} \leq 4 \cdot 10^{+307}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

Alternative 4: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-57} \lor \neg \left(t \leq 8.8 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.25e-57) (not (<= t 8.8e-10)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.25e-57) || !(t <= 8.8e-10)) {
		tmp = x + (y * (1.0 - (z / t)));
	} 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 <= (-2.25d-57)) .or. (.not. (t <= 8.8d-10))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    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 <= -2.25e-57) || !(t <= 8.8e-10)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.25e-57) or not (t <= 8.8e-10):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.25e-57) || !(t <= 8.8e-10))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.25e-57) || ~((t <= 8.8e-10)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.25e-57], N[Not[LessEqual[t, 8.8e-10]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.24999999999999986e-57 or 8.7999999999999996e-10 < t

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around 0 84.4%

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

      1. neg-mul-1 84.4%

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

      2. distribute-neg-frac 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*r/ 86.0%

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

   9. Simplified 86.0%

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

   10. Taylor expanded in y around 0 86.6%

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

   if -2.24999999999999986e-57 < t < 8.7999999999999996e-10

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      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 t around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-/l* 77.7%

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

   6. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. associate-/r/ 77.6%

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

      3. clear-num 77.7%

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

   8. Applied egg-rr 77.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-57} \lor \neg \left(t \leq 8.8 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 5: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-46} \lor \neg \left(t \leq 15500\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e-46) (not (<= t 15500.0)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e-46) || !(t <= 15500.0)) {
		tmp = x + (y * (1.0 - (z / t)));
	} 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 <= (-2.3d-46)) .or. (.not. (t <= 15500.0d0))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    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 <= -2.3e-46) || !(t <= 15500.0)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e-46) or not (t <= 15500.0):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e-46) || !(t <= 15500.0))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	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 <= -2.3e-46) || ~((t <= 15500.0)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e-46], N[Not[LessEqual[t, 15500.0]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $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 < -2.2999999999999999e-46 or 15500 < t

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in a around 0 84.6%

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

      1. neg-mul-1 84.6%

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

      2. distribute-neg-frac 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r/ 86.3%

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

   9. Simplified 86.3%

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

   10. Taylor expanded in y around 0 86.9%

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

   if -2.2999999999999999e-46 < t < 15500

   1. Initial program 96.3%

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

      1. clear-num 96.3%

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

      2. inv-pow 96.3%

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

   3. Applied egg-rr 96.3%

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

      1. unpow-1 96.3%

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

      2. associate-/r* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in z around inf 84.9%

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

      1. associate-/l* 86.0%

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

   8. Simplified 86.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-46} \lor \neg \left(t \leq 15500\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 6: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5200000000:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.45e-49)
   (+ x (* y (- 1.0 (/ z t))))
   (if (<= t 5200000000.0)
     (+ x (/ y (/ (- a t) z)))
     (- x (/ t (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.45e-49) {
		tmp = x + (y * (1.0 - (z / t)));
	} else if (t <= 5200000000.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	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 <= (-2.45d-49)) then
        tmp = x + (y * (1.0d0 - (z / t)))
    else if (t <= 5200000000.0d0) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x - (t / ((a - t) / y))
    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 <= -2.45e-49) {
		tmp = x + (y * (1.0 - (z / t)));
	} else if (t <= 5200000000.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.45e-49:
		tmp = x + (y * (1.0 - (z / t)))
	elif t <= 5200000000.0:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.45e-49)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	elseif (t <= 5200000000.0)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.45e-49)
		tmp = x + (y * (1.0 - (z / t)));
	elseif (t <= 5200000000.0)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.45e-49], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5200000000.0], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4500000000000001e-49

   1. Initial program 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around 0 86.6%

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

      1. neg-mul-1 86.6%

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

      2. distribute-neg-frac 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in z around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*r/ 87.2%

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

   9. Simplified 87.2%

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

   10. Taylor expanded in y around 0 88.4%

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

   if -2.4500000000000001e-49 < t < 5.2e9

   1. Initial program 96.4%

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

      1. clear-num 96.4%

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

      2. inv-pow 96.4%

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

   3. Applied egg-rr 96.4%

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

      1. unpow-1 96.4%

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

      2. associate-/r* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 86.2%

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

   8. Simplified 86.2%

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

   if 5.2e9 < t

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      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 z around 0 64.0%

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

      1. associate-*r/ 85.7%

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

      2. neg-mul-1 85.7%

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

      3. unsub-neg 85.7%

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

      4. associate-*r/ 64.0%

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

      5. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5200000000:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 7: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq 3000000000:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e-49)
   (- x (/ y (/ t (- z t))))
   (if (<= t 3000000000.0)
     (+ x (/ y (/ (- a t) z)))
     (- x (/ t (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-49) {
		tmp = x - (y / (t / (z - t)));
	} else if (t <= 3000000000.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	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 <= (-2.6d-49)) then
        tmp = x - (y / (t / (z - t)))
    else if (t <= 3000000000.0d0) then
        tmp = x + (y / ((a - t) / z))
    else
        tmp = x - (t / ((a - t) / y))
    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 <= -2.6e-49) {
		tmp = x - (y / (t / (z - t)));
	} else if (t <= 3000000000.0) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e-49:
		tmp = x - (y / (t / (z - t)))
	elif t <= 3000000000.0:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e-49)
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	elseif (t <= 3000000000.0)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e-49)
		tmp = x - (y / (t / (z - t)));
	elseif (t <= 3000000000.0)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e-49], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3000000000.0], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.59999999999999995e-49

   1. Initial program 79.5%

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

      1. +-commutative 79.5%

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

      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 a around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

   if -2.59999999999999995e-49 < t < 3e9

   1. Initial program 96.4%

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

      1. clear-num 96.4%

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

      2. inv-pow 96.4%

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

   3. Applied egg-rr 96.4%

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

      1. unpow-1 96.4%

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

      2. associate-/r* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 86.2%

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

   8. Simplified 86.2%

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

   if 3e9 < t

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      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 z around 0 64.0%

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

      1. associate-*r/ 85.7%

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

      2. neg-mul-1 85.7%

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

      3. unsub-neg 85.7%

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

      4. associate-*r/ 64.0%

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

      5. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq 3000000000:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e-47) (+ y x) (if (<= t 3e-8) (+ x (/ z (/ a y))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e-47) {
		tmp = y + x;
	} else if (t <= 3e-8) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	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 <= (-3.7d-47)) then
        tmp = y + x
    else if (t <= 3d-8) then
        tmp = x + (z / (a / y))
    else
        tmp = y + x
    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 <= -3.7e-47) {
		tmp = y + x;
	} else if (t <= 3e-8) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e-47:
		tmp = y + x
	elif t <= 3e-8:
		tmp = x + (z / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e-47)
		tmp = Float64(y + x);
	elseif (t <= 3e-8)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e-47)
		tmp = y + x;
	elseif (t <= 3e-8)
		tmp = x + (z / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e-47], N[(y + x), $MachinePrecision], If[LessEqual[t, 3e-8], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7e-47 or 2.99999999999999973e-8 < t

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*l/ 96.2%

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

      3. fma-def 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 78.1%

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

      1. +-commutative 78.1%

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

   6. Simplified 78.1%

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

   if -3.7e-47 < t < 2.99999999999999973e-8

   1. Initial program 96.2%

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

      1. clear-num 96.2%

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

      2. inv-pow 96.2%

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

   3. Applied egg-rr 96.2%

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

      1. unpow-1 96.2%

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

      2. associate-/r* 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 77.4%

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

   8. Simplified 77.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e-47) (+ y x) (if (<= t 3.4e-11) (+ x (* y (/ z a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e-47) {
		tmp = y + x;
	} else if (t <= 3.4e-11) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	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 <= (-3.8d-47)) then
        tmp = y + x
    else if (t <= 3.4d-11) then
        tmp = x + (y * (z / a))
    else
        tmp = y + x
    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 <= -3.8e-47) {
		tmp = y + x;
	} else if (t <= 3.4e-11) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e-47:
		tmp = y + x
	elif t <= 3.4e-11:
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e-47)
		tmp = Float64(y + x);
	elseif (t <= 3.4e-11)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e-47)
		tmp = y + x;
	elseif (t <= 3.4e-11)
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e-47], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.4e-11], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.80000000000000015e-47 or 3.3999999999999999e-11 < t

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*l/ 96.2%

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

      3. fma-def 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 78.1%

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

      1. +-commutative 78.1%

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

   6. Simplified 78.1%

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

   if -3.80000000000000015e-47 < t < 3.3999999999999999e-11

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      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 t around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-/l* 77.7%

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

   6. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. associate-/r/ 77.6%

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

      3. clear-num 77.7%

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

   8. Applied egg-rr 77.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-*l/ 96.0%

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

3. Applied egg-rr 96.0%

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

4. Final simplification 96.0%

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

Alternative 11: 60.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return y + 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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. +-commutative 84.8%

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

   2. associate-*l/ 96.0%

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

   3. fma-def 96.0%

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

3. Simplified 96.0%

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

4. Taylor expanded in t around inf 59.6%

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

   1. +-commutative 59.6%

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

6. Simplified 59.6%

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

7. Final simplification 59.6%

   \[\leadsto y + x \]

Alternative 12: 50.3% 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 84.8%

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

   1. +-commutative 84.8%

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

   2. associate-*l/ 96.0%

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

   3. fma-def 96.0%

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

3. Simplified 96.0%

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

4. Taylor expanded in y around 0 46.5%

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

5. Final simplification 46.5%

   \[\leadsto x \]

Developer target: 98.4% 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 2023275 
(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))))