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

Percentage Accurate: 98.0% → 98.0%

Time: 8.7s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+57} \lor \neg \left(t \leq 1.15 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+57) (not (<= t 1.15e+29)))
   (+ x (* y (/ t (- t a))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+57) || !(t <= 1.15e+29)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	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+57)) .or. (.not. (t <= 1.15d+29))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z * (y / (a - t)))
    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+57) || !(t <= 1.15e+29)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+57) or not (t <= 1.15e+29):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e+57) || !(t <= 1.15e+29))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.5e+57) || ~((t <= 1.15e+29)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e+57], N[Not[LessEqual[t, 1.15e+29]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4999999999999997e57 or 1.1500000000000001e29 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-*r/ 71.7%

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

      3. mul-1-neg 71.7%

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

      4. distribute-lft-neg-out 71.7%

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

      5. *-commutative 71.7%

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

      6. *-lft-identity 71.7%

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

      7. times-frac 93.1%

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

      8. /-rgt-identity 93.1%

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

      9. distribute-neg-frac 93.1%

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

      10. distribute-neg-frac2 93.1%

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

      11. neg-sub0 93.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 93.1%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 93.1%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 93.1%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 93.1%

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

      16. remove-double-neg 93.1%

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

   5. Simplified 93.1%

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

   if -6.4999999999999997e57 < t < 1.1500000000000001e29

   1. Initial program 97.2%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.6%

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

      1. div-inv 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l* 92.7%

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

      4. div-inv 92.8%

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

   5. Applied egg-rr 92.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+57} \lor \neg \left(t \leq 1.15 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+152} \lor \neg \left(t \leq 1.6 \cdot 10^{+40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+152) (not (<= t 1.6e+40)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+152) || !(t <= 1.6e+40)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	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 <= (-1.45d+152)) .or. (.not. (t <= 1.6d+40))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    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 <= -1.45e+152) || !(t <= 1.6e+40)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e+152) or not (t <= 1.6e+40):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+152) || !(t <= 1.6e+40))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e+152) || ~((t <= 1.6e+40)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e+152], N[Not[LessEqual[t, 1.6e+40]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e152 or 1.5999999999999999e40 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 89.9%

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

      1. +-commutative 89.9%

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

   5. Simplified 89.9%

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

   if -1.4499999999999999e152 < t < 1.5999999999999999e40

   1. Initial program 97.6%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.7%

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

      1. div-inv 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-*l* 90.7%

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

      4. div-inv 90.7%

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

   5. Applied egg-rr 90.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+152} \lor \neg \left(t \leq 1.6 \cdot 10^{+40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+36)
   (- x (* y (+ (/ z t) -1.0)))
   (if (<= t 3.8e+24) (+ x (* z (/ y (- a t)))) (+ x (* y (/ t (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+36) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 3.8e+24) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - 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 <= (-2.8d+36)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= 3.8d+24) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y * (t / (t - 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 <= -2.8e+36) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 3.8e+24) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+36:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= 3.8e+24:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+36)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= 3.8e+24)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+36)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= 3.8e+24)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+36], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+24], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000001e36

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 91.8%

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

      4. div-sub 91.8%

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

      5. sub-neg 91.8%

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

      6. *-inverses 91.8%

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

      7. metadata-eval 91.8%

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

   5. Simplified 91.8%

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

   if -2.8000000000000001e36 < t < 3.80000000000000015e24

   1. Initial program 97.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.4%

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

      1. div-inv 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l* 93.9%

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

      4. div-inv 93.9%

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

   5. Applied egg-rr 93.9%

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

   if 3.80000000000000015e24 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. associate-*r/ 75.3%

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

      3. mul-1-neg 75.3%

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

      4. distribute-lft-neg-out 75.3%

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

      5. *-commutative 75.3%

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

      6. *-lft-identity 75.3%

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

      7. times-frac 95.4%

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

      8. /-rgt-identity 95.4%

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

      9. distribute-neg-frac 95.4%

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

      10. distribute-neg-frac2 95.4%

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

      11. neg-sub0 95.4%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 95.4%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 95.4%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 95.4%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 95.4%

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

      16. remove-double-neg 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+15} \lor \neg \left(t \leq 9 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+15) (not (<= t 9e-7))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+15) || !(t <= 9e-7)) {
		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 <= (-1.2d+15)) .or. (.not. (t <= 9d-7))) 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 <= -1.2e+15) || !(t <= 9e-7)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+15) or not (t <= 9e-7):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+15) || !(t <= 9e-7))
		tmp = Float64(x + y);
	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 <= -1.2e+15) || ~((t <= 9e-7)))
		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, -1.2e+15], N[Not[LessEqual[t, 9e-7]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e15 or 8.99999999999999959e-7 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.1%

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

      1. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -1.2e15 < t < 8.99999999999999959e-7

   1. Initial program 96.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+15} \lor \neg \left(t \leq 9 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+14} \lor \neg \left(t \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e+14) (not (<= t 2.1e-9))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e+14) || !(t <= 2.1e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / 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 <= (-3d+14)) .or. (.not. (t <= 2.1d-9))) then
        tmp = x + y
    else
        tmp = x + (y / (a / 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 <= -3e+14) || !(t <= 2.1e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e+14) or not (t <= 2.1e-9):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e+14) || !(t <= 2.1e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e+14) || ~((t <= 2.1e-9)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e+14], N[Not[LessEqual[t, 2.1e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e14 or 2.10000000000000019e-9 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.1%

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

      1. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -3e14 < t < 2.10000000000000019e-9

   1. Initial program 96.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.0%

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

      2. un-div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in t around 0 82.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+14} \lor \neg \left(t \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+31} \lor \neg \left(t \leq 9 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+31) (not (<= t 9e-40))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+31) || !(t <= 9e-40)) {
		tmp = x + y;
	} else {
		tmp = 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 <= (-1.45d+31)) .or. (.not. (t <= 9d-40))) then
        tmp = x + y
    else
        tmp = 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 <= -1.45e+31) || !(t <= 9e-40)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e+31) or not (t <= 9e-40):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+31) || !(t <= 9e-40))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e+31) || ~((t <= 9e-40)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e+31], N[Not[LessEqual[t, 9e-40]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e31 or 9.0000000000000002e-40 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.5%

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

      1. +-commutative 83.5%

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

   5. Simplified 83.5%

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

   if -1.45e31 < t < 9.0000000000000002e-40

   1. Initial program 96.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.8%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+31} \lor \neg \left(t \leq 9 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.5% 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 98.4%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 56.9%

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

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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