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

Percentage Accurate: 85.3% → 98.1%

Time: 7.7s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.25 \cdot 10^{-30}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+37) (not (<= z 1.25e-30)))
   (+ x (* (- z t) (/ y z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+37) || !(z <= 1.25e-30)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (t * (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 ((z <= (-2.5d+37)) .or. (.not. (z <= 1.25d-30))) then
        tmp = x + ((z - t) * (y / z))
    else
        tmp = x + (t * (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 ((z <= -2.5e+37) || !(z <= 1.25e-30)) {
		tmp = x + ((z - t) * (y / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+37) or not (z <= 1.25e-30):
		tmp = x + ((z - t) * (y / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+37) || !(z <= 1.25e-30))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+37) || ~((z <= 1.25e-30)))
		tmp = x + ((z - t) * (y / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+37], N[Not[LessEqual[z, 1.25e-30]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999994e37 or 1.24999999999999993e-30 < z

   1. Initial program 72.9%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 89.5%

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

   if -2.49999999999999994e37 < z < 1.24999999999999993e-30

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. associate-/l* 83.4%

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

      2. associate-/r/ 83.5%

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

   6. Applied egg-rr 83.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.25 \cdot 10^{-30}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37} \lor \neg \left(z \leq 7.6 \cdot 10^{-31}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+37) (not (<= z 7.6e-31)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+37) || !(z <= 7.6e-31)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (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 ((z <= (-2.5d+37)) .or. (.not. (z <= 7.6d-31))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t * (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 ((z <= -2.5e+37) || !(z <= 7.6e-31)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+37) or not (z <= 7.6e-31):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+37) || !(z <= 7.6e-31))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+37) || ~((z <= 7.6e-31)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+37], N[Not[LessEqual[z, 7.6e-31]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999994e37 or 7.5999999999999999e-31 < z

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

      1. clear-num 92.5%

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

      2. associate-/r/ 92.5%

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

      3. clear-num 92.6%

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

      4. div-sub 92.6%

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

      5. *-inverses 92.6%

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

   8. Applied egg-rr 92.6%

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

   if -2.49999999999999994e37 < z < 7.5999999999999999e-31

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. associate-/l* 83.4%

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

      2. associate-/r/ 83.5%

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

   6. Applied egg-rr 83.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37} \lor \neg \left(z \leq 7.6 \cdot 10^{-31}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+37)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 7.5e-31) (+ x (* t (/ y a))) (+ x (/ y (/ z (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+37) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 7.5e-31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (z / (z - 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 (z <= (-2.5d+37)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 7.5d-31) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y / (z / (z - 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 (z <= -2.5e+37) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 7.5e-31) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+37:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 7.5e-31:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+37)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 7.5e-31)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+37)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 7.5e-31)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+37], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-31], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999994e37

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-/l* 94.6%

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

   6. Simplified 94.6%

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

      1. clear-num 94.6%

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

      2. associate-/r/ 94.6%

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

      3. clear-num 94.6%

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

      4. div-sub 94.6%

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

      5. *-inverses 94.6%

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

   8. Applied egg-rr 94.6%

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

   if -2.49999999999999994e37 < z < 7.49999999999999975e-31

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. associate-/l* 83.4%

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

      2. associate-/r/ 83.5%

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

   6. Applied egg-rr 83.5%

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

   if 7.49999999999999975e-31 < z

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 5: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+37)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 1.55e-30) (+ x (/ (- t z) (/ a y))) (+ x (/ y (/ z (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+37) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 1.55e-30) {
		tmp = x + ((t - z) / (a / y));
	} else {
		tmp = x + (y / (z / (z - 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 (z <= (-2.5d+37)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 1.55d-30) then
        tmp = x + ((t - z) / (a / y))
    else
        tmp = x + (y / (z / (z - 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 (z <= -2.5e+37) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 1.55e-30) {
		tmp = x + ((t - z) / (a / y));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+37:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 1.55e-30:
		tmp = x + ((t - z) / (a / y))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+37)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 1.55e-30)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+37)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 1.55e-30)
		tmp = x + ((t - z) / (a / y));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+37], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-30], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999994e37

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-/l* 94.6%

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

   6. Simplified 94.6%

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

      1. clear-num 94.6%

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

      2. associate-/r/ 94.6%

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

      3. clear-num 94.6%

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

      4. div-sub 94.6%

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

      5. *-inverses 94.6%

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

   8. Applied egg-rr 94.6%

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

   if -2.49999999999999994e37 < z < 1.54999999999999995e-30

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 85.7%

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

      1. +-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. mul-1-neg 85.7%

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

      4. unsub-neg 85.7%

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

      5. *-commutative 85.7%

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

      6. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   if 1.54999999999999995e-30 < z

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+37) (+ x y) (if (<= z 2.6e-30) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+37) {
		tmp = x + y;
	} else if (z <= 2.6e-30) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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 (z <= (-3.1d+37)) then
        tmp = x + y
    else if (z <= 2.6d-30) then
        tmp = x + (y * (t / a))
    else
        tmp = x + 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 (z <= -3.1e+37) {
		tmp = x + y;
	} else if (z <= 2.6e-30) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+37:
		tmp = x + y
	elif z <= 2.6e-30:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+37)
		tmp = Float64(x + y);
	elseif (z <= 2.6e-30)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+37)
		tmp = x + y;
	elseif (z <= 2.6e-30)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+37], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.6e-30], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000002e37 or 2.59999999999999987e-30 < z

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.6%

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

   if -3.1000000000000002e37 < z < 2.59999999999999987e-30

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in z around 0 83.2%

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

      1. associate-*r/ 82.7%

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

   8. Simplified 82.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+39) (+ x y) (if (<= z 2.6e-30) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+39) {
		tmp = x + y;
	} else if (z <= 2.6e-30) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + 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 (z <= (-1.85d+39)) then
        tmp = x + y
    else if (z <= 2.6d-30) then
        tmp = x + (t * (y / a))
    else
        tmp = x + 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 (z <= -1.85e+39) {
		tmp = x + y;
	} else if (z <= 2.6e-30) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+39:
		tmp = x + y
	elif z <= 2.6e-30:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+39)
		tmp = Float64(x + y);
	elseif (z <= 2.6e-30)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+39)
		tmp = x + y;
	elseif (z <= 2.6e-30)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+39], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.6e-30], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000006e39 or 2.59999999999999987e-30 < z

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.6%

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

   if -1.85000000000000006e39 < z < 2.59999999999999987e-30

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*r/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. associate-/l* 83.4%

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

      2. associate-/r/ 83.5%

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

   6. Applied egg-rr 83.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - a)) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Final simplification 96.6%

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

Alternative 9: 59.6% 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 85.9%

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

   1. +-commutative 85.9%

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

   2. associate-*r/ 98.4%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Taylor expanded in z around inf 61.4%

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

5. Final simplification 61.4%

   \[\leadsto x + y \]

Alternative 10: 51.0% 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 85.9%

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

   1. +-commutative 85.9%

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

   2. associate-*r/ 98.4%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Taylor expanded in y around 0 49.4%

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

5. Final simplification 49.4%

   \[\leadsto x \]

Developer target: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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