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

Percentage Accurate: 85.6% → 98.1%

Time: 14.9s

Alternatives: 13

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: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% 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 87.4%

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

   1. +-commutative 87.4%

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

   2. *-commutative 87.4%

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

   3. associate-*l/ 98.8%

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

   4. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.72e+118)
     (+ y x)
     (if (<= t -1.1e+54)
       t_1
       (if (<= t -1.1e+18)
         (+ y x)
         (if (<= t -4500000.0)
           (* y (/ z (- a t)))
           (if (<= t 2.6e+14) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = y + x;
	} else if (t <= -1.1e+54) {
		tmp = t_1;
	} else if (t <= -1.1e+18) {
		tmp = y + x;
	} else if (t <= -4500000.0) {
		tmp = y * (z / (a - t));
	} else if (t <= 2.6e+14) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-1.72d+118)) then
        tmp = y + x
    else if (t <= (-1.1d+54)) then
        tmp = t_1
    else if (t <= (-1.1d+18)) then
        tmp = y + x
    else if (t <= (-4500000.0d0)) then
        tmp = y * (z / (a - t))
    else if (t <= 2.6d+14) then
        tmp = t_1
    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 t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = y + x;
	} else if (t <= -1.1e+54) {
		tmp = t_1;
	} else if (t <= -1.1e+18) {
		tmp = y + x;
	} else if (t <= -4500000.0) {
		tmp = y * (z / (a - t));
	} else if (t <= 2.6e+14) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.72e+118:
		tmp = y + x
	elif t <= -1.1e+54:
		tmp = t_1
	elif t <= -1.1e+18:
		tmp = y + x
	elif t <= -4500000.0:
		tmp = y * (z / (a - t))
	elif t <= 2.6e+14:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.72e+118)
		tmp = Float64(y + x);
	elseif (t <= -1.1e+54)
		tmp = t_1;
	elseif (t <= -1.1e+18)
		tmp = Float64(y + x);
	elseif (t <= -4500000.0)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 2.6e+14)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.72e+118)
		tmp = y + x;
	elseif (t <= -1.1e+54)
		tmp = t_1;
	elseif (t <= -1.1e+18)
		tmp = y + x;
	elseif (t <= -4500000.0)
		tmp = y * (z / (a - t));
	elseif (t <= 2.6e+14)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e+118], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.1e+54], t$95$1, If[LessEqual[t, -1.1e+18], N[(y + x), $MachinePrecision], If[LessEqual[t, -4500000.0], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+14], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.71999999999999999e118 or -1.09999999999999995e54 < t < -1.1e18 or 2.6e14 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*l/ 95.2%

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

      3. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 83.6%

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

   if -1.71999999999999999e118 < t < -1.09999999999999995e54 or -4.5e6 < t < 2.6e14

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      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 71.4%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 76.9%

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

   6. Applied egg-rr 76.9%

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

   if -1.1e18 < t < -4.5e6

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 69.8%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in z around inf 85.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+118)
   (+ y x)
   (if (<= t -1.05e+54)
     (+ x (* z (/ y a)))
     (if (<= t -1.1e+18)
       (+ y x)
       (if (<= t -4500000.0)
         (* y (/ z (- a t)))
         (if (<= t 5e+14) (+ x (/ z (/ a y))) (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+118) {
		tmp = y + x;
	} else if (t <= -1.05e+54) {
		tmp = x + (z * (y / a));
	} else if (t <= -1.1e+18) {
		tmp = y + x;
	} else if (t <= -4500000.0) {
		tmp = y * (z / (a - t));
	} else if (t <= 5e+14) {
		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 <= (-2.55d+118)) then
        tmp = y + x
    else if (t <= (-1.05d+54)) then
        tmp = x + (z * (y / a))
    else if (t <= (-1.1d+18)) then
        tmp = y + x
    else if (t <= (-4500000.0d0)) then
        tmp = y * (z / (a - t))
    else if (t <= 5d+14) 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 <= -2.55e+118) {
		tmp = y + x;
	} else if (t <= -1.05e+54) {
		tmp = x + (z * (y / a));
	} else if (t <= -1.1e+18) {
		tmp = y + x;
	} else if (t <= -4500000.0) {
		tmp = y * (z / (a - t));
	} else if (t <= 5e+14) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+118:
		tmp = y + x
	elif t <= -1.05e+54:
		tmp = x + (z * (y / a))
	elif t <= -1.1e+18:
		tmp = y + x
	elif t <= -4500000.0:
		tmp = y * (z / (a - t))
	elif t <= 5e+14:
		tmp = x + (z / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+118)
		tmp = Float64(y + x);
	elseif (t <= -1.05e+54)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= -1.1e+18)
		tmp = Float64(y + x);
	elseif (t <= -4500000.0)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 5e+14)
		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 <= -2.55e+118)
		tmp = y + x;
	elseif (t <= -1.05e+54)
		tmp = x + (z * (y / a));
	elseif (t <= -1.1e+18)
		tmp = y + x;
	elseif (t <= -4500000.0)
		tmp = y * (z / (a - t));
	elseif (t <= 5e+14)
		tmp = x + (z / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+118], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.05e+54], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e+18], N[(y + x), $MachinePrecision], If[LessEqual[t, -4500000.0], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+14], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.55000000000000001e118 or -1.04999999999999993e54 < t < -1.1e18 or 5e14 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*l/ 95.2%

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

      3. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 83.6%

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

   if -2.55000000000000001e118 < t < -1.04999999999999993e54

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. associate-/l* 78.6%

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

      2. associate-/r/ 78.6%

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

   6. Applied egg-rr 78.6%

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

   if -1.1e18 < t < -4.5e6

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 69.8%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in z around inf 85.4%

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

   if -4.5e6 < t < 5e14

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-*l/ 95.3%

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

      3. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. associate-/l* 76.7%

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

      3. add-cube-cbrt 76.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\frac{a}{y}} + x \]

      4. *-un-lft-identity 76.3%

         \[\leadsto \frac{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}{\color{blue}{1 \cdot \frac{a}{y}}} + x \]

      5. times-frac 76.3%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]

      6. pow2 76.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

   6. Applied egg-rr 76.3%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}}} + x \]
   7. Step-by-step derivation

      1. /-rgt-identity 76.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}} \cdot \frac{\sqrt[3]{z}}{\frac{a}{y}} + x \]

      2. associate-*r/ 76.3%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}}{\frac{a}{y}}} + x \]

      3. unpow2 76.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}}{\frac{a}{y}} + x \]

      4. rem-3cbrt-lft 76.7%

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

   8. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y}}} + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -270000000000:\\ \;\;\;\;\frac{z - t}{\frac{t}{-y}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1250000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.72e+118)
     (+ y x)
     (if (<= t -6.2e+51)
       t_1
       (if (<= t -270000000000.0)
         (/ (- z t) (/ t (- y)))
         (if (<= t -7.5e-161)
           (+ x (/ y (/ a z)))
           (if (<= t 1250000000000.0) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = y + x;
	} else if (t <= -6.2e+51) {
		tmp = t_1;
	} else if (t <= -270000000000.0) {
		tmp = (z - t) / (t / -y);
	} else if (t <= -7.5e-161) {
		tmp = x + (y / (a / z));
	} else if (t <= 1250000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-1.72d+118)) then
        tmp = y + x
    else if (t <= (-6.2d+51)) then
        tmp = t_1
    else if (t <= (-270000000000.0d0)) then
        tmp = (z - t) / (t / -y)
    else if (t <= (-7.5d-161)) then
        tmp = x + (y / (a / z))
    else if (t <= 1250000000000.0d0) then
        tmp = t_1
    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 t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = y + x;
	} else if (t <= -6.2e+51) {
		tmp = t_1;
	} else if (t <= -270000000000.0) {
		tmp = (z - t) / (t / -y);
	} else if (t <= -7.5e-161) {
		tmp = x + (y / (a / z));
	} else if (t <= 1250000000000.0) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.72e+118:
		tmp = y + x
	elif t <= -6.2e+51:
		tmp = t_1
	elif t <= -270000000000.0:
		tmp = (z - t) / (t / -y)
	elif t <= -7.5e-161:
		tmp = x + (y / (a / z))
	elif t <= 1250000000000.0:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.72e+118)
		tmp = Float64(y + x);
	elseif (t <= -6.2e+51)
		tmp = t_1;
	elseif (t <= -270000000000.0)
		tmp = Float64(Float64(z - t) / Float64(t / Float64(-y)));
	elseif (t <= -7.5e-161)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1250000000000.0)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.72e+118)
		tmp = y + x;
	elseif (t <= -6.2e+51)
		tmp = t_1;
	elseif (t <= -270000000000.0)
		tmp = (z - t) / (t / -y);
	elseif (t <= -7.5e-161)
		tmp = x + (y / (a / z));
	elseif (t <= 1250000000000.0)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e+118], N[(y + x), $MachinePrecision], If[LessEqual[t, -6.2e+51], t$95$1, If[LessEqual[t, -270000000000.0], N[(N[(z - t), $MachinePrecision] / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-161], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1250000000000.0], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.71999999999999999e118 or 1.25e12 < t

   1. Initial program 80.6%

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

      1. +-commutative 80.6%

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

      2. associate-*l/ 95.1%

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

      3. fma-def 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around inf 83.0%

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

   if -1.71999999999999999e118 < t < -6.20000000000000022e51 or -7.49999999999999991e-161 < t < 1.25e12

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-*l/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 78.3%

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

   6. Applied egg-rr 78.3%

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

   if -6.20000000000000022e51 < t < -2.7e11

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.1%

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

      1. associate-/l* 73.8%

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

      2. associate-/r/ 73.8%

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

   6. Applied egg-rr 73.8%

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

   7. Taylor expanded in a around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. associate-/l* 73.8%

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

   9. Simplified 73.8%

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

   if -2.7e11 < t < -7.49999999999999991e-161

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-*l/ 97.1%

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

      3. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. associate-/l* 77.5%

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

   6. Simplified 77.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -270000000000:\\ \;\;\;\;\frac{z - t}{\frac{t}{-y}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1250000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+114}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+215}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= y -4.2e+199)
     t_1
     (if (<= y 8.8e+48)
       (+ y x)
       (if (<= y 2.5e+114)
         (* (- z t) (/ y a))
         (if (<= y 6.2e+215) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (y <= -4.2e+199) {
		tmp = t_1;
	} else if (y <= 8.8e+48) {
		tmp = y + x;
	} else if (y <= 2.5e+114) {
		tmp = (z - t) * (y / a);
	} else if (y <= 6.2e+215) {
		tmp = y + x;
	} 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 = y * (z / (a - t))
    if (y <= (-4.2d+199)) then
        tmp = t_1
    else if (y <= 8.8d+48) then
        tmp = y + x
    else if (y <= 2.5d+114) then
        tmp = (z - t) * (y / a)
    else if (y <= 6.2d+215) then
        tmp = y + x
    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 = y * (z / (a - t));
	double tmp;
	if (y <= -4.2e+199) {
		tmp = t_1;
	} else if (y <= 8.8e+48) {
		tmp = y + x;
	} else if (y <= 2.5e+114) {
		tmp = (z - t) * (y / a);
	} else if (y <= 6.2e+215) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if y <= -4.2e+199:
		tmp = t_1
	elif y <= 8.8e+48:
		tmp = y + x
	elif y <= 2.5e+114:
		tmp = (z - t) * (y / a)
	elif y <= 6.2e+215:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (y <= -4.2e+199)
		tmp = t_1;
	elseif (y <= 8.8e+48)
		tmp = Float64(y + x);
	elseif (y <= 2.5e+114)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (y <= 6.2e+215)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (y <= -4.2e+199)
		tmp = t_1;
	elseif (y <= 8.8e+48)
		tmp = y + x;
	elseif (y <= 2.5e+114)
		tmp = (z - t) * (y / a);
	elseif (y <= 6.2e+215)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+199], t$95$1, If[LessEqual[y, 8.8e+48], N[(y + x), $MachinePrecision], If[LessEqual[y, 2.5e+114], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+215], N[(y + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999999e199 or 6.1999999999999998e215 < y

   1. Initial program 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-*l/ 91.9%

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

      3. fma-def 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 63.5%

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

      1. associate-/l* 85.7%

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

      2. associate-/r/ 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around inf 65.4%

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

   if -4.1999999999999999e199 < y < 8.7999999999999997e48 or 2.5e114 < y < 6.1999999999999998e215

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      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 75.2%

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

   if 8.7999999999999997e48 < y < 2.5e114

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 64.9%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in a around inf 57.5%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 57.7%

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

   9. Simplified 57.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+114}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+215}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.2e+59)
   (+ x (/ y (/ a z)))
   (if (<= x -1.15e-46)
     (+ y x)
     (if (<= x 3.6e-62) (* (/ (- z t) (- a t)) y) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+59) {
		tmp = x + (y / (a / z));
	} else if (x <= -1.15e-46) {
		tmp = y + x;
	} else if (x <= 3.6e-62) {
		tmp = ((z - t) / (a - t)) * 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 (x <= (-2.2d+59)) then
        tmp = x + (y / (a / z))
    else if (x <= (-1.15d-46)) then
        tmp = y + x
    else if (x <= 3.6d-62) then
        tmp = ((z - t) / (a - t)) * 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 (x <= -2.2e+59) {
		tmp = x + (y / (a / z));
	} else if (x <= -1.15e-46) {
		tmp = y + x;
	} else if (x <= 3.6e-62) {
		tmp = ((z - t) / (a - t)) * y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.2e+59:
		tmp = x + (y / (a / z))
	elif x <= -1.15e-46:
		tmp = y + x
	elif x <= 3.6e-62:
		tmp = ((z - t) / (a - t)) * y
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.2e+59)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (x <= -1.15e-46)
		tmp = Float64(y + x);
	elseif (x <= 3.6e-62)
		tmp = Float64(Float64(Float64(z - t) / Float64(a - t)) * y);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.2e+59)
		tmp = x + (y / (a / z));
	elseif (x <= -1.15e-46)
		tmp = y + x;
	elseif (x <= 3.6e-62)
		tmp = ((z - t) / (a - t)) * y;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.2e+59], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-46], N[(y + x), $MachinePrecision], If[LessEqual[x, 3.6e-62], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e59

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 88.5%

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

      1. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   if -2.2e59 < x < -1.15e-46 or 3.6e-62 < x

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-*l/ 95.7%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 74.3%

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

   if -1.15e-46 < x < 3.6e-62

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in x around 0 69.0%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 82.8%

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

   6. Applied egg-rr 82.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185} \lor \neg \left(t \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e+185) (not (<= t 3.3e+121)))
   (+ y x)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e+185) || !(t <= 3.3e+121)) {
		tmp = y + x;
	} 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 <= (-2.7d+185)) .or. (.not. (t <= 3.3d+121))) then
        tmp = y + x
    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 <= -2.7e+185) || !(t <= 3.3e+121)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e+185) or not (t <= 3.3e+121):
		tmp = y + x
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e+185) || !(t <= 3.3e+121))
		tmp = Float64(y + x);
	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 <= -2.7e+185) || ~((t <= 3.3e+121)))
		tmp = y + x;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e+185], N[Not[LessEqual[t, 3.3e+121]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000007e185 or 3.29999999999999979e121 < t

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-*l/ 92.0%

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

      3. fma-def 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 91.1%

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

   if -2.70000000000000007e185 < t < 3.29999999999999979e121

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. associate-*l/ 87.0%

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

      2. *-commutative 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185} \lor \neg \left(t \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 8: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118} \lor \neg \left(t \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.72e+118) (not (<= t 1.75e+86)))
   (- x (/ y (/ t (- z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.72e+118) || !(t <= 1.75e+86)) {
		tmp = x - (y / (t / (z - t)));
	} 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 <= (-1.72d+118)) .or. (.not. (t <= 1.75d+86))) then
        tmp = x - (y / (t / (z - t)))
    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 <= -1.72e+118) || !(t <= 1.75e+86)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.72e+118) or not (t <= 1.75e+86):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.72e+118) || !(t <= 1.75e+86))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	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 <= -1.72e+118) || ~((t <= 1.75e+86)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.72e+118], N[Not[LessEqual[t, 1.75e+86]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $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 < -1.71999999999999999e118 or 1.75000000000000009e86 < t

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 94.2%

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

      3. fma-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. *-commutative 75.9%

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

      5. associate-/l* 96.2%

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

   6. Simplified 96.2%

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

   if -1.71999999999999999e118 < t < 1.75000000000000009e86

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 82.6%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118} \lor \neg \left(t \leq 1.75 \cdot 10^{+86}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 9: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+59) (not (<= z 4.5e-66)))
   (+ x (* z (/ y (- a t))))
   (+ x (/ y (/ (- t a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+59) || !(z <= 4.5e-66)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / ((t - 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 ((z <= (-4d+59)) .or. (.not. (z <= 4.5d-66))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y / ((t - 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 ((z <= -4e+59) || !(z <= 4.5e-66)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / ((t - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+59) or not (z <= 4.5e-66):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y / ((t - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+59) || !(z <= 4.5e-66))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+59) || ~((z <= 4.5e-66)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y / ((t - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+59], N[Not[LessEqual[z, 4.5e-66]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999989e59 or 4.4999999999999998e-66 < z

   1. Initial program 87.7%

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

   2. Taylor expanded in z around inf 83.2%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   4. Simplified 91.8%

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

   if -3.99999999999999989e59 < z < 4.4999999999999998e-66

   1. Initial program 87.2%

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

      1. clear-num 87.2%

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

      2. associate-/r/ 87.2%

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

   3. Applied egg-rr 87.2%

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

      1. associate-*l/ 87.2%

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

      2. *-un-lft-identity 87.2%

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

      3. associate-/l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 92.0%

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

      1. associate-*r/ 92.0%

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

      2. mul-1-neg 92.0%

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

   8. Simplified 92.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 10: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. clear-num 87.4%

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

   2. associate-/r/ 87.4%

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

3. Applied egg-rr 87.4%

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

   1. associate-*l/ 87.4%

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

   2. *-un-lft-identity 87.4%

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

   3. associate-/l* 98.8%

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

5. Applied egg-rr 98.8%

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

6. Final simplification 98.8%

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

Alternative 11: 53.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.4e-124) x (if (<= x 1.5e-140) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e-124) {
		tmp = x;
	} else if (x <= 1.5e-140) {
		tmp = 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 (x <= (-1.4d-124)) then
        tmp = x
    else if (x <= 1.5d-140) then
        tmp = 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 (x <= -1.4e-124) {
		tmp = x;
	} else if (x <= 1.5e-140) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.4e-124:
		tmp = x
	elif x <= 1.5e-140:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.4e-124)
		tmp = x;
	elseif (x <= 1.5e-140)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.4e-124)
		tmp = x;
	elseif (x <= 1.5e-140)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.4e-124], x, If[LessEqual[x, 1.5e-140], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999999e-124 or 1.50000000000000009e-140 < x

   1. Initial program 87.4%

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

      1. +-commutative 87.4%

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

      2. associate-*l/ 96.4%

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

      3. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 65.9%

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

   if -1.39999999999999999e-124 < x < 1.50000000000000009e-140

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 77.7%

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

      1. associate-/l* 83.6%

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

      2. associate-/r/ 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 37.2%

      \[\leadsto \color{blue}{1} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 60.5% 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 87.4%

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

   1. +-commutative 87.4%

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

   2. associate-*l/ 95.6%

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

   3. fma-def 95.6%

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

3. Simplified 95.6%

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

4. Taylor expanded in t around inf 63.7%

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

5. Final simplification 63.7%

   \[\leadsto y + x \]

Alternative 13: 50.7% 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 87.4%

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

   1. +-commutative 87.4%

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

   2. associate-*l/ 95.6%

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

   3. fma-def 95.6%

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

3. Simplified 95.6%

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

4. Taylor expanded in y around 0 51.6%

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

5. Final simplification 51.6%

   \[\leadsto x \]

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023274 
(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))))