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

Percentage Accurate: 85.4% → 98.1%

Time: 10.7s

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: 85.4% 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, 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 87.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 84.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- a t))))))
   (if (<= t -1.22e+67)
     (+ x y)
     (if (<= t -1e-126)
       t_1
       (if (<= t 2.1e-184)
         (+ x (* y (/ (- z t) a)))
         (if (<= t 4.8e+107) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -1.22e+67) {
		tmp = x + y;
	} else if (t <= -1e-126) {
		tmp = t_1;
	} else if (t <= 2.1e-184) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 4.8e+107) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / (a - t)))
    if (t <= (-1.22d+67)) then
        tmp = x + y
    else if (t <= (-1d-126)) then
        tmp = t_1
    else if (t <= 2.1d-184) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 4.8d+107) then
        tmp = t_1
    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 t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -1.22e+67) {
		tmp = x + y;
	} else if (t <= -1e-126) {
		tmp = t_1;
	} else if (t <= 2.1e-184) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 4.8e+107) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (a - t)))
	tmp = 0
	if t <= -1.22e+67:
		tmp = x + y
	elif t <= -1e-126:
		tmp = t_1
	elif t <= 2.1e-184:
		tmp = x + (y * ((z - t) / a))
	elif t <= 4.8e+107:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.22e+67)
		tmp = Float64(x + y);
	elseif (t <= -1e-126)
		tmp = t_1;
	elseif (t <= 2.1e-184)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 4.8e+107)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (a - t)));
	tmp = 0.0;
	if (t <= -1.22e+67)
		tmp = x + y;
	elseif (t <= -1e-126)
		tmp = t_1;
	elseif (t <= 2.1e-184)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 4.8e+107)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+67], N[(x + y), $MachinePrecision], If[LessEqual[t, -1e-126], t$95$1, If[LessEqual[t, 2.1e-184], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+107], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22000000000000004e67 or 4.8000000000000001e107 < t

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -1.22000000000000004e67 < t < -9.9999999999999995e-127 or 2.0999999999999999e-184 < t < 4.8000000000000001e107

   1. Initial program 93.6%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 77.3%

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

      1. associate-*l/ 83.3%

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

      2. *-commutative 83.3%

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

   7. Simplified 83.3%

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

   if -9.9999999999999995e-127 < t < 2.0999999999999999e-184

   1. Initial program 97.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around inf 94.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-126}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-184}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+107}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a - t}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-31}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-142}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- a t))))))
   (if (<= z -2.6e+77)
     t_1
     (if (<= z -5.1e-31)
       (- x (/ y (/ t (- z t))))
       (if (<= z -6e-58)
         (+ x (/ z (/ (- a t) y)))
         (if (<= z 1.15e-142) (- x (/ y (+ (/ a t) -1.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (z <= -2.6e+77) {
		tmp = t_1;
	} else if (z <= -5.1e-31) {
		tmp = x - (y / (t / (z - t)));
	} else if (z <= -6e-58) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.15e-142) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / (a - t)))
    if (z <= (-2.6d+77)) then
        tmp = t_1
    else if (z <= (-5.1d-31)) then
        tmp = x - (y / (t / (z - t)))
    else if (z <= (-6d-58)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 1.15d-142) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (z <= -2.6e+77) {
		tmp = t_1;
	} else if (z <= -5.1e-31) {
		tmp = x - (y / (t / (z - t)));
	} else if (z <= -6e-58) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.15e-142) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (a - t)))
	tmp = 0
	if z <= -2.6e+77:
		tmp = t_1
	elif z <= -5.1e-31:
		tmp = x - (y / (t / (z - t)))
	elif z <= -6e-58:
		tmp = x + (z / ((a - t) / y))
	elif z <= 1.15e-142:
		tmp = x - (y / ((a / t) + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (z <= -2.6e+77)
		tmp = t_1;
	elseif (z <= -5.1e-31)
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	elseif (z <= -6e-58)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 1.15e-142)
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (a - t)));
	tmp = 0.0;
	if (z <= -2.6e+77)
		tmp = t_1;
	elseif (z <= -5.1e-31)
		tmp = x - (y / (t / (z - t)));
	elseif (z <= -6e-58)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 1.15e-142)
		tmp = x - (y / ((a / t) + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+77], t$95$1, If[LessEqual[z, -5.1e-31], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-58], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-142], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000002e77 or 1.15000000000000001e-142 < z

   1. Initial program 87.4%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   7. Simplified 91.0%

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

   if -2.6000000000000002e77 < z < -5.0999999999999997e-31

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*l/ 95.2%

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

      3. fma-def 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in a around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. associate-/l* 95.0%

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

   7. Simplified 95.0%

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

   if -5.0999999999999997e-31 < z < -6.00000000000000015e-58

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. clear-num 100.0%

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

      3. associate-*l/ 100.0%

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

      4. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. clear-num 100.0%

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

       3. un-div-inv 100.0%

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

   11. Applied egg-rr 100.0%

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

   if -6.00000000000000015e-58 < z < 1.15000000000000001e-142

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      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. Add Preprocessing

   5. Taylor expanded in z around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. *-commutative 80.6%

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

      4. associate-/l* 91.0%

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

      5. div-sub 91.0%

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

      6. sub-neg 91.0%

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

      7. *-inverses 91.0%

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

      8. metadata-eval 91.0%

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

   7. Simplified 91.0%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+77}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-31}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-142}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+66} \lor \neg \left(t \leq 1.85 \cdot 10^{+105}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+66) (not (<= t 1.85e+105)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+66) || !(t <= 1.85e+105)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7d+66)) .or. (.not. (t <= 1.85d+105))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+66) || !(t <= 1.85e+105)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+66) or not (t <= 1.85e+105):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+66) || !(t <= 1.85e+105))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e+66) || ~((t <= 1.85e+105)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+66], N[Not[LessEqual[t, 1.85e+105]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999994e66 or 1.84999999999999992e105 < t

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -6.9999999999999994e66 < t < 1.84999999999999992e105

   1. Initial program 94.9%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 81.8%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+66} \lor \neg \left(t \leq 1.85 \cdot 10^{+105}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-55} \lor \neg \left(t \leq 1.4 \cdot 10^{+87}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-55) (not (<= t 1.4e+87)))
   (+ x (* (/ y t) (- t z)))
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-55) || !(t <= 1.4e+87)) {
		tmp = x + ((y / t) * (t - z));
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.45d-55)) .or. (.not. (t <= 1.4d+87))) then
        tmp = x + ((y / t) * (t - z))
    else
        tmp = x + (z / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-55) || !(t <= 1.4e+87)) {
		tmp = x + ((y / t) * (t - z));
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-55) or not (t <= 1.4e+87):
		tmp = x + ((y / t) * (t - z))
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-55) || !(t <= 1.4e+87))
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e-55) || ~((t <= 1.4e+87)))
		tmp = x + ((y / t) * (t - z));
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-55], N[Not[LessEqual[t, 1.4e+87]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e-55 or 1.40000000000000008e87 < t

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. associate-*l/ 96.9%

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

      3. fma-def 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

      1. associate-/r/ 86.2%

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

   9. Applied egg-rr 86.2%

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

   if -1.45e-55 < t < 1.40000000000000008e87

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-*l/ 94.9%

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

      3. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-udef 94.9%

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

      2. clear-num 94.8%

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

      3. associate-*l/ 95.1%

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

      4. *-un-lft-identity 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in z around inf 85.8%

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

      1. associate-/l* 89.0%

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

      2. associate-/r/ 87.2%

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

   9. Simplified 87.2%

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

       1. *-commutative 87.2%

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

       2. clear-num 87.1%

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

       3. un-div-inv 87.4%

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

   11. Applied egg-rr 87.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-55} \lor \neg \left(t \leq 1.4 \cdot 10^{+87}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.15 \cdot 10^{-141}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+37) (not (<= z 1.15e-141)))
   (+ x (* z (/ y (- a t))))
   (- x (/ y (+ (/ a t) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+37) || !(z <= 1.15e-141)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	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 <= (-1.5d+37)) .or. (.not. (z <= 1.15d-141))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    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 <= -1.5e+37) || !(z <= 1.15e-141)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+37) or not (z <= 1.15e-141):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+37) || !(z <= 1.15e-141))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+37) || ~((z <= 1.15e-141)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+37], N[Not[LessEqual[z, 1.15e-141]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000011e37 or 1.14999999999999997e-141 < z

   1. Initial program 87.5%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 84.2%

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

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   7. Simplified 90.8%

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

   if -1.50000000000000011e37 < z < 1.14999999999999997e-141

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-*l/ 92.2%

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

      3. fma-def 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

      3. *-commutative 77.3%

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

      4. associate-/l* 88.7%

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

      5. div-sub 88.8%

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

      6. sub-neg 88.8%

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

      7. *-inverses 88.8%

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

      8. metadata-eval 88.8%

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

   7. Simplified 88.8%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} + -1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+37} \lor \neg \left(z \leq 1.15 \cdot 10^{-141}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-57} \lor \neg \left(t \leq 1.35 \cdot 10^{-31}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.6e-57) (not (<= t 1.35e-31))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e-57) || !(t <= 1.35e-31)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.6d-57)) .or. (.not. (t <= 1.35d-31))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e-57) || !(t <= 1.35e-31)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.6e-57) or not (t <= 1.35e-31):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.6e-57) || !(t <= 1.35e-31))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.6e-57) || ~((t <= 1.35e-31)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.6e-57], N[Not[LessEqual[t, 1.35e-31]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-57 or 1.35000000000000007e-31 < t

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-*l/ 97.4%

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

      3. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -1.6e-57 < t < 1.35000000000000007e-31

   1. Initial program 97.3%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around 0 77.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-57} \lor \neg \left(t \leq 1.35 \cdot 10^{-31}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-53} \lor \neg \left(t \leq 1.1 \cdot 10^{-30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e-53) (not (<= t 1.1e-30))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e-53) || !(t <= 1.1e-30)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d-53)) .or. (.not. (t <= 1.1d-30))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e-53) || !(t <= 1.1e-30)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e-53) or not (t <= 1.1e-30):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e-53) || !(t <= 1.1e-30))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e-53) || ~((t <= 1.1e-30)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e-53], N[Not[LessEqual[t, 1.1e-30]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999989e-53 or 1.09999999999999992e-30 < t

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-*l/ 97.4%

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

      3. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -1.04999999999999989e-53 < t < 1.09999999999999992e-30

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-*l/ 94.0%

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

      3. fma-def 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 78.8%

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

   7. Simplified 78.8%

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

      1. clear-num 78.8%

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

      2. associate-/r/ 78.8%

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

      3. clear-num 78.8%

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

   9. Applied egg-rr 78.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-53} \lor \neg \left(t \leq 1.1 \cdot 10^{-30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-54} \lor \neg \left(t \leq 5.1 \cdot 10^{-30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e-54) (not (<= t 5.1e-30))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e-54) || !(t <= 5.1e-30)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.5d-54)) .or. (.not. (t <= 5.1d-30))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e-54) || !(t <= 5.1e-30)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e-54) or not (t <= 5.1e-30):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e-54) || !(t <= 5.1e-30))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e-54) || ~((t <= 5.1e-30)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e-54], N[Not[LessEqual[t, 5.1e-30]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000005e-54 or 5.09999999999999972e-30 < t

   1. Initial program 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-*l/ 97.4%

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

      3. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. +-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -7.5000000000000005e-54 < t < 5.09999999999999972e-30

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-*l/ 94.0%

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

      3. fma-def 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-54} \lor \neg \left(t \leq 5.1 \cdot 10^{-30}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-56} \lor \neg \left(t \leq 1.66 \cdot 10^{-124}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e-56) (not (<= t 1.66e-124))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e-56) || !(t <= 1.66e-124)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.8d-56)) .or. (.not. (t <= 1.66d-124))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e-56) || !(t <= 1.66e-124)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e-56) or not (t <= 1.66e-124):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e-56) || !(t <= 1.66e-124))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e-56) || ~((t <= 1.66e-124)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e-56], N[Not[LessEqual[t, 1.66e-124]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999982e-56 or 1.6599999999999999e-124 < t

   1. Initial program 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-*l/ 97.2%

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

      3. fma-def 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around inf 70.2%

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

      1. +-commutative 70.2%

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

   7. Simplified 70.2%

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

   if -5.79999999999999982e-56 < t < 1.6599999999999999e-124

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. associate-*l/ 93.6%

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

      3. fma-def 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around 0 46.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-56} \lor \neg \left(t \leq 1.66 \cdot 10^{-124}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

   1. associate-/r/ 95.7%

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

6. Applied egg-rr 95.7%

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

7. Final simplification 95.7%

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

Alternative 12: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

   1. clear-num 98.7%

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

   2. associate-/r/ 98.7%

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

   3. clear-num 98.7%

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

6. Applied egg-rr 98.7%

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

7. Final simplification 98.7%

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

Alternative 13: 51.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. +-commutative 87.5%

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

   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. Add Preprocessing

5. Taylor expanded in y around 0 48.2%

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

6. Final simplification 48.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.1% 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 2024020 
(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))))